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Introduction

The physical properties of colloids (nanoparticles) and suspensions are strongly dependent on the nature and extent of the particle-liquid interface. The behavior of aqueous dispersions between particles and liquid is especially sensitive to the ionic and electrical structure of the interface.

Zeta potential is a parameter that measures the electrochemical equilibrium at the particle-liquid interface. It measures the magnitude of electrostatic repulsion/attraction between particles and thus, it has become one of the fundamental parameters known to affect stability of colloidal particles. It should be noted that that term stability, when applied to colloidal dispersions, generally means the resistance to change of the dispersion with time. Figure 2.5.12.5.1 illustrates the basic concept of zeta potential.

From the fundamental theory’s perspective, zeta potential is the electrical potential in the interfacial double layer (DL) at the location of the slipping plane (shown in Figure 2.5.12.5.1 ). We can regard zeta potential as the potential difference between the dispersion medium and the stationary layer of the fluid attached to the particle layer. Therefore, in experimental concerns, zeta potential is key factor in processes such as the preparation of colloidal dispersions, utilization of colloidal phenomena and the destruction of unwanted colloidal dispersions. Moreover, zeta potential analysis and measurements nowadays have a lot of real-world applications. In the field of biomedical research, zeta potential measurement, in contrast to chemical methods of analysis which can disrupt the organism, has the particular merit of providing information referring to the outermost regions of an organism. It is also largely utilized in water purification and treatment. Zeta potential analysis has established optimum coagulation conditions for removal of particulate matter and organic dyestuffs from aqueous waste products.

Brief History and Development of Zeta Potential

Zeta potential is a scientific term for electrokinetic potential in colloidal dispersions. In prior literature, it is usually denoted using the Greek letter zeta, Ζ, hence it has obtained the name zeta potential as Ζ-potential. The earliest theory for calculating Zeta potential from experimental data was developed by Marian Smoluchowski in 1903 (Figure 2.5.22.5.2 ). Even till today, this theory is still the most well-known and widely used method for calculating zeta potential.

Interestingly, this theory was originally developed for electrophoresis. Later on, people started to apply his theory in calculation of zeta potential. The main reason that this theory is powerful is because of its universality and validity for dispersed particles of any shape and any concentration. However, there still some limitations to this early theory as it was mainly determined experimentally. The main limitations are that Smoluchowski’s theory neglects the contribution of surface conductivity and only works for particles which have sizes much larger than the interface layer, denoted as κ_a (1/κ is called Debye length and a is the particle radius).

Overbeek and Booth as early pioneers in this direction started to develop more theoretical and rigorous electrokinetic theories that were able to incorporate surface conductivity for electrokinetic applications. Modern rigorous electrokinetic theories that are valid almost any κa mostly are generated from Ukrainian (Dukhin) and Australian (O’Brien) scientists.

Principle of Zeta Potential Analysis

Electrokinetic Phenomena

Because an electric double-layer (EDL) exists between a surface and solution, then any relative motion between the rigid and mobile parts of the EDL will result in the generation of an electrokinetic potential. As described above, zeta potential is essentially a electrokinetic potential which rises from electrokinetic phenomena. So it is important to understand different situations where electrokinetic potential can be produced. There are generally four fundamental ways which zeta potential can be produced, via electrophoresis, electro-osmosis, streaming potential, and sedimentation potential as shown from Figure 2.5.32.5.3 .

Calculations of Zeta Potential

There are many different ways of calculating zeta potential . In this section, the methods of calculating zeta potential in electrophoresis and electroosmosis will be introduced.

Zeta Potential in Electrophoresis

Electrophoresis is the movement of charged colloidal particles or polyelectrolytes, immersed in a liquid, under the influence of an external electric field. In such case, the electrophoretic velocity, v_e (ms^-1) is the velocity during electrophoresis and the electrophoretic mobility, u­­_e (m ² V ^-1 s ^-1 ) is the magnitude of the velocity divided by the magnitude of the electric field strength. The mobility is counted positive if the particles move toward lower potential and negative in the opposite case. And therefore, we have the relationship v_e­= u_eE, where E is the externally applied field.

Thus, the formula accounted for zeta potential in electrophoresis case is given in EQ, where ε_rs is the relative permittivity of the electrolyte solution, ε₀ is the electric permittivity of vacuum and η is the viscosity.ue =εrsε0ζη(2.5.1)(2.5.1)ue =εrsε0ζηve =εrsε0ζηE(2.5.2)(2.5.2)ve =εrsε0ζηE

There are two cases regarding the size of κa:

1. κa < 1: the formula is similar, 2.5.32.5.3 .
2. κa > 1: the formula is rather complicated and we need to solve equation for zeta potential, 2.5.42.5.4 , where yeζ= eζ/kTyeζ= eζ/kT , m is about 0.15 for aqueous solution.

ue=23εrsε0ζη(2.5.3)(2.5.3)ue=23εrsε0ζη32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2(2.5.4)(2.5.4)32ηeεrsε0kTue=32yek−6[yek2−ln 2ζ{1−e−ζyek}]2+ka1+3m/ζ2e−ζyek2

Zeta Potential in Electroosmosis

Electroosmosis is the motion of a liquid through an immobilized set of particles, a porous plug, a capillary, or a membrane, in response to an applied electric field. Similar to electrophoresis, it has the electroosmotic velocity, v_eo (ms ^-1 ) as the uniform velocity of the liquid far from the charged interface. Usually, the measured quantity is the volume flow rate of liquid divided by electric field strength, Q_eo,E (m ⁴ V ^-1 s ^-1 ) or diveided by the electric current, Q_eo,I (m ³ C ^-1 ). Therefore, the relationship is given by 2.5.52.5.5 .Qeo= ∫∫veodS(2.5.5)(2.5.5)Qeo= ∫∫veodS

Thus the formula accounted for Zeta potential in electroosmosis is given in EQ.

As with electrophoresis there are two cases regarding the size of κa:

• κa >>1 and there is no surface conduction, where Ac is the cross-section area and KL is the bulk conductivity of particle.
• κa < 1, 2.5.82.5.8 , where Δu =KσKLΔu =KσKL is the Dukhin number account for surface conductivity, KσKσ is the surface conductivity of the particle.

Qeo,E=−εrsε0ζηAc(2.5.6)(2.5.6)Qeo,E=−εrsε0ζηAcQeo,I=−εrsε0ζη1KL(2.5.7)(2.5.7)Qeo,I=−εrsε0ζη1KLQeo,I=−εrsε0ζη1KL(1+2Δu)(2.5.8)(2.5.8)Qeo,I=−εrsε0ζη1KL(1+2Δu)

Relationship Between Zeta Potential and Particle Stability in Electrophoresis

Using the above theoretical methods, we can calculate zeta potential for particles in electrophoresis. The following table summarizes the stability behavior of the colloid particles with respect to zeta potential. Thus, we can use zeta potential to predict the stability of colloidal particles in the electrokinetic phenomena of electrophoresis.

Instrumentation

In this section, a market-available zeta potential analyzer will be used as an example of how experimentally zeta potential is analyzed. Figure 2.5.42.5.4 shows an example of a typical zeta potential analyzer for electrophoresis.

The inside measuring principle is described in the following diagram, which shows the detailed mechanism of zeta potential analyzer (Figure 2.5.52.5.5 ).

When a voltage is applied to the solution in which particles are dispersed, particles are attracted to the electrode of the opposite polarity, accompanied by the fixed layer and part of the diffuse double layer, or internal side of the “sliding surface”. Using the following formula below of this specific Analyzer and the computer program, we can obtain the zeta potential for electrophoresis using this typical zeta potential analyzer (Figure 2.5.62.5.6 .

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Dynamic light scattering (DLS), which is also known as photon correlation spectroscopy (PCS) or quasi-elastic light scattering (QLS), is a spectroscopy method used in the fields of chemistry, biochemistry, and physics to determine the size distribution of particles (polymers, proteins, colloids, etc.) in solution or suspension. In the DLS experiment, normally a laser provides the monochromatic incident light, which impinges onto a solution with small particles in Brownian motion.

And then through the Rayleigh scattering process, particles whose sizes are sufficiently small compared to the wavelength of the incident light will diffract the incident light in all direction with different wavelengths and intensities as a function of time. Since the scattering pattern of the light is highly correlated to the size distribution of the analyzed particles, the size-related information of the sample could be then acquired by mathematically processing the spectral characteristics of the scattered light.

Herein a brief introduction of basic theories of DLS will be demonstrated, followed by descriptions and guidance on the instrument itself and the sample preparation and measurement process. Finally, data analysis of the DLS measurement, and the applications of DLS as well as the comparison against other size-determine techniques will be shown and summarized.

DLS Theory

The theory of DLS can be introduced utilizing a model system of spherical particles in solution. According to the Rayleigh scattering (Figure 2.4.12.4.1), when a sample of particles with diameter smaller than the wavelength of the incident light, each particle will diffract the incident light in all directions, while the intensity II is determined by 2.4.12.4.1 , where I0I0 and λλ is the intensity and wavelength of the unpolarized incident light, RR is the distance to the particle, θθ is the scattering angel, nnis the refractive index of the particle, and rr is the radius of the particle.

I = I01 +cos2θ2R2(2πλ)4(n2 − 1n2 + 2)2r6(2.4.1)(2.4.1)I = I01 +cos2⁡θ2R2(2πλ)4(n2 − 1n2 + 2)2r6

If that diffracted light is projected as an image onto a screen, it will generate a “speckle” pattern (Figure 2.4.22.4.2 ); the dark areas represent regions where the diffracted light from the particles arrives out of phase interfering destructively and the bright area represent regions where the diffracted light arrives in phase interfering constructively.

In practice, particle samples are normally not stationary but moving randomly due to collisions with solvent molecules as described by the Brownian motion, 2.4.22.4.2, where (Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯(Δx)2¯ is the mean squared displacement in time t, and D is the diffusion constant, which is related to the hydrodynamic radius a of the particle according to the Stokes-Einstein equation, 2.4.32.4.3 , where kB is Boltzmann constant, T is the temperature, and μ is viscosity of the solution. Importantly, for a system undergoing Brownian motion, small particles should diffuse faster than large ones.(Δx)2¯¯¯¯¯¯¯¯¯¯¯¯¯ = 2Δt(2.4.2)(2.4.2)(Δx)2¯ = 2ΔtD =kBT6πμa(2.4.3)(2.4.3)D =kBT6πμa

As a result of the Brownian motion, the distance between particles is constantly changing and this results in a Doppler shift between the frequency of the incident light and the frequency of the scattered light. Since the distance between particles also affects the phase overlap/interfering of the diffracted light, the brightness and darkness of the spots in the “speckle” pattern will in turn fluctuate in intensity as a function of time when the particles change position with respect to each other. Then, as the rate of these intensity fluctuations depends on how fast the particles are moving (smaller particles diffuse faster), information about the size distribution of particles in the solution could be acquired by processing the fluctuations of the intensity of scattered light. Figure 2.4.32.4.3 shows the hypothetical fluctuation of scattering intensity of larger particles and smaller particles.

In order to mathematically process the fluctuation of intensity, there are several principles/terms to be understood. First, the intensity correlation function is used to describe the rate of change in scattering intensity by comparing the intensity I(t) at time t to the intensity I(t + τ) at a later time (t + τ), and is quantified and normalized by 2.4.42.4.4 and 2.4.52.4.5 , where braces indicate averaging over t.G2(τ)= ⟨I(t)I(t + τ)⟩(2.4.4)(2.4.4)G2(τ)= ⟨I(t)I(t + τ)⟩g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2(2.4.5)(2.4.5)g2(τ)=⟨I(t)I(t + τ)⟩⟨I(t)⟩2

Second, since it is not possible to know how each particle moves from the fluctuation, the electric field correlation function is instead used to correlate the motion of the particles relative to each other, and is defined by 2.4.62.4.6 and 2.4.72.4.7 , where E(t) and E(t + τ) are the scattered electric fields at times t and t+ τ.G1(τ)= ⟨E(t)E(t + τ)⟩(2.4.6)(2.4.6)G1(τ)= ⟨E(t)E(t + τ)⟩g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩(2.4.7)(2.4.7)g1(τ)=⟨E(t)E(t + τ)⟩⟨E(t)E(t)⟩

For a monodisperse system undergoing Brownian motion, g₁(τ) will decay exponentially with a decay rate Γ which is related by Brownian motion to the diffusivity by 2.4.82.4.8 , 2.4.92.4.9 , and 2.4.102.4.10 , where q is the magnitude of the scattering wave vector and q² reflects the distance the particle travels, n is the refraction index of the solution and θ is angle at which the detector is located.g1(τ)= e−Γτ(2.4.8)(2.4.8)g1(τ)= e−ΓτΓ = −Dq2(2.4.9)(2.4.9)Γ = −Dq2q=4πnλsinΘ2(2.4.10)(2.4.10)q=4πnλsinΘ2

For a polydisperse system however, g₁(τ) can no longer be represented as a single exponential decay and must be represented as a intensity-weighed integral over a distribution of decay rates G(Γ) by 2.4.112.4.11 where G(Γ) is normalized, 2.4.122.4.12 .g1(τ)=∫∞0G(Γ)e−ΓτdΓ(2.4.11)(2.4.11)g1(τ)=∫0∞G(Γ)e−ΓτdΓ∫∞0G(Γ)dΓ = 1(2.4.12)(2.4.12)∫0∞G(Γ)dΓ = 1

Third, the two correlation functions above can be equated using the Seigert relationship based on the principles of Gaussian random processes (which the scattering light usually is), and can be expressed as 2.4.132.4.13 , where β is a factor that depends on the experimental geometry, and B is the long-time value of g₂(τ), which is referred to as the baseline and is normally equal to 1. Figure 2.4.42.4.4 shows the decay of g₂(τ) for small size sample and large size sample.g2(τ)= B + β[g1(τ)]2(2.4.13)(2.4.13)g2(τ)= B + β[g1(τ)]2

When determining the size of particles in solution using DLS, g₂(τ) is calculated based on the time-dependent scattering intensity, and is converted through the Seigert relationship to g₁(τ) which usually is an exponential decay or a sum of exponential decays. The decay rate Γ is then mathematically determined (will be discussed in section ) from the g₁(τ) curve, and the value of diffusion constant D and hydrodynamic radius a can be easily calculated afterwards.

Experimental

Instrument of DLS

In a typical DLS experiment, light from a laser passes through a polarizer to define the polarization of the incident beam and then shines on the scattering medium. When the sizes of the analyzed particles are sufficiently small compared to the wavelength of the incident light, the incident light will scatters in all directions known as the Rayleigh scattering. The scattered light then passes through an analyzer, which selects a given polarization and finally enters a detector, where the position of the detector defines the scattering angle θ. In addition, the intersection of the incident beam and the beam intercepted by the detector defines a scattering region of volume V. As for the detector used in these experiments, a phototube is normally used whose dc output is proportional to the intensity of the scattered light beam. Figure 2.4.52.4.5 shows a schematic representation of the light-scattering experiment.

In modern DLS experiments, the scattered light spectral distribution is also measured. In these cases, a photomultiplier is the main detector, but the pre- and postphotomultiplier systems differ depending on the frequency change of the scattered light. The three different methods used are filter (f > 1 MHz), homodyne (f > 10 GHz), and heterodyne methods (f < 1 MHz), as schematically illustrated in Figure 2.4.62.4.6 . Note that that homodyne and heterodyne methods use no monochromator of “filter” between the scattering cell and the photomultiplier, and optical mixing techniques are used for heterodyne method. shows the schematic illustration of the various techniques used in light-scattering experiments.

As for an actual DLS instrument, take the Zetasizer Nano (Malvern Instruments Ltd.) as an example (Figure 2.4.72.4.7), it actually looks like nothing other than a big box, with components of power supply, optical unit (light source and detector), computer connection, sample holder, and accessories. The detailed procedure of how to use the DLS instrument will be introduced afterwards.

Sample Preparation

Although different DLS instruments may have different analysis ranges, we are usually looking at particles with a size range of nm to μm in solution. For several kinds of samples, DLS can give results with rather high confidence, such as monodisperse suspensions of unaggregated nanoparticles that have radius > 20 nm, or polydisperse nanoparticle solutions or stable solutions of aggregated nanoparticles that have radius in the 100 – 300 nm range with a polydispersity index of 0.3 or below. For other more challenging samples such as solutions containing large aggregates, bimodal solutions, very dilute samples, very small nanoparticles, heterogeneous samples, or unknown samples, the results given by DLS could not be really reliable, and one must be aware of the strengths and weaknesses of this analytical technique.

Then, for the sample preparation procedure, one important question is how much materials should be submit, or what is the optimal concentration of the solution. Generally, when doing the DLS measurement, it is important to submit enough amount of material in order to obtain sufficient signal, but if the sample is overly concentrated, then light scattered by one particle might be again scattered by another (known as multiple scattering), and make the data processing less accurate. An ideal sample submission for DLS analysis has a volume of 1 – 2 mL and is sufficiently concentrated as to have strong color hues, or opaqueness/turbidity in the case of a white or black sample. Alternatively, 100 – 200 μL of highly concentrated sample can be diluted to 1 mL or analyzed in a low-volume microcuvette.

In order to get high quality DLS data, there are also other issues to be concerned with. First is to minimize particulate contaminants, as it is common for a single particle contaminant to scatter a million times more than a suspended nanoparticle, by using ultra high purity water or solvents, extensively rinsing pipettes and containers, and sealing sample tightly. Second is to filter the sample through a 0.2 or 0.45 μm filter to get away of the visible particulates within the sample solution. Third is to avoid probe sonication to prevent the particulates ejected from the sonication tip, and use the bath sonication in stead.

Measurement

Now that the sample is readily prepared and put into the sample holder of the instrument, the next step is to actually do the DLS measurement. Generally the DLS instrument will be provided with software that can help you to do the measurement rather easily, but it is still worthwhile to understand the important parameters used during the measurement.

Firstly, the laser light source with an appropriate wavelength should be selected. As for the Zetasizer Nano series (Malvern Instruments Ltd.), either a 633 nm “red” laser or a 532 nm “green” laser is available. One should keep in mind that the 633 nm laser is least suitable for blue samples, while the 532 nm laser is least suitable for red samples, since otherwise the sample will just absorb a large portion of the incident light.

Then, for the measurement itself, one has to select the appropriate stabilization time and the duration time. Normally, longer striation/duration time can results in more stable signal with less noises, but the time cost should also be considered. Another important parameter is the temperature of the sample, as many DLS instruments are equipped with the temperature-controllable sample holders, one can actually measure the size distribution of the data at different temperature, and get extra information about the thermal stability of the sample analyzed.

Next, as is used in the calculation of particle size from the light scattering data, the viscosity and refraction index of the solution are also needed. Normally, for solutions with low concentration, the viscosity and refraction index of the solvent/water could be used as an approximation.

Finally, to get data with better reliability, the DLS measurement on the same sample will normally be conducted multiple times, which can help eliminate unexpected results and also provide additional error bar of the size distribution data.

Data Analysis

Although size distribution data could be readily acquired from the software of the DLS instrument, it is still worthwhile to know about the details about the data analysis process.

Cumulant method

As is mentioned in the Theory portion above, the decay rate Γ is mathematically determined from the g₁(τ) curve; if the sample solution is monodispersed, g₁(τ) could be regard as a single exponential decay function e^-Γτ, and the decay rate Γ can be in turn easily calculated. However, in most of the practical cases, the sample solution is always polydispersed, g₁(τ) will be the sum of many single exponential decay functions with different decay rates, and then it becomes significantly difficult to conduct the fitting process.

There are however, a few methods developed to meet this mathematical challenge: linear fit and cumulant expansion for mono-modal distribution, exponential sampling and CONTIN regularization for non-monomodal distribution. Among all these approaches, cumulant expansion is most common method and will be illustrated in detail in this section.

Generally, the cumulant expansion method is based on two relations: one between g₁(τ) and the moment-generating function of the distribution, and one between the logarithm of g₁(τ) and the cumulant-generating function of the distribution.

To start with, the form of g₁(τ) is equivalent to the definition of the moment-generating function M(-τ, Γ) of the distribution G(Γ), 2.4.142.4.14 .g1(τ)= ∫∞0G(Γ)e−ΓτdΓ = M(−τ,Γ)(2.4.14)(2.4.14)g1(τ)= ∫0∞G(Γ)e−ΓτdΓ = M(−τ,Γ)

The mth moment of the distribution mm(Γ)mm(Γ) is given by the mth derivative of M(-τ, Γ) with respect to τ, 2.4.152.4.15 .mm(Γ)= ∫∞0G(Γ)Γme−ΓτdΓ∣−τ=0(2.4.15)(2.4.15)mm(Γ)= ∫0∞G(Γ)Γme−ΓτdΓ∣−τ=0

Similarly, the logarithm of g₁(τ) is equivalent to the definition of the cumulant-generating function K(-τ, Γ), EQ, and the mth cumulant of the distribution km(Γ) is given by the mth derivative of K(-τ, Γ) with respect to τ, 2.4.162.4.16 and 2.4.172.4.17 .ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)(2.4.16)(2.4.16)ln g1(τ)=ln M(−τ,Γ) = K(−τ,Γ)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0(2.4.17)(2.4.17)km(Γ)=dmK(−τ,Γ)d(−τ)m∣−τ=0

By making use of that the cumulants, except for the first, are invariant under a change of origin, the km(Γ) could be rewritten in terms of the moments about the mean as 2.4.182.4.18 , 2.4.192.4.19 , 2.4.202.4.20 , and 2.4.212.4.21 where here μm are the moments about the mean, defined as given in 2.4.222.4.22 .k1(τ)k2(τ)k3(τ)k4(τ)= ∫∞0G(Γ)ΓdΓ=Γ¯= μ2= μ3= μ4−3μ22⋯(2.4.18)(2.4.19)(2.4.20)(2.4.21)(2.4.18)k1(τ)= ∫0∞G(Γ)ΓdΓ=Γ¯(2.4.19)k2(τ)= μ2(2.4.20)k3(τ)= μ3(2.4.21)k4(τ)= μ4−3μ22⋯μm = ∫∞0G(Γ)(Γ − Γ¯)mdΓ(2.4.22)(2.4.22)μm = ∫0∞G(Γ)(Γ − Γ¯)mdΓ

Based on the Taylor expansion of K(-τ, Γ) about τ = 0, the logarithm of g₁(τ) is given as 2.4.232.4.23 .ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯(2.4.23)(2.4.23)ln g1(τ)= K(−τ,Γ)= −Γ¯τ +k22!τ2 −k33!τ3 +k44!τ4⋯

Importantly, if look back at the Seigert relationship in the logarithmic form, 2.4.242.4.24 .ln(g2(τ)−B)=lnβ + 2ln g1(τ)(2.4.24)(2.4.24)ln(g2(τ)−B)=lnβ + 2ln g1(τ)

The measured data of g₂(τ) could be fitted with the parameters of km using the relationship of 2.4.252.4.25 , where Γ¯Γ¯ (k₁), k₂, and k₃ describes the average, variance, and skewness (or asymmetry) of the decay rates of the distribution, and polydispersity index γ = k2Γ¯2γ = k2Γ¯2 is used to indicate the width of the distribution. And parameters beyond k₃ are seldom used to prevent overfitting the data. Finally, the size distribution can be easily calculated from the decay rate distribution as described in theory section previously. Figure 2.4.62.4.6 shows an example of data fitting using the cumulant method.ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)(2.4.25)(2.4.25)ln(g2(τ)−B)=]lnβ + 2(−Γ¯τ +k22!τ2 −k33!τ3⋯)

When using the cumulant expansion method however, one should keep in mind that it is only suitable for monomodal distributions (Gaussian-like distribution centered about the mean), and for non-monomodal distributions, other methods like exponential sampling and CONTIN regularization should be applied instead.

Three Index of Size Distribution

Now that the size distribution is able to be acquired from the fluctuation data of the scattered light using cumulant expansion or other methods, it is worthwhile to understand the three kinds of distribution index usually used in size analysis: number weighted distribution, volume weighted distribution, and intensity weighted distribution.

First of all, based on all the theories discussed above, it should be clear that the size distribution given by DLS experiments is the intensity weighted distribution, as it is always the intensity of the scattering that is being analyzed. So for intensity weighted distribution, the contribution of each particle is related to the intensity of light scattered by that particle. For example, using Rayleigh approximation, the relative contribution for very small particles will be proportional to a⁶.

For number weighted distribution, given by image analysis as an example, each particle is given equal weighting irrespective of its size, which means proportional to a⁰. This index is most useful where the absolute number of particles is important, or where high resolution (particle by particle) is required.

For volume weighted distribution, given by laser diffraction as an example, the contribution of each particle is related to the volume of that particle, which is proportional to a³. This is often extremely useful from a commercial perspective as the distribution represents the composition of the sample in terms of its volume/mass, and therefore its potential money value.

When comparing particle size data for the same sample represented using different distribution index, it is important to know that the results could be very different from number weighted distribution to intensity weighted distribution. This is clearly illustrated in the example below (Figure 2.4.92.4.9 ), for a sample consisting of equal numbers of particles with diameters of 5 nm and 50 nm. The number weighted distribution gives equal weighting to both types of particles, emphasizing the presence of the finer 5 nm particles, whereas the intensity weighted distribution has a signal one million times higher for the coarser 50 nm particles. The volume weighted distribution is intermediate between the two.

Furthermore, based on the different orders of correlation between the particle contribution and the particle size a, it is possible to convert particle size data from one type of distribution to another type of distribution, and that is also why the DLS software can also give size distributions in three different forms (number, volume, and intensity), where the first two kinds are actually deducted from the raw data of intensity weighted distribution.

An Example of an Application

As the DLS method could be used in many areas towards size distribution such as polymers, proteins, metal nanoparticles, or carbon nanomaterials, here gives an example about the application of DLS in size-controlled synthesis of monodisperse gold nanoparticles.

The size and size distribution of gold particles are controlled by subtle variation of the structure of the polymer, which is used to stabilize the gold nanoparticles during the reaction. These variations include monomer type, polymer molecular weight, end-group hydrophobicity, end-group denticity, and polymer concentration; a total number of 88 different trials have been conducted based on these variations. By using the DLS method, the authors are able to determine the gold particle size distribution for all these trials rather easily, and the correlation between polymer structure and particle size can also be plotted without further processing the data. Although other sizing techniques such as UV-V spectroscopy and TEM are also used in this paper, it is the DLS measurement that provides a much easier and reliable approach towards the size distribution analysis.

Comparison with TEM and AFM

Since DLS is not the only method available to determine the size distribution of particles, it is also necessary to compare DLS with the other common-used general sizing techniques, especially TEM and AFM.

First of all, it has to be made clear that both TEM and AFM measure particles that are deposited on a substrate (Cu grid for TEM, mica for AFM), while DLS measures particles that are dispersed in a solution. In this way, DLS will be measuring the bulk phase properties and give a more comprehensive information about the size distribution of the sample. And for AFM or TEM, it is very common that a relatively small sampling area is analyzed, and the size distribution on the sampling area may not be the same as the size distribution of the original sample depending on how the particles are deposited.

On the other hand however, for DLS, the calculating process is highly dependent on the mathematical and physical assumptions and models, which is, monomodal distribution (cumulant method) and spherical shape for the particles, the results could be inaccurate when analyzing non-monomodal distributions or non-spherical particles. Yet, since the size determining process for AFM or TEM is nothing more than measuring the size from the image and then using the statistic, these two methods can provide much more reliable data when dealing with “irregular” samples.

Another important issue to consider is the time cost and complication of size measurement. Generally speaking, the DLS measurement should be a much easier technique, which requires less operation time and also cheaper equipment. And it could be really troublesome to analysis the size distribution data coming out from TEM or AFM images without specially programmed software.

In addition, there are some special issues to consider when choosing size analysis techniques. For example, if the originally sample is already on a substrate (synthesized by the CVD method), or the particles could not be stably dispersed within solution, apparently the DLS method is not suitable. Also, when the particles tend to have a similar imaging contrast against the substrate (carbon nanomaterials on TEM grid), or tend to self-assemble and aggregate on the surface of the substrate, the DLS approach might be a better choice.

In general research work however, the best way to do size distribution analysis is to combine these analyzing methods, and get complimentary information from different aspects. One thing to keep in mind, since the DLS actually measures the hydrodynamic radius of the particles, the size from DLS measurement is always larger than the size from AFM or TEM measurement. As a conclusion, the comparison between DLS and AFM/TEM is shown in Table 2.4.12.4.1 .

Conclusion

In general, relying on the fluctuating Rayleigh scattering of small particles that randomly moves in solution, DLS is a very useful and rapid technique used in the size distribution of particles in the fields of physics, chemistry, and bio-chemistry, especially for monomodally dispersed spherical particles, and by combining with other techniques such as AFM and TEM, a comprehensive understanding of the size distribution of the analyte can be readily acquired.

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Light interacts with matter in different ways, transmitting through some materials, while reflecting or scattering off others. Both the material and the colour (wavelength) of the light affect this interaction. We call the study of this light ‘spectroscopy’. Which parts of the visible spectrum enter our eyes determines which colours we perceive.

A substance might appear blue, for example, if it absorbs the red parts of the spectrum of light falling upon it, only reflecting (or scattering) the blue parts into our eyes.

Raman spectroscopy looks at the scattered light

If you were to shine blue light—from just one part of the spectrum—onto the material, you might expect to just see blue light reflected from it, or no light at all if it is completely absorbed (i.e. a black material).

However, by using a Raman spectrometer, you can see that often a very tiny fraction of the scattered light has a different colour. It has changed frequency because, during the scattering process, its energy changed by interacting with molecular vibrations. This is the Raman scattering process, named after its discoverer, the famous Indian physicist C.V. Raman. He was awarded the 1930 physics Nobel Prize for this great discovery.

By studying the vibration of the atoms we can discover the chemical composition and other useful information about the material.

The Raman effect is very weak; only about 1 part in 10 million of the scattered light has a shifted colour. This is too weak to see with the naked eye, so we analyse the light with a highly sensitive spectrometer.

Raman spectrometers

These systems consist of:

• one or more single coloured light sources (lasers)
• lenses (both to focus the light onto the sample and to collect the scattered light)
• filters (to purify the reflected and scattered light so that only the Raman light is collected)
• a means of splitting the light into its constituent colours (normally a diffraction grating or prism)
• a very sensitive detector (to detect the weak light)
• a device such as a computer to control the whole system, display the spectrum and enable this information to be analysed

Raman scattering offers significant advantages for the investigation of materials over other analytical techniques, such as x-raying them or seeing how they absorb light (e.g. infrared absorption or ultraviolet absorption).

aman spectroscopy reveals the chemical and structural composition of samples. Generally, all materials produce Raman spectra, with the exception of pure metals.

Raman scattering

Raman scattering occurs when light interacts with molecular vibrations. This is similar to the more widely known infrared absorption spectroscopy, but different rules apply. A change in molecular polarisability is required during the vibration for the Raman effect to occur.

You will see some vibrations in the Raman spectrum that are not visible in the infrared spectrum, and vice-versa, because of the different selection rules. For example, Raman spectroscopy is superb for studying the carbon atoms that make up the structure of diamond, unlike infrared absorption spectroscopy.

Scattered light

The first step in producing a Raman spectrum is to illuminate your sample with a monochromatic light source, such as a laser.

Most of the light that scatters off is unchanged in energy (‘Rayleigh scattered’). A minute fraction—perhaps 1 part in 10 million—has lost or gained energy (‘Raman scattered’). This Raman shift occurs because photons (particles of light) exchange part of their energy with molecular vibrations in the material.

Where energy is lost the Raman scattering is designated as ‘Stokes’; where energy is gained the Raman scattering is designated as ‘anti-Stokes’. We rarely use anti-Stokes Raman light as it is less intense than the Stokes, however it does represent equivalent vibrational information of the molecule.

Vibrating atoms

The change in energy depends on the frequency of vibration of the molecule. If it is very fast (high frequency)—light atoms held together with strong bonds—the energy change is significant. If it is very slow (low frequency)—heavy atoms held together with weak bonds—the energy change is small.

Raman spectrometers

Renishaw inVia systems consist of:

• single or multiple lasers, from UV (244 nm) to IR (1064 nm) – switch with a single click
• high quality objective lenses, from high confocal 100× to long working distance and immersion options
• custom designed motorised spectrometer lenses­ – automatically align for each configuration
• laser-line-specific Rayleigh filters with a dual filter arrangement to optimise sensitivity
• highest quality master diffraction gratings provide exceptional dispersion and longevity
• thermoelectrically cooled (- 70 ºC) CCD detector – stable and sensitive
• high specification multi-core PC for data collection and analysis

Raman spectra

We graphically depict the results of our measurements as Raman spectra. We plot the intensity of the scattered light (y-axis) for each energy (frequency) of light (x-axis). The frequency is traditionally measured in a unit called the wavenumber (number of waves per cm, cm^-1).

We plot the x-axis frequencies relative to that of the laser as it is the shift in energy of the light that is of particular interest.

How do I get the information I want from my spectrum?

You can tell a great deal about a material from its Raman spectrum, with different features relating to different aspects of the material.

The key features are:

The Raman shifts and relative intensities of all of the Raman bands of the material
With this, we can identify the material.

Individual band changes
A band may shift, narrow or broaden, or vary in intensity. These changes can reveal information about stresses in the sample, variations in crystallinity, and the amount of material respectively.

Variations in spectra with position on the sample
This will reveal changes in the uniformity (homogeneity) of the material. You can analyse at several arbitrary points, or systematically measure an array of points (enabling the production of images of composition, stress, crystallinity, etc.)

What do the Raman bands represent?

It is easy to understand the Raman spectrum of crystals with a regular array of identical atoms, all in the same configuration (such as the carbon atoms in diamond). In these cases, you often see just one dominant Raman band (because there is just one molecular environment of the crystal).

The Raman spectrum of polystyrene, however, is much more complex because the molecule is less symmetric and has hydrogen atoms in addition to carbon atoms. There are also different bond types connecting the atoms.

Vibration frequencies

The frequencies of vibration depend on the masses of the atoms involved and the strength of the bonds between them. Heavy atoms and weak bonds have low Raman shifts. Light atoms and strong bonds have high Raman shifts.

We see the high frequency carbon-hydrogen (C-H) vibrations in the polystyrene spectrum at about 3000 cm^-1. The low frequency carbon-carbon (C-C) vibrations are at around 800 cm^-1. The C-H vibrations have a higher frequency than the C-C vibrations because hydrogen is lighter than carbon.

We see the vibrations of two carbon atoms linked by strong double bonds (C=C) at around 1600 cm^-1. This is at a higher frequency than two carbon atoms lined by a weaker single bond (C-C, 800 cm^-1).

You can use these simple rules to explain many of the features of Raman spectra.

Vibrations in detail

You can see more subtle effects if you inspect spectra closely. The strength of bonds also affects their vibration rates. For example, the C-H vibrations of polystyrene appear in two bands, at approximately 2900 cm^-1 and 3050 cm^-1. The carbons in the former are part of carbon chains (‘aliphatic’), whereas the carbons in the latter form part of carbon rings (‘aromatic’).

You can view the vibrations of a complex molecule as partly consisting of many simple diatomic vibrations. However the full richness of the Raman spectrum can only be understood by considering the vibrations of larger groups of atoms (such as the expanding/contracting ‘breathing mode’ of the aromatic carbon ring that appears at 1000 cm^-1 in polystyrene).

Low frequency vibrations

You can also study Raman bands with low Raman shifts, below 100 cm^-1. These originate from very heavy atoms or very large-scale vibrations, such as the whole crystal lattice vibrating. Renishaw’s Raman instruments enable you to study these modes and explore a wide range of materials and crystals, and distinguish between different crystalline forms (polymorphs).

The big picture

A Raman spectrum therefore consists of a range of features, each associated with a vibrational mode. The spectrum is unique to the material and enables you to identify it. It is important to note that, although a full understanding of the vibrational modes is of interest, you rarely need this as you can use a reference database for identification.

When a sample is illuminated by a laser, both Raman scattering and photoluminescence (PL) can occur. The latter can be many times stronger than the former and can prevent successful Raman analysis.

PL comprises both fluorescence and phosphorescence processes and originates from an absorption/emission process between different electronic energy levels in the material. The amount and type of PL depends on which material you are studying and which laser wavelength you are using. Unwanted fluorescence interference can normally be avoided by choosing an appropriate laser wavelength.

• Energy diagram showing absorption of light and the processes involved in the emission of light as fluorescence and phosphorescence.

What PL can tell us

In many cases photoluminescence carries useful information that can facilitate sample analysis and augment the Raman data. inVia confocal Raman microscopes are suited to the analysis of both Raman scattering and PL.

Fluorescence imaging (a type of PL) is often employed in the biological sciences, where fluorescent tags are used to reveal the presence and distribution of molecular species. However, this approach is more invasive than Raman analysis, which is typically tag-free. Renishaw’s inVia confocal Raman microscope can be used to generate images of fluorescent tags, but more commonly provides valuable tag-free chemical information.

You can also use PL to study crystal defects, such as atomic vacancies and substitutions. This is of particular importance for materials such as diamond and silicon carbide (SiC). Not only can you identify the defect, but you can also tell if the crystal has internal stresses.

• Stress image generated from the ruby R2 PL band position

How to avoid PL backgrounds

Occasionally PL bands are strong and broad, masking Raman information. You can counter this by using a different laser wavelength. This can move the Raman bands away from the peak emission of the PL band and may even avoid generation of the PL entirely.

Ideally, a Raman instrument should be able to switch rapidly and easily between different laser wavelengths, so that you can select or avoid PL features, depending on your requirements.

Raman images (sometimes referred to as maps) depict a variation in spectral information from different points on, or in your sample. They can take the form of one-dimensional profiles, two-dimensional images, or three-dimensional rendered volumes. With them, you can rapidly see how a Raman parameter alters with position.

The parameter could be as simple as the intensity of a particular Raman band, or you could derive it from a more complicated analysis of the whole Raman spectrum.

The two main methods of collecting the spectral data to generate these images are Raman mapping and Raman imaging.

• White light and Raman images of washing powder

Raman mapping

Raman mapping collects a spectral hypercube (a Raman spectrum from each position on the sample in a single file), rather than a simple intensity image. The hypercube is analysed to produce Raman images.

There are several Raman mapping methods, such as:

• Point-by-point mapping
  The laser is focused to a spot. A motorised stage moves the sample under the laser. Spectra are sequentially acquired from an array of sample points spanning the defined region of interest. Fast versions of this are Renishaw’s StreamHR™ and StreamHR Rapide.
• Line focus mapping
  This is similar to point-by-point mapping, but the laser illuminates a line on the sample, rather than a spot. This enables you to simultaneously collect spectra from multiple positions on the sample, saving time. With this method you can use higher laser powers without damaging the sample (reducing exposure times). Renishaw’s StreamLine™ is a sophisticated modern implementation of this concept.

It is important to consider the potentially undesirable effects of undersampling when mapping. This is most clearly illustrated when point-by-point mapping: parts of the sample will be ‘missed’ if the laser spot is smaller than the spacing between acquisition points. Renishaw has solved this problem through the use of the StreamLine™ Slalom mode.

Generating Raman images from map data

Once all the Raman spectra are collected from the mapping experiment, they can be analysed to produce profiles, images or rendered volumes. Analysis options in Renishaw’s WiRE software include:

• Intensity at one frequency in the spectrum
  This produces an equivalent image to that from Raman imaging. These are quick to generate but may be misleading because it is not possible to differentiate between intensities arising from a Raman band of interest and those associated with a broad background fluorescence.
• Curve fit parameters
  All the spectra in the set have a theoretical curve fitted to one of the Raman bands. Images are then made based on the theoretical curve parameters for each spectrum. Images are often made using the centre frequency of the curve (band), or the full width at half maximum (FWHM), as this is sensitive to stresses and crystallinity within the sample respectively.
• Multivariate parameters
  Images can be generated using chemometric tools, such as generic principal component analysis (PCA), or Renishaw’s Empty Modelling™, which is optimised for Raman data. The Empty Modelling method reveals systematic variations between the Raman spectra, and highlights the distribution of these variations across the sample as an image. This is achieved without the need for prior knowledge of what is present within the sample, which greatly simplifies the analysis process. Multivariate analysis is very powerful because it uses information from the entire spectrum, not just one part of it (intensity at one frequency) or one curve-fitted band. This typically results in higher quality Raman images.

Raman imaging

Raman imaging is analogous to taking a photograph; spectral intensity values are collected simultaneously from the entire area of interest. The laser illuminates a square or circular region on the sample. The light is filtered so that the intensity of just one narrow part of the spectrum is recorded on the detector.

The single image collected contains limited information, just the intensity of the light at that frequency. However, these images can be acquired rapidly. This is especially true if you have a high power laser; because the light is spread over an area, you can use all the power without damaging your samples, with correspondingly short exposure times.

Two-dimensional images are typically produced using this method. Renishaw’s True Raman Imaging is an example of Raman imaging.

Note that it is possible to collect intensity values covering multiple points of the spectrum by using multiple and/or tuneable filters.

Spatial resolution

Point-by-point Raman mapping

Spatial resolution is determined by a combination of the laser spot size and the spacing between acquisition points on the sample.

• Laser spot size
  This is a function of the objective magnification and the laser wavelength (higher magnification and shorter wavelengths produce smaller spot sizes)
• Spacing between acquisition points on the sample (sampling)
  This is a function of the sample stage (ideally stages should have a large travel range while still enabling a step size down to 100 nm, smaller than the smallest spot size)

Raman imaging

Spatial resolution is determined by the magnification of the optics in the system and the size of the elements in the detector. Ultimately this is limited, by the inherent wavelike nature of light, to a little under a micrometre.

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Driven by applications in chemical sensing, biological imaging and material characterisation, Raman spectroscopies are attracting growing interest from a variety of scientific disciplines. The Raman effect originates from the inelastic scattering of light, and it can directly probe vibration/rotational-vibration states in molecules and materials.

Despite numerous advantages over infrared spectroscopy, spontaneous Raman scattering is very weak, and consequently, a variety of enhanced Raman spectroscopic techniques have emerged. These techniques include stimulated Raman scattering and coherent anti-Stokes Raman scattering, as well as surface- and tip-enhanced Raman scattering spectroscopies. The present review provides the reader with an understanding of the fundamental physics that govern the Raman effect and its advantages, limitations and applications. The review also highlights the key experimental considerations for implementing the main experimental Raman spectroscopic techniques. The relevant data analysis methods and some of the most recent advances related to the Raman effect are finally presented. This review constitutes a practical introduction to the science of Raman spectroscopy; it also highlights recent and promising directions of future research developments.

Introduction

Raman Spectroscopy

There are numerous forms of light-matter interaction: fluorescence and phosphorescence are examples of absorption and subsequent emission of light by matter. Elastic scattering of light, such as Rayleigh scattering by atoms, molecules or phonons, and Mie/Tyndall scattering by dust particles are examples where the wavelength of the light is unchanged. Inelastic scattering such as Brillouin scattering by acoustic waves in crystals, Compton scattering by charged particles and Raman scattering by molecules or phonons are examples where the wavelength of the light does change [1]. Raman scattering of light by molecules was first predicted using classical quantum theory by Smekal in 1923 [2] and experimentally observed by Raman and Krishnan in 1928 [3, 4].

There are now more than 25 different types of known Raman spectroscopy techniques, such as spontaneous Raman, hyper-Raman scattering, Fourier transform Raman scattering [5], Raman-induced Kerr effect spectroscopy [6] and stimulated/coherent Raman scattering [1]. This review considers spontaneous and stimulated Raman scattering, coherent anti-Stokes Raman scattering (CARS), surface-enhanced Raman scattering (SERS) and tip-enhanced Raman scattering (TERS).

Fifty years after its first observation, Raman spectroscopy started to become a prominent analysis technique among other optical metrology techniques, such as those involving absorption of infrared light; particularly when water and other useful polar solvents were present, because these media typically strongly absorb light in the infrared region. For example, in 1974, Fleischmann et al. [7] used Raman spectroscopy to distinguish two types of adsorbed pyridine (a basic cyclic heterodyne compound molecule) on the surface of a silver electrode to mitigate absorption effects. This experiment was incidentally the first serendipitous observation of SERS.

Raman spectroscopy is now an eminent technique for the characterisation of 2D materials (e.g. graphene [8,9,10] and transition metal dichalcogenides [11,12,13]) and phonon modes in crystals [14,15,16]. Properties such as number of monolayers [9, 12, 17, 18], inter-layer breathing and shear modes [19], in-plane anisotropy [20], doping [21,22,23], disorder [10, 24,25,26], thermal conductivity [11], strain [27] and phonon modes [14, 16, 28] can be extracted using Raman spectroscopy.

The biological and medical fields of research are greatly impacted by the development of Raman spectroscopy as it is a label-free (does not require fluorescent marker molecules [29, 30]) chemically selective hyperspectral imaging technique [31]. For instance, studying the transdermal delivery of drugs into skin often ordains ex vivo and invasive analysis techniques. Ex vivo transdermal delivery studies are unfavourable because skin regeneration stops, the immune response ceases, and metabolic activity is usually lost. Hence, the performance of transdermal drug delivery ex vivo is not an accurate reflection of the in vivo situation [32]. However, non-invasive in vivo measurements can be performed using Raman spectroscopy to gain detailed information about the molecular composition and concentration gradients in the skin [33]. In many biological processes, living microorganisms such as bacteria act as biocatalysts. Raman spectroscopy can probe inhomogeneity in the properties and physiological status of individual cells in biocatalytic processes [34]. Raman spectroscopy has also been used to identify and differentiate benign and malignant breast cancer lesions by probing their unique chemical compositions [35].

For biological samples, approximately 90% of the peaks are found in the ‘fingerprint’ spectral region, covering (Δν∼Δν∼ ~ 500 cm⁻¹ to ~ 1800 cm⁻¹; Δν∼Δν∼ is the wavenumber shift defined in the “Analysis methods” section), with the remaining found in the higher energy CH/OH stretching vibrational modes covering (Δν∼Δν∼ ~ 2700 cm⁻¹ to ~ 3300 cm⁻¹) [36].

Coherent Raman Spectroscopy

Coherent light-scattering events involving multiple incident photons simultaneously interacting with the scattering material was not observed until laser sources became available in the 1960s, despite predictions being made as early as the 1930s [37, 38]. The first laser-based Raman scattering experiment was demonstrated in 1961 [39]. Stimulated Raman scattering (SRS) and CARS have become prominent four-wave mixing techniques and are of interest in this review.

SRS is a coherent process providing much stronger signals relative to spontaneous Raman spectroscopy as well as the ability to time-resolve the vibrational motions. SRS is relevant to numerous areas of research such as plasma physics [40], atomic interferometry [41], supercontinuum generation [42], imaging of biomolecules in food products [43], imaging chemistry inside living cells [44], bulk media and nanoscale specimens [45]. The exchange of photon orbital angular momentum by SRS in plasma is gaining interest, particularly in the context of inertial fusion research [40, 46,47,48]. Supercontinuum generation is a complex nonlinear phenomenon that is characterized by the dramatic spectral broadening of intense light pulses passing through a nonlinear material [49]. Knight et al. [42] demonstrated flat ultrabroadband octave-spanning white-light supercontinuum generation by SRS and parametric four-wave mixing with 60-ps pump pulses of sub-kilowatt peak power in a photonic crystal fibre. Kasevich and Chu [41] demonstrated a matter-wave interferometer with laser-cooled sodium atoms using the mechanical effects of stimulated Raman transitions. SRS has even been used to observe time-resolved vibrational spectra of the primary isomerisation of retinal in the visual pigment rhodopsin [50].

Since its resurgence in 1999, CARS has become a prominent vibrational mode imaging tool in biological medicine [51, 52]. As anti-Stokes photons are blue shifted from the pump and Stokes frequencies, they are more easily detected in the presence of single-photon fluorescence [53]. CARS microscopy has been successfully applied to live-cell imaging [51, 54], skeletal stem cells [55], tracing toxic nanomaterials in biological tissues [56], volumetric imaging of human somatic cell division [57], flow cytometry [58, 59], detection of brain tumours [60] and tracking organelle transport in living cells [61]. Zirak et al. [62] has developed a CARS endoscope for in vivo imaging and demonstrated the instrument with murine adipose tissue and human nervus suralis samples. Evans et al. [63] have combined CARS with video rate microscopy to chemically image tissue in vivo. Potma and Xie [64] have directly visualised lipid phase segregation in single lipid bilayers with CARS. CARS can even be used as a high temporal and spatial resolution thermography technique and has found applications in electronic and opto-electronic device characterisation [65] and even turbomachinery [66].

Orientational order is a salient feature of many soft matter systems. Detail in structural molecular organisation is a prevailing goal in the field of biology, biomedicine, material sciences and molecular physics [67]. Polarisation-resolved optical microscopy is becoming a powerful tool to address molecular orientational distributions into the focal volume of a microscope [68]. In coherent nonlinear optics, polarised second harmonic generation [69,70,71], polarised third harmonic generation [72] and polarised four-wave mixing [73, 74] have already been used to recover orientational information on endogeneous proteins and lipids in biological tissues. In addition to the orientational information, coherent Raman scattering (CRS) processes are sensitive to molecular bond vibrations, allowing chemical specificity without the need for fluorescence labelling/dyes [75,76,77]. CARS microscopy can be used to image chemical and orientational order of liquid crystalline (commonly used in display technology) samples [78]. Polarisation-resolved hyperspectral SRS microscopy has also been demonstrated as a label-free biomolecular imaging technique with teeth [79]. In addition, polarised-CARS has been used to study the molecular order of lipids in myelin at sub-diffraction scales in mice [80].

Enhanced Raman Spectroscopy

The sensitivity of Raman spectroscopy can be enhanced through various techniques such as resonance Raman spectroscopy [81], TERS [82, 83] or SERS [84]. SERS is particularly interesting since it allows an enhancement of several orders of magnitude of the Raman signal by modifying the surface upon which an analyte material is to be placed. The enhanced light-matter interaction in TERS and SERS is tuneable (to some extent) by modifying the surface nanostructure of metallic films on dielectric surfaces [85, 86]. The wavelength of charge density oscillations, known as plasmons, is dependent on these surface nanostructures and can enhance the light-matter interaction locally [87]. Plasmons are a prominent topic in physics and plasmonic devices such as filters [88], waveguides [88, 89], polarisers [90] and nanoscale light sources [91] have now been realised.

Fleischmann et al. [7] first observed SERS in 1974 when investigating pyridine on the rough surface of a silver electrode [92]. The sensitivity of SERS makes it well-suited to study electron transfer reactions, which lie at the heart of numerous fundamental processes: electro-catalysis, solar energy conversion, energy storage in batteries, and biological events such as photosynthesis [93]. SERS has also been identified as a valuable technique for the detection of explosives/chemical weapons [94], unmodified DNA [95], aerosol pollutants [96] and pathogens [97].

TERS is a technique that provides spectral information with a spatial resolution on the nanometre scale [98]. Since the first reports of TERS emerged in 2000 [99, 100], TERS has become a powerful technique for studying thin crystalline materials [101], carbon nanotubes[86, 102, 103], single strands of RNA/DNA [104, 105], redox reactions [106], mapping of individual molecules [83], semi-conductor nanostructures and microcavities [107].

In the following sections, the fundamental physics that underpins the spontaneous Raman effect, stimulated- and coherent Raman spectroscopy, SERS and TERS are detailed in the context of their applications. Experimental considerations are discussed, and examples of Raman spectroscopy instrumentation setups are presented. The conventions for presenting spectra are detailed and examples of analysis techniques are given for each of the applications of Raman spectroscopy. In the final sections, the recent advances that constitute the current frontiers of Raman spectroscopy are presented from various fields of research worldwide.

Fundamental Principles

When light interacts with matter, the oscillatory electro-magnetic (EM) field of the light perturbs the charge distribution in the matter which can lead to the exchange of energy and momentum leaving the matter in a modified state. Examples include electronic excitations and molecular vibrations or rotational-vibrations (ro-vibrations) in liquids and gases, electronic excitations and optical phonons in solids, and electron-plasma oscillations in plasmas [108].

Spontaneous Raman

When an incident photon interacts with a crystal lattice or molecule, it can be scattered either elastically or inelastically. Predominantly, light is elastically scattered (i.e. the energy of the scattered photon is equal to that of the incident photon). This type of scattering is often referred to as Rayleigh scattering. The inelastic scattering of light by matter (i.e. the energy of the scattered photon is not equal to that of the incident photon) is known as the Raman effect[1, 4, 6]. This inelastic process leaves the molecule in a modified (ro-)vibrational state. In the case of a crystal lattice, the energy transfer creates a quantum of vibration in the lattice known as a phonon (a quasi-particle). Raman scattering in crystals can also lead to paramagnetic ions, surface plasmons (which are discussed later in this review) and spin waves [15]. The shift in angular frequency of the scattered light can be described by the following equation:ωscat=ωp±ωosc,ωscat=ωp±ωosc,(1)

where subscripts osc denotes the lattice or molecule vibration, p denotes the incident photon (often referred to as the pump photon) and scat denotes the scattered light [1]. The binary operator (±) is determined by energy conservation. When the energy of the scattered photon is lower than that of the incident photon (i.e. red shifted), the process is referred to as Stokes Raman scattering. Conversely, when the energy of the scattered photon is higher than that of the incident photon (i.e. blue shifted), the process is referred to as anti-Stokes Raman scattering. The Raman process must also conserve momentum, which is expressed in wave vector form as:k⇀scat=k⇀p±q⇀,k⇀scat=k⇀p±q⇀,(2)

where k⇀scatk⇀scat, k⇀pk⇀p and q⇀q⇀ are the wave vectors of the scattered light, the incident light and the phonon or molecular (ro-)vibration, respectively.

In molecules and crystals, the charge distribution has an equilibrium state to which it tends. An externally applied field can modify or perturb the charge distribution but only in accordance with the molecule or crystal’s ability to form dipoles which may be anisotropic. This anisotropic property of molecules and crystals is called the polarisability and dielectric susceptibility, respectively. The classical approach theorises that the existence of the Raman effect is associated with the modulation of the polarisability (for molecular (ro-)vibrations) or dielectric susceptibility (for crystal lattice vibrations) due to the oscillatory nature of their interatomic displacement [6, 109]. For crystal lattice vibrations, consider the polarisation vector of the material, P⇀P⇀. If the suffixes j and k represent the vector components in the x, yand z directions, the j^th component of P⇀P⇀ (to first-order) is related to the oscillatory electric field vector E⇀E⇀ associated with the light by [110]:P(1)j=ε0χ(1)jkEk,Pj(1)=ε0χjk(1)Ek,(3)

where ε₀ is the permittivity of free space, χ_jk is the dielectric susceptibility of the material (a rank two tensor) and the convention of summation over repeated indices is implied [109]; the superscript (1) signifies that this is the first-order contribution to the polarisation [1]. The polarisability tensor is a function of the nuclear coordinates which, by extension, means that it will also depend on the (ro-)vibrational frequency. Assuming the modulation is small, the dependence can be expressed in a Taylor series with respect to the coordinates of vibration as follows:χ(1)jk(k⇀p,ωp)≈χ(1)jk(k⇀p,ωp)u⇀=0+ul⎛⎝⎜∂χ(1)jk(k⇀p,ωp)∂ul⎞⎠⎟u⇀=0+ulum⎛⎝⎜∂2χ(1)jk(k⇀p,ωp)∂ul∂um⎞⎠⎟u⇀=0+…,χjk(1)(k⇀p,ωp)≈χjk(1)(k⇀p,ωp)u⇀=0+ul(∂χjk(1)(k⇀p,ωp)∂ul)u⇀=0+ulum(∂2χjk(1)(k⇀p,ωp)∂ul∂um)u⇀=0+…,(4)

where u⇀u⇀ is the nuclear displacement vector, the indices j, k, l and m indicate different spatial coordinates with repeated indices in any of the terms implying the summation of the constituents of that index. If we write the electric field associated with the light as follows:E⇀(r⇀,t)=E⇀(k⇀p,ωp)cos(k⇀p∙r⇀−ωpt),E⇀(r⇀,t)=E⇀(k⇀p,ωp)cos⁡(k⇀p∙r⇀−ωpt),(5)

and the nuclear displacement as follows:u⇀(r⇀,t)=u⇀(q⇀,ωosc)cos(q⇀∙r⇀−ωosct),u⇀(r⇀,t)=u⇀(q⇀,ωosc)cos⁡(q⇀∙r⇀−ωosct),(6)

an explicit expression for time dependence of P(1)jPj(1) can be found by substitution of these two mathematical equations of the monochromatic light and displacement. The numerous resulting terms pertain to optical processes such as Rayleigh scattering, optical absorption and Raman scattering. The term which pertains to the first-order Raman scattering is derived from the second term on the right-hand side of Eq. 4 and yields:Pj(r⇀,t,u⇀)=12ε0⎛⎝⎜∂χ(1)jk(k⇀p,ωp)∂ul⎞⎠⎟u⇀=0ul(q⇀,ωosc)Ek(k⇀p,ωp)×{cos[(k⇀p+q⇀)∙r⇀−(ωp+ωosc)t]∙+cos[(k⇀p−q⇀)∙r⇀−(ωp−ωosc)t]}Pj(r⇀,t,u⇀)=12ε0(∂χjk(1)(k⇀p,ωp)∂ul)u⇀=0ul(q⇀,ωosc)Ek(k⇀p,ωp)×{cos⁡[(k⇀p+q⇀)∙r⇀−(ωp+ωosc)t]∙+cos⁡[(k⇀p−q⇀)∙r⇀−(ωp−ωosc)t]}(7)

This term contains sum (anti-Stokes) and difference (Stokes) frequencies and demonstrates conservation of momentum as per Eqs. 1 and 2. This formulation follows the classical description from refs. [1, 109].

The quantum mechanical description of the Raman process states that the (ro-)vibrational energy of the molecules/phonons are discrete quanta. Figure 1a shows an energy level diagram illustrating the Raman processes with Stokes emission at ω_S and anti-Stokes emission at ω_AS.

In Raman scattering, the intermediate states of the perturbation imposed by the incident pump photon (| r 〉 and | l 〉 in Fig. 1a, b) generally do not correspond to electronic states of the system and are said to be virtual energy states. These virtual intermediate states do not represent a well-defined energy state of the system. As the frequency of the pump photon approaches the energy of the electronic states, the strength of the Raman effect increases due to resonance effects and is termed pre-resonance Raman. If the intermediate state corresponds to a discrete electronic energy state, the interaction is described as resonance Raman scattering and the signal strength is expected to exceed that of virtual-intermediate-state Raman scattering by orders of magnitude. If the energy of the incident light is in the range of dissociative energy levels, the process is described as continuum resonance Raman scattering [1].

Raman scattering transitions between certain quantum states are forbidden. In materials with inversion symmetry (i.e. centrosymmetric crystal structure [113]), the initial and final states must have the same parity and are mutually exclusive with absorptive transitions (optically active transitions). In other words, transitions can be either Raman active or optically active. For linear molecules, the symmetric stretching modes of vibration or bending are Raman active and are optically inactive; those with anti-symmetric modes are Raman inactive and optically active (i.e. mutually exclusive) [1]. This rule is general and for nonlinear molecules, mutual exclusion is relaxed. In materials without inversion symmetry, (ro-)vibrational mode transition can be both Raman and optically active [1, 108].

The Stokes Raman signal for molecules is more intense than the anti-Stokes signal as the population of energy states is governed by thermal statistics [1, 108]. For bosonic systems, such as phonons in crystals, the probability of the scattering target occupying a given vibrational quantum energy state obeys Bose-Einstein statistics. Under nonresonant Raman scattering and thermal equilibrium, the ratio of the anti-Stokes and Stokes scattered intensity is given by [109]:IASIS=(ωp+ωoscωp−ωosc)4e(−ℏωosckT)IASIS=(ωp+ωoscωp−ωosc)4e(−ℏωosckT)(8)

where I_S and I_AS are the intensity of the Stokes and anti-Stokes light, respectively, ℏ is Planck’s constant divided by 2π, k is the Boltzmann constant and T is the temperature associated with the scattering species. This equation is sometimes used to measure the temperature via Raman spectroscopy [65]. This relation becomes inaccurate for resonance Raman scattering because the Stokes and anti-Stokes processes occur at different pump photon frequencies [109].

In the case of spontaneous Raman scattering, the Raman effect is very weak; typically, 1 in 10⁸of the incident radiation undergoes spontaneous Raman scattering [6]. The transition from the virtual excited state to the final state can occur at any point in time and to any possible final state based on probability. Hence, spontaneous Raman scattering is an incoherent process. The output signal power is proportional to the input power, scattered in random directions and is dependent on the orientation of the polarisation. For example, in a system of gaseous molecules, the molecular orientation relative to the incident light is random and hence their polarisation wave vector will also be random. Furthermore, as the excited state has a finite lifetime, there is an associated uncertainty in the transition energy which leads to natural line broadening of the wavelength as per the Heisenberg uncertainty principle (∆E∆t ≥ ℏ/2) [1]. The scattered light, in general, has polarisation properties that differ from that of the incident radiation. Furthermore, the intensity and polarisation are dependent on the direction from which the light is measured [1]. The scattered spectrum exhibits peaks at all Raman active modes; the relative strength of the spectral peaks are determined by the scattering cross-section of each Raman mode [108]. Photons can undergo successive Rayleigh scattering events before Raman scattering occurs as Raman scattering is far less probable than Rayleigh scattering.

Nonlinear Susceptibility

The polarisation described by Eq. 3 is in agreement with first-order (i.e. linear) optics and describes the single-photon scattering process (two-wave mixing process). In wave mixing processes with more than two waves, nonlinear optical polarisation must be considered due to the products of the mixed electric field components. Nonlinear optical polarisation can be described by [110] the following:Pj=ε0[χ(1)jkEk+χ(2)jklEkEl+χ(3)jklmEkElEm+…],Pj=ε0[χjk(1)Ek+χjkl(2)EkEl+χjklm(3)EkElEm+…],(9)

where χ⁽²⁾ is the second-order susceptibility (rank three tensor), χ⁽³⁾ is the third-order susceptibility (rank four tensor) and the sum over repeated subscript indices is again implied. Each of the terms in Eq. 9 can be written in shorthand by P⇀(1)P⇀(1), P⇀(2)P⇀(2), P⇀(3)P⇀(3), etc. The physical processes that occur because of the second-order polarisation, P⇀(2)P⇀(2), tend to be distinct from those arising from the third-order polarisation, P⇀(3)P⇀(3). This polarisation can have electric dipole, quadrupolar, octupolar, (etc.) contributions. Under the electric dipole approximation, the second-order polarisation can only occur in crystals that are noncentrosymmetric (lack inversion symmetry). Hence, χ⁽²⁾ vanishes for media such as fluids (e.g. liquid/gas) and amorphous solids (e.g. glass). Third-order nonlinear optical interactions (i.e. those described by a χ⁽³⁾ susceptibility) can occur for both centrosymmetric and noncentrosymmetric systems [109, 110]. Electric quadrupolar, octupolar, (etc.) χ⁽²⁾ contributions do not disappear under inversion symmetry.

Stimulated Raman Scattering

While spontaneous Raman scattering is an incoherent process, SRS is a coherent four-wave nonlinear optical mixing process. The modes of oscillation are in phase forming a coherent modulation of polarisation in the sample with susceptibility χ⁽³⁾(ω_S; ω_p + ω_S − ω_p) [110]. The scattered light is also coherent [45]. The SRS process is dependent on the spontaneous Raman cross-section, the spectral linewidth, the path length of the light-field-matter interaction, the input intensity and optical feedback (light generation) of Stokes frequency light [110].

When photons of frequency ω_p and ω_S simultaneously interact with a molecule or crystal lattice in the ground state, the system vibrates with an induced frequency: ω_osc = ω_p − ω_S. Unlike spontaneous Raman scattering, the de-excitation (relaxation) time to and energy of the final state are determined by the stimulation effect. The interaction results in the transfer of energy from the pump photon to the molecule/lattice, and the molecule/crystal scatters a new photon with frequency and phase matching that of the incident light of frequency ω_S. Figure 2a shows the process schematically.

It is common to employ an external radiation source tuned to the Stokes frequency in tandem with the pump laser beam to provoke this effect. This technique can lead to exponential gain in the Stokes signal, by transferring energy from the pump radiation, and rapid population of the final (ro-)vibrational state |f 〉 [115]. However, if the intensity of the incident light of frequency ω_p is sufficient, the generation of Stokes frequency photons within the material can self-promote SRS without the need for an external ω_S source. The intensity threshold of incident light in organic liquids, such as ethanol, for this kind of self-generated SRS typically requires an incident peak intensity of pump light > 10⁹ W/cm² for an optical path length of a few centimetres. However, the SRS threshold can be significantly reduced by extending the length of the pump and Stokes field interaction with an optical resonator, such as internal reflection in a droplet of liquid. The example shown in Fig. 2b is the SRS spectrum taken with droplets of ethanol directly compared to the spontaneous Raman spectrum of bulk ethanol. The droplets act to confine the light by internal reflection which feeds back the Stokes light as a self-SRS inducing optical resonator [114].

Coherent Anti-Stokes Raman Scattering

CARS is a third-order nonlinear four-wave optical mixing process. Figure 1b shows the energy level diagram for the process. A pump beam and probe beam of frequency ω_p and ω_pr are mixed with a third beam of frequency ω_S (Stokes frequency) and incident on the sample. The frequency difference (ω_p − ω_S) needs to match the frequency associated with the Raman active (ro-) vibrational mode ω_osc = ω_p − ω_S [4, 53, 56, 116]. The frequency of the Stokes beam is usually adjusted/tuned to satisfy this criterion [117]. Next, a probe photon of frequency ω_prprovides a perturbation for the anti-Stokes scattering process to occur at frequency ω_AS = ω_p − ω_S + ω_pr [5]. A macroscopic third-order polarisation, P⁽³⁾, is induced due to the coherent superposition of the microscopic dipole oscillations [53]. Hence, CARS is governed by the third-order susceptibility of the form: χ⁽³⁾(ω_AS; ω_p − ω_S + ω_pr).

There are numerous treatments and approaches to formulating expressions for χ⁽³⁾. If one assumes that the excitation field is much weaker than the intramolecular forces, then a perturbative approach can be adopted [5, 110]. If this is not the case, non-perturbative treatments can be considered [118]. By considering the density matrix equation of the system and expressing the external field interaction as a perturbation in the Hamiltonian, the semi-classical nonlinear optics theory generates an expression for χ⁽³⁾ with 48 terms, each of which contribute to the third-order susceptibility [5]. A generalised expression for dominant terms in resonant CARS is given by the following [51, 119]:χ(3)=ARωosc−(ωp−ωS)−iΓR+χ(3)NR,χ(3)=ARωosc−(ωp−ωS)−iΓR+χNR(3),(10)

where Γ_R is the half width at half maximum for the Raman line [51]; A_R is a constant representing the Raman scattering cross-section. The first term is the contribution due to CARS vibrational resonance as in Fig. 1b (ω_osc = ω_p − ω_S). The second term is the nonresonant background signal and is independent of the Raman shift (ω_osc ≠ ω_p − ω_S). The nonresonant background occurs because not all quantum pathways of the scattering process involve a resonance with a (ro-)vibrational state. This nonresonant contribution interferes with the resonant part of the signal. The nonresonant background causes distinctive distortions of CARS spectra in comparison with spontaneous Raman spectra and has prevented CARS from becoming a widespread technique [120].

The incident light beams of differing frequency move in and out of phase with each other in both time and space. Hence, the CARS signal reaches its first maximum when the field-sample interaction length scale is less than the coherence length scale to yield constructive interference [121, 122]. For plane-wave pump and Stokes beams, the intensity of the anti-Stokes signal is as follows [53, 123]:IAS∝∣∣χ(3)∣∣2IpIprIS⎛⎝⎜⎜sin(Δk⇀∙z⇀2)∣∣Δk⇀∣∣2⎞⎠⎟⎟2,IAS∝|χ(3)|2IpIprIS(sin⁡(Δk⇀∙z⇀2)|Δk⇀|2)2,(11)

where z⇀z⇀ is the sample thickness (vector normal to the lattice cell surface), k⇀k⇀ is the wavevector of light, Δk⇀=k⇀p−k⇀S+k⇀pr−k⇀ASΔk⇀=k⇀p−k⇀S+k⇀pr−k⇀AS is the wavevector mismatch (the velocity difference between the four waves) and I_i is the intensity of the wave denoted by the subscript. Phase matching is achieved when Δk⇀=0Δk⇀=0 and the intensity of the anti-Stokes signal is maximised because the energy and momentum transfer processes correspond to allowed transitions. As the magnitude of χ⁽³⁾ is linearly proportional to the number oscillators involved in the process, the intensity of the anti-Stokes signal is quadratically proportional to the number/concentration of oscillators [53].

Researchers typically employ the pump beam to provide the second virtual excitation (i.e. the probe light shown in Fig. 1b; i.e ω_pr = ω_p and ω_AS = 2ω_p − ω_S) [119]. The intensity of the CARS signal is therefore quadratically proportional to the intensity of the pump beam (see Eq. 11). The CARS signal is monodirectional due to the phase-matching condition [120]. However, high numerical aperture (NA) lenses or microscope objectives (confocal light) are commonly employed to satisfy the phase-matching condition without the need for complex mechanical systems to achieve phase-matched beam alignment [5, 117].

Raman resonances typically have coherence times of ~ 1 ps. Hence, the pump and Stokes beams are typically pulsed in picosecond timescales to obtain coherent excitation [124] and to inhibit multiphoton effects [53]. The CARS process takes place in the immediate vicinity of the beam’s focal spot. The signal produced is typically 10⁶ times that of spontaneous Raman scattering. CARS microscopy offers non-invasive characterisation and imaging of (ro-)vibrational spectra with high sensitivity and spectral resolution as well as three dimensional sectioning capabilities [116].

Surface Plasmons and Polaritons

Surface plasmons can occur at the interface between a dielectric and conducting material, such as a metal or degenerate semi-conductor [88, 125]. They are the light-induced coherent oscillations of surface conduction electrons about their equilibrium position. The nanoscale volume of opposing charge that remains acts as a restoring force on the electrons. The result can be described with a damped simple harmonic oscillator model, in which the oscillations of the free-charge carriers have an associated resonance. Surface plasmons can be excited by EM radiation and plasmonics is the study of these light-matter interactions [126].

Plasmonic nanoparticles that are much smaller than the wavelength of the incident light can support non-propagating surface plasmons that oscillate with a frequency known as the local surface plasmon resonance (LSPR) [127, 128]. The wavelength of surface plasmons is much shorter than that of the associated propagating light for a given frequency [129]. The LSPR wavelength is dependent on the nanoparticle’s size, shape, material, external dielectric properties and inter-nanoparticle separation [85, 127, 128, 130,131,132,133].

Surface plasmons that propagate are referred to as surface plasmon polaritons (SPPs) [134,135,136]. They are essentially light waves that are trapped at the interface due to their interaction with the free electrons of the conducting material [88]. For a planar dielectric-conducting interface, polaritons propagate in 2-dimensional space along the surface interface for length scales of tens to hundreds of micrometres [126, 134,135,136]. They decay evanescently in the direction perpendicular to the surface interface with 1/e decay lengths of up to 200 nm [126, 137]. The field intensity in this evanescent decay region is amplified by orders of 10 to 100 relative to the incident radiation [136]. Hence, light-matter interactions with adsorbed molecules on the surface are also enhanced.

In the case of LSPR, the surface roughness or surface nanoparticles cause local concentrations of charge carriers which further amplify the evanescent EM field due to the lightning rod effect [138]. Even larger field-enhancements (up to 10⁶) can be observed in gap plasmons (in the gap between two neighbouring plasmonic nanoparticles; see Fig. 1c) [85, 111]. This enhanced near-field effect gives rise to the technique known as SERS and is discussed in the next section.

Surface-Enhanced Raman Scattering

Raman is generally a very weak process; it is estimated that approximately one in every 10⁸photons undergo Raman scattering spontaneously [6]. This inherent weakness poses a limitation on the intensity of the obtainable Raman signal. Various methods can be used to increase the Raman throughput of an experiment, such as increasing the incident laser power and using microscope objectives to tightly focus the laser beam into small areas. However, this can have negative consequences such as sample photobleaching [139]. Placing the analyte on a rough metal surface can provide orders of magnitude enhancement of the measured Raman signal, i.e. SERS.

Two mechanisms have been proposed to explain the increase in Raman signal provided by SERS. The first is via EM enhancements where local surface plasmons concentrate the local electric field near the surface of the metal in ‘hot spots’ located on the sharp edges of nanostructures or in regions of concentrated free-charge carriers due to the lighting rod effect [140]. Figure 1c, illustrates the SERS process. This process can increase Raman generation by a factor of 10⁸ to 10¹¹ [86, 141,142,143,144]. The second method is chemical enhancement via charge transfer between the metal surface and the analyte, which enhances Raman scattering by a factor of approximately 10² to 10³ [86, 145,146,147]. However, the charge transfer mechanism only applies to specific molecules, whereas the EM mechanism is applicable for all analytes [4, 92, 102, 148].

The ubiquity of EM enhancements has led to the development of numerous SERS substrates, which can be divided into two groups: metallic nanostructures fabricated on a solid substrate [85] and colloidal suspensions of plasmonic nanoparticles [96, 141]. The most common materials used to fabricate SERS substrates are gold and silver because of their good plasmonic response [149]. Gold also benefits from chemical stability as it is a noble metal. Other metals are also being investigated, such as aluminium for UV Raman spectroscopy [150, 151].

Tip-Enhanced Raman Scattering

The diffraction limit of light restricts the focus spot size in standard optical techniques (such as Raman spectroscopy) to be at least half of the wavelength of the light according to Abbe’s criterion [152,153,154]. Light from the sample is composed of both propagating and non-propagating radiation. The non-propagating evanescent waves remain in the vicinity of their sources and do not participate in image formation in the far field. Instead, they extend laterally on the sample among the plasmon-active sites. Hence the spatial resolution is restricted by the size of the focal spot of the light. Even with a focal spot size of a half-wavelength (~ 250 nm for visible light), any objects that are much smaller than the half-wavelength would appear as a defuse shape.

TERS is a relatively new optical nanoimaging technique that combined Raman spectroscopy with scattering (or apertureless) scanning near-field optical microscopy. TERS offers spatial resolution far beyond the diffraction limit of the probing light. In the context of the a priori description, this is achieved by forcing the near-field evanescent light into the far-field image formation [86]. At the present date, the spatial resolution of TERS is typically reported to be 10–30 nm and is largely assumed to scale with the size of the tip’s apex [103, 155,156,157]. Incremental improvements to this resolution have been reported [104, 158]. Enhancement factors for TERS are significantly weaker than SERS due to the relative size of the probed signal volume. The enhancement factor (relative to spontaneous Raman scattering) is typically reported to be 10³ to 10⁶. As with SERS, two field enhancement mechanisms are thought to contribute to the Raman signal: EM and chemical enhancement [86].

TERS is implemented by positioning a plasmon-active (plasmonic) nanotip approximately 50 nm above the sample’s region of interest. The Raman probe light is focused onto the tip-surface cavity to induce LSPR within the tip’ apex and (in some circumstances) the sample surface. The surface plasmons may then enhance evanescent or near-field light with the incident probe light and/or the Raman scattered light. Hence, the LSPRs both confine and enhance the light field in the vicinity of the tip’s apex. The enhanced local EM field is most concentrated at the tip apex due to the lightning rod effect. This evanescent light at the tip apex can then excite or stimulate Raman, two-photon or second harmonic scattering from a nanoscale volume of the sample under the tip. A Raman image of the sample surface can be obtained by raster scanning the sample under the nanometric tip.

Experimental Considerations

Instrumentation

The nonresonant Raman effect is a very weak process. Hence, monochromatic, narrow-beam and high-intensity lasers are preferable to produce quality Raman spectra. The exploitation of microelectronics, such as stepper motor drives, photon counters, digital data acquisition and computational processing systems can further enhance the quality of spectra. As spontaneous Raman spectroscopy is naturally an incoherent process, continuous-wave laser sources are commonly used because pulsed lasers require higher peak powers for sufficient signal-to-noise ratio, which can photobleach/damage samples.

The choice of wavelength of the laser source depends on the required application. Lower visible wavelengths and UV cause strong photoluminescence in organic materials, which can mask the Raman peaks. Therefore, a longer visible or near-IR wavelength (500—830 nm) laser source is often suited for studying organic materials, because of the reduced photoluminescence. However, the Raman signal intensity is inversely proportional to the wavelength of the pump light. Hence, longer wavelengths of light require longer acquisition times [1, 6].

Raman spectroscopy is most often performed using laser sources at λ = 785 nm. This wavelength source is often selected as it balances the competing factors between Raman signal intensity, fluorescence, detector sensitivity and cost, and cost-effective/compact high-quality laser sources. However, visible lasers in the blue and green (e.g. λ = 532 nm) are becoming more common in Raman spectroscopy [159].

Raman scattering is measured in terms of the wavelength shift from the source wavelength. Ideally the illumination source for Raman measurements should be purely monochromatic, in other words, a single wavelength. However, all laser sources possess a spectrum of wavelengths known as a linewidth. The linewidth of a laser is usually measured in Hertz and is typically > 1 MHz for solid-state lasers used in Raman applications. A narrow linewidth is preferable for Raman spectroscopy because the measured shift in the Raman scattering process is limited by the laser’s linewidth.

Laser sources for Raman spectroscopy need to be stable in wavelength and power over extended periods of time and from use to use. Raman spectra are usually collected over long integration times and for many acquisitions. If the wavelength of the source drifts during a measurement, then the Raman peaks will drift as well, because Raman is measured as a shift relative to the pump light. Wavelength drift is also problematic from measurement to measurement as it causes peaks to shift, in turn making comparisons between measurements difficult. The output power stability of the source is important for similar reasons. If the laser power drifts from measurement to measurement, then quantitative comparisons cannot be made easily.

Spectral purity is another key criterion for Raman laser sources. The spectral purity of laser sources often requires side-mode suppression better than 60 dB. In many cases, side-mode suppression is sufficient if > 60 dB spectral purity is reached at ~ 1–2 nm from the laser wavelength peak. However longer wavelength (near-IR) Raman spectroscopy requires side-mode suppression ratios within a few hundreds of pm from the main peak. These criteria are discussed in the context of common Raman laser sources in the following paragraphs [159].

Most modern Raman systems use solid-state laser sources rather than gas lasers because of their spectral quality and stability. There are three main categories of continuous-wave solid-state laser sources used in Raman spectroscopy: Diode-pumped single-longitudinal mode (SLM) lasers; single-mode diode lasers (distributed feedback (DFB) or distributed Bragg reflection (DBR)); and volume Bragg-grating (VBG) frequency-stabilised diode lasers. These laser sources have varying optical characteristics.

Diode-pumped SLM lasers are readily available in compact form from the UV to the near-IR. Power levels of several Watts are achievable at 1064 nm in the near-IR. In the visible range, numerous lines in the blue-green-red region (457 to 660 nm) are available with output powers of ~ 100 mW. In the UV spectral range, power outputs of 10–50 mW at 355 nm are available. Hermite-Gaussian laser beam modes are described by their transverse electro-magnetic mode (TEM): TEM_m,n, where m and n represent the Hermite-Gaussian mode index [46]. Diode-pumped SLM lasers provide excellent TEM₀₀ mode beams, precise wavelengths with low drift, and a single-frequency linewidth > 1 MHz. The spectral purity of diode-pumped SLM lasers is typically > 60 dB in terms of their side-mode suppression ratio. Weak emissions that neighbour the laser’s main peak several nanometres in spectral shift can occur in diode-pumped SLM lasers. However, these neighbouring lines can be mitigated with dielectric band-pass filters. The wavelength of diode-pumped SLM lasers is typically stable to within 4 pm over a temperature change of 30 °C.

Single-mode diode lasers are compact and cost-effective pump illumination sources with single-frequency linewidth (> 1 MHz), single-TEM beam quality and output powers of up to ~ 100 mW. Wavelengths of λ = 785, 830, 980 and 1064 nm are most common in Raman spectroscopy. The side-mode suppression ratio is typically limited by sideband emission to ~ 50 dB at ~ 100 pm from the main peak.

VBG frequency-stabilised diode lasers use a narrow-linewidth VBG element with a diode-laser emitter to achieve narrow-line emission. These lasers are often used for applications requiring narrow-line emission at wavelengths that are not available for DFB or DBR laser sources. Frequency-locking multi-TEM diode lasers can be used to increase the output power of the narrow-linewidth emission. The stability of the output wavelength and linewidth requires careful thermomechanical control and high-precision alignment inside VBG frequency-stabilised diode lasers. Linewidths can range from single-frequency emission to ~ 10s of pm, depending on the wavelength and the output power. The side-mode suppression ratio is limited to ~ 50 dB, ~ 250 pm from the main peak emission. However, this can be improved using filters.

In confocal Raman imaging applications, it is necessary to use diffraction-limited TEM₀₀beams for optimum spatial resolution. However, this is relaxed for probe-based quantitative Raman analysis. In addition, confocal Raman setups require laser beam isolation as samples may generate optical feedback that is well aligned to the incident pump light. This counter-propagating feedback can induce power and noise instability and can even damage the laser source. Optical isolators are often integrated into the laser system itself because careful alignment must be achieved in the output after the isolator [4, 6, 159].

The spectrometer is a core component of any set-up used for measuring Raman spectra. The spectrometer should match the wavelength(s) of the laser source(s) used. The spectral range and resolution required will depend on the application. For example, the spectral range is determined by the position of the Raman peaks of interest (i.e. at large Δν∼Δν∼ ~ 3000 cm⁻¹or low Δν∼Δν∼ ~ 1 cm⁻¹). If the application requires closely spaced Raman peaks to be resolved, then spectral resolution is key. The spectral resolution of a spectrometer is largely determined by the slit width at the spectrometer entrance, the focal length of the spectrometer, the dispersion, the size of the grating (or prism) and the size and sensitivity/quality of the detector. There is a trade-off between the overall spectral range and resolution when considering the design of the experiment for a given application. In the case of weak Raman signals, optimising the signal-to-noise ratio is a priority.

Spectral filtering plays a vital role in the acquisition of Raman spectra. Firstly, the incident laser light must be spectrally pure, which is accomplished with a narrow-linewidth laser source as discussed previously. However, if the laser light is delivered to the sample by an optical fibre, then it is inevitable that Raman generation will occur in the fibre. Therefore, it is important to use a narrow band-pass filter to reject any Raman signal generated in delivering the laser to the sample. Narrow band-pass filters can provide transmission > 90 % at the laser wavelength while suppressing light to an optical density of OD > 5 at wavelengths differing by just 1% from the laser wavelength.

Importantly, light collected for detection requires filtering to block the laser wavelength. If the laser light is not filtered out, it can go on to generate Raman in the detection arm of the set-up and drown out the desired Raman signal when it reaches the spectrometer. The type of filter required depends on whether Stokes, anti-Stokes or both are to be measured. To only detect anti-Stokes Raman, a short-pass filter should be used as anti-Stokes Raman light has a higher energy and hence shorter wavelength than the laser source. To only detect Stokes Raman, a long-pass filter should be used as the Stokes Raman light has a lower energy and hence longer wavelength than the laser source. Long pass edge filters with edge-transition widths of < 3 nm and edge steepness < 40 cm⁻¹ are available. To detect both Stokes and anti-Stokes Raman light, a notch filter centred on the laser wavelength should be used as it allows both shorter and longer wavelengths to be detected. Notch filters with OD > 6 at the laser line wavelength are available. Multi-notch filters are also available and can block multiple laser lines simultaneously. Holographic notch filters significantly outperform dielectric notch filters, providing excellent attenuation of the Rayleigh line while passing light as near as 50 cm^–1from the Rayleigh line. Acousto-optic modulators can also be used in conjunction with an excitation laser to select emissions with a desired wavelength (as a filter) [160] or as a time-gated illumination system in tapping mode atomic force microscopy (AFM)-based TERS [161].

The quantum efficiency of standard room-temperature silicon-based CCD devices for Raman signal detection degenerates above λ = 800 nm. For longer wavelengths, indium gallium arsenide array devices can be used, but these are less sensitive with higher noise levels and cost.

The visible to near-infrared wavelength range (λ = 500–830 m) is particularly suitable for inorganic materials (e.g. graphene, carbon nanotubes (CNTs) and fullerenes) and SERS. UV lasers are attractive for organic materials (e.g. pathogens, proteins, DNA, and RNA). For materials with strong fluorescence that require near-IR illumination, it is common to use a 1064-nm wavelength.

Spontaneous and Coherent Raman Scattering Setups

Spontaneous Raman spectroscopy is most commonly used for modes with forbidden single-photon absorption or emission experiments [108]. SRS is sometimes used for wavelength shifting of coherent light, light amplification, pulse compression, phase conjugation and beam combining [108]. Unlike spontaneous Raman scattering, SRS is highly directional and offers enhanced signal strength and the ability to time-resolve the evolution and dephasing of coherent (ro-)vibrational motion [45].

Figure 3a shows a typical Raman setup based on a confocal geometry used by Wiedemeier et al. [162]. Confocal setups of this type are commonly used and employ an infinity-corrected objective lens (large numerical aperture (NA) lens) to focus the pump light. Wiedemeier et al. [162] used a diode-pumped solid-state laser as a monochromatic light source centred at 532 nm. Confocal mode is achieved by the use of a pinhole module in front of the spectrometer to spatially filter the light. The pinhole only passes light that originates from the focal plane to the detector. For detection of the Raman signal, a holographic-imaging spectrometer with an attached CCD camera is used. A holographic transmission grating with high light throughput served as a dispersive element, which enables large spectral ranges in a comparatively short time period to be acquired. Raster scanning of the sample in a confocal setup needs to be precise. Hence, a piezo actuated nano-positioner is used for positioning of the specimen.

Spontaneous anti-Stokes scattering is weaker than Stokes Raman scattering due to the relatively low probability of thermal excitation. Hence, anti-Stokes Raman spectroscopy is typically used with stimulated or coherent spectroscopy. CARS spectroscopy offers a 10⁵increase in conversion efficiency, spectral and spatial discrimination against fluorescence and, most importantly, does not require a monochromator. Due to the required coherence of the process, high-peak power pulsed tuneable laser sources are employed. These peaks are readily available using picosecond or femtosecond light lasers, the choice of which is determined by the spectral resolution required and the timescale of interest [139].

Avoiding direct electronic excitations in the sample is an important consideration as photochemical damage (due to photobleaching) can occur in samples. Djaker et al. [139], for example, use near-infrared laser sources to mitigate photobleaching in their samples of polystyrene beads.

Figure 3b shows a typical CARS setup that measures both forward scattered light (F-CARS) and back- or epi-scattered light (E-CARS) [116, 139, 163]. The system has two synchronised picosecond pulse trains. The pump and Stokes beams are generated by two picosecond Ti:Sapphire lasers operating at 80 MHz and are tuneable from 700 to 1000 nm to cover the entire spectrum of molecular (ro-)vibrations in biological systems (up to Δν∼Δν∼ ~ 3000 cm⁻¹). The ps pulse duration is adjustable by a Gires-Tournois interferometer. The Ti:Sapphire lasers are pumped by a frequency-doubled CW Nd:Vanadate laser that provides monochromatic light at 532 nm. The two pulse trains were polarised with a pulse duration of 3 ps, corresponding to a spectral width of 1.76 cm⁻¹. The pump and Stokes beams are synchronously pulse picked through two Bragg cells to reduce the repetition rate of the pulse trains to several hundred kilohertz, thus avoiding photodamage of the sample while still maintaining high-peak power for CARS generation. The pump and Stokes beams are temporally synchronised by a SynchroLock system, which electronically adjusts the time delay between the two pulse trains. A small part of the output of the lasers are launched in optical fibres coupled to photodiodes and connected to a SynchroLock controller, which measures the lasers frequency or phase difference between the master and the slave; the timing jitter was reported to be ~ 250 fs. The spectral resolution was estimated to be 2.5 cm⁻¹, which is high enough to resolve Raman spectral features of biological samples. The use of a broadband Stokes wave enables the acquisition of a full CARS spectrum in only one measurement, with this configuration being known as multiplex or broadband CARS [164,165,166,167].

The two pulse trains are spatially filtered, collinearly combined and expanded through beam expanders. They are then sent into an inverted microscope and focused onto the sample by a water-immersion objective lens with a large NA. The E-CARS signal is collected by the same objective lens while the F-CARS signal is collected by a condenser lens with a lower NA. The E-CARS and F-CARS signals are filtered through a set of band-pass filters and detected by two avalanche photodiodes with a 200 μm × 200 μm active area. The CARS images are collected by raster scanning the sample, using an XYZ piezo flexure stage.

Several methods have been developed to suppress the nonresonant background associated with CARS. E-CARS is relatively insensitive to the nonresonant background of sample solvents [168]. Polarisation-sensitive CARS can differentiate the resonant and nonresonant signals by their polarisation [169]. However, these two techniques reduce the anti-Stokes signal strength [120]. Time-resolved CARS [170], temporal or spectral interferometry CARS [52, 171] and frequency-modulated CARS [172] can also suppress the nonresonant background. However, the setup in terms of both optics and electronics is challenging [120].

SERS Specific Considerations

A variety of nanostructures, such as bowtie antennas [173], nano-rings [174], nanovoids [175], nanoparticle aggregates [87, 176, 177], nanoflower [178], nanorod arrays [97] and nanowells [179] can be used for SERS. Each nanostructure can have a number of plasmonic resonances, and matching the excitation laser to these wavelengths can greatly enhance the SERS intensity [141, 180, 181]. Matching the plasmonic resonance to the pump laser can be done either by tuning the laser wavelength or by tuning the LSPR of the nanostructures [85, 182,183,184].

The difficulty faced in producing SERS substrates is consistency in fabrication and repeatability in measurements due to the inhomogeneity and randomness of SERS active hot spots [85, 185, 186]. For SERS substrates produced by top-down methods, such as electron beam lithography [187], the main challenge is scaling the fabrication. Conventional top-down methods limit the active area of the SERS substrate and are not conducive to large-area manufacturing. Bottom-up fabrication methods have their own set of problems. Even though bottom-up approaches allow wafer scale fabrication, consistency across the wafer is usually lacking [188]. This inconsistency hinders the repeatability of measurements, which is problematic for quantitative analysis. Colloidal SERS schemes suffer from complications introduced by stabilising agents at the surface of the nanoparticles, which help to keep nanoparticles in suspension. These stabilising agents can either impede or augment the measured Raman signal [189]. The chemical synthesis for nanoparticle colloids also requires precise optimisation. The poor reproducibility of nanoparticle colloidal synthesis hampers batch-to-batch consistency.

Often, only very few sites exhibit the highest SERS enhancement and the variability in size and shape can alter the plasmonic properties from the desired LSPR [85]. Figure 3c, shows a setup which combines SERS with dark-field spectroscopy. The dark-field spectrometer analyses the light scattered from the nanostructures (illuminated by the white-light source) to select nanostructures with the desired plasmonic properties.

TERS Specific Considerations

Scanning probe microscopy (SPM) techniques, such as atomic force microscopy (AFM), scanning tunnelling microscopy (STM) or shear force microscopy (SFM), are usually the tools of choice for TERS [86]. TERS has the ability to simultaneously measure topography by the conventional SPM mode of the system and obtain corresponding spectral information from a sample with nanometric spatial resolution and high sensitivity [86]. Certain SPM techniques ordain probe modifications for the plasmonically induced nanoscale evanescent light to activate/enhance the Raman signal. The tips can either be made of a metal or coated with a thin layer of metal to modify them for TERS. When the apex of a metallic or a metal-coated nanotip is illuminated with focused light at the LSPR wavelength, local surface plasmons around the tip apex are excited, and evanescent light is produced at the tip apex. This evanescent light can generate Raman scattering from a sample placed right under the tip apex. The process of Raman scattering takes place in the near-field and the spectral signal is scattered and converted back to the far-field by the tip apex, which is then collected by the usual optics and spectrometer in the far-field. Figure 3d shows such a TERS setup with a modified AFM. The setup consists of largely similar equipment shown in Fig. 3a (discussed in an earlier section). An inverted microscope illuminates the sample from underneath and the tip is placed at the top surface of the sample. The Raman back-scattered signal is then directed to the spectrometer. An evanescent mask blocks the central part of the laser beam inhibiting the low NA component of the incident light, so that only the high-NA component of the incident light reaches the sample so that total internal reflection occurs. This limits the transmitted light that falls onto the tip and, hence, only the evanescent light participates in the Raman scattering signal. Suppressing the participation of transmitted far-field light reduces the unfavourable background signal.

Polarisation-dependent TERS can be performed with light polarisation parallel to the tip apex in addition to the in-plane linear and radial polarisations. Polarisation dependent TERS is enabled by the large incidence angle from the high-NA objective lens and the use of devices that modify the polarisation state of the light such as a λ/2 waveplate [190]. The Raman scattered light is then collected in the low NA region through an apertured mask, which inhibits any residual laser light. As the tip apex approaches the sample within the focal spot, evanescent light is created at the tip’s apex [86]. Since the intensity distribution within laser focus is not uniform, it is very important to lock the relative position of laser focus to the tip [191, 192].

The strength and resolution of TERS depends on the ability of the tip to enhance and confine the light field at the tip’s apex, respectively. In STM systems, the tips are made of solid metal and the substrates need to be conductive in order to control the tunnelling current [193]. The STM tip resembles a long and smooth nanocone, with an apex diameter of ~ 20 nm. The length of the tip (~ tens of micrometres) makes them plasmonically unfavourable for visible light enhancement. However, the tunnelling gap between the tip and the sample can be tuned to the desired LSPR wavelength, creating a strong hotspot within the gap [143, 194, 195]. Some of the more advanced STM systems allow high-vacuum and low-temperature measurements [196]. As the substrate in STM needs to be conductive (often opaque in the visible wavelength range), the setup shown in Fig. 3d would not be suitable. Hence, a side illumination and side collection configuration is more common with STM-based TERS. To prevent the objective from mechanically interfering with the STM tip, a lens with a long working distance is required. It is therefore not trivial to tightly focus the incident light on the tip apex. A parabolic mirror can be used to mitigate mechanical interference and tightly focus the incident light to the tip apex as well as to collect the Raman signal [196, 197].

The spatial resolution in TERS is comparable to the size of the metallic nanostructure at the tip apex [86]. The gain in spatial resolution comes at a cost to overall signal enhancement (relative to SERS) due to the reduction of the Raman active volume.

In AFM systems, the tips are usually semiconductor cantilevers, with an apex diameter of ~ 5 nm. Figure 4 shows five examples of AFM-based TERS tips that have been demonstrated in the literature. The semiconductor tips are usually coated with metal either by thermal evaporation under high-vacuum [202] or electroless metal plating (mirror reaction) [203] techniques. Figure 4a shows an example of a smooth AFM TERS tip. As the substrate does not need to be conductive, AFM-based TERS can be performed in either bottom-up transmissive illumination (as in Fig. 3d) or in side/top reflective illumination configurations; the transmissive configuration in Fig. 3d is more common.

The surface of AFM tips becomes nanostructured during the coating process resembling aggregated nanoparticles on the semiconducting tip (Fig. 4b) [198]. These nanostructures are suitable for the resonant excitation of LSPR and SPPs. The smooth tip shown in Fig. 4a has been fabricated by subsequently depositing a thin granular layer of additional metal. Other researchers have tested AFM tips with a metallic nanoparticle attached to the tip apex (Fig. 4c) [198], or a segregation in the tips coating to form an antenna (Fig. 4d) by focused ion beam lithography [115]. Tips can also be created by electrochemical deposition [204].

For transparent dielectric substrates, a thin metal film (thin enough to be transparent) can be coated onto the substrate to further enhance the field in the tip-sample gap [205]. It is also possible to perform TERS in liquids with AFM-based systems, which is favourable for biological specimens which require liquid environments to function [206]. Performing TERS in liquid with STM systems is much more difficult [86, 106]. SFM-based TERS is also an attractive technique and maintains many of the properties of AFM-based TERS with the exception of the tip material which resembles similar TERS properties of STM-based TERS [86, 156, 207, 208].

Some TERS setups have demonstrated vastly improved signal-to-noise ratio in TERS by SPP nanofocusing [201, 209, 210]. This technique focuses the laser onto a plasmon-coupling nanostructure (in the form of a grating) on the upper area of the tip, usually at a distance of ~ 10 μm from the tip apex. Figure 4e shows a typical nanofocused SPP-based TERS setup (i), the process of SPP nanofocusing by coupling the incident light to a focused ion beam-fabricated grating (ii), and an example SEM image of a SPP-nanofocusing tip (iii). The excited plasmons then propagate toward the tip apex through the process of adiabatic compression and create a confined EM field at the tip apex [209].

Tuning the Plasmon Resonance

The size, shape, composition of the nanostructures and inter-nanostructure spacing all affect the wavelength of the surface plasmon resonance [85, 86]. Metals are most often used as the conducting medium for surface plasmons; however, semiconductors also possess plasmonic characteristics [125]. Gold shows strong enhancement factors in the red spectral region [111, 177, 211, 212], silver in the blue-green spectral region [132, 213] and aluminium in the UV and deep UV spectral regions [150, 151, 175]. The blue-green spectral region is the most commonly used Raman spectroscopy range. However, silver is prone to oxidation which degrades the plasmonic characteristics within a few hours of exposure to atmosphere. For this reason, silver is often mixed with other metals, such as titanium [214].

The range of plasmon resonance can be tuned by the thickness and choice of coating metal, e.g. tungsten, gold, silver or aluminium. In TERS, the grain size of the metal coating corrugations (Fig. 4b) is roughly comparable to the wavelength of the LSPR/SSP. Unlike STM tips, it is possible to control the LSPR/SPP wavelength by adjusting the size of the nanoparticles. The surface plasmon resonance wavelength is also dependent on the refractive index of the dielectric material. In AFM-based TERS, for example, the silicon cantilever tip can be heated to ~ 1000 °C in the presence of water vapour to oxidise the silicon into silicon dioxide [215]. As SiO₂ has a lower refractive index than Si, the surface plasmon resonance is blue shifted [86].

The size and shape of the metal-coated AFM tip apex can also be modified to tune the LSPR [199, 200]. Fabricating a single metallic nanoparticle attached to the tip’s apex (Fig. 4c) or segregated antenna-shaped tip (Fig. 4d) has been demonstrated as a means to finely tune the surface plasmon resonance in AFM-based TERS [199, 200, 208, 216]. However, the most commonly used tips for AFM-based TERS are the tips that have disconnected metal nanoparticles evaporated on a semiconductor cantilever in the standard coating process (Fig. 4b) described a priori [198].

Analysis Methods

A Note on Units

By convention, Raman spectra are considered in terms of the wavenumber ν∼ν∼ in units of cm⁻¹. The conversion from angular frequency is as follows:ν∼=ω2πc0,ν∼=ω2πc0,(12)

where c₀ is the speed of light in vacuum and ω is the angular frequency. Raman spectra are usually plotted in terms of the wavenumber shift from the incident excitation radiation. This shift is defined as follows:Δν∼=ν∼p−ν∼scat,Δν∼=ν∼p−ν∼scat,(13)

where ν∼pν∼p is the wavenumber of the pump beam with angular frequency ω_p and ν∼scatν∼scat is the wavenumber of the scattered light accordingly. For Stokes Raman scattering, ν∼scat=ν∼p−ν∼oscν∼scat=ν∼p−ν∼osc (where ν∼oscν∼osc is the molecule or lattice vibration wavenumber) and Δν∼Δν∼ is positive. By contrast, for anti-Stokes Raman scattering, ν∼scat=ν∼p+ν∼oscν∼scat=ν∼p+ν∼osc and Δν∼Δν∼ is negative [1].

Raman spectra are (by standard) presented with the wavenumber shift linearly increasing from right to left on the horizontal axis. The vertical axis ordinate is linear and proportional to intensity. However, researchers also present Raman spectra with wavenumber shift denoted simply as wavenumber and/or increasing from left to right instead of right to left [1].

Spontaneous Raman Spectra

Figure 5a shows the Rayleigh and the Raman spectrum of carbon tetrachloride (liquid) excited by an argon ion laser, ν∼1ν∼1 ~ 20,487 cm⁻¹ (487.99 nm). This spectrum is presented according to recommendations of the International Union of Pure and Applied Chemistry. It contains a strong band at ν∼1ν∼1 ~ 20,487 cm⁻¹ due to the Rayleigh scattering of the incident laser radiation and a number of weaker bands with wavenumbers, ν∼1±ν∼oscν∼1±ν∼osc: ν∼oscν∼osc = 218, 314, 459, 762 and 790 cm⁻¹. The Stokes Raman lines are shown on the left-hand side of the plot (Fig. 5a); the anti-Stokes Raman lines are shown on the right. The ν∼oscν∼osc values relate to the fundamental vibrations of the carbon tetrachloride molecule [1]. In the original work by Raman and Krishnan [220], the same spectrum was measured using mercury arc radiation (ν∼1ν∼1 = 22,938 cm⁻¹, 435.83 nm). In this seminal work, the anti-Stokes bands at ν∼1+762ν∼1+762 and ν∼1+790ν∼1+790 cm⁻¹ were not observed. Hence, after the invention of the laser, Rayleigh and Raman scattering experiments are preferably performed using monochromatically intense lasers.

Layered Two-Dimensional Systems

Raman spectroscopy can be used to determine the layer thickness in two-dimensional materials with atomic level precision, using either the inter-layer or intra-layer vibrational modes [19]. Lee et al. [12] demonstrated the technique with two intra-layer Raman modes of molybdenum disulphide (MoS₂). Figure 5b shows representative Raman spectra for single- and few-layer MoS₂ samples. Among the four Raman-active modes of bulk 2H phase MoS₂crystal (shown in Fig. 5b v), Lee et al. [12] only observed the E12gE2g1 and A_1g modes near Δν∼Δν∼ = 400 cm⁻¹. The authors surmised that the other modes were not observed either because of the selection rules for the scattering geometry (E_1g) [217] or because of the limited rejection of the Rayleigh scattering radiation (E22gE2g2) [13]. The authors [12] report that single-layer MoS₂exhibits a strong in-plane vibrational mode at Δν∼Δν∼ ~ 384 cm⁻¹, corresponding to the E12gE2g1mode of the bulk 2H-MoS₂ crystal. For all film thickness, the Raman spectra in Fig. 5b i show strong in-plane E12gE2g1 and out-of-plane A_1gvibration signals. As the sample thickness increases (Fig. 5b i and ii), the E12gE2g1 mode red shifts and the A_1g mode blue shifts. For films of four of more layers, the E12gE2g1 and A_1g modes converge on the bulk values. Spatial maps of a MoS₂ film sample for the E12gE2g1 mode is shown in Fig. 5b iii; that of the A_1g mode is shown in Fig. 5b iv. These maps demonstrate that the frequency of the two modes only slightly vary in regions of the sample with a given layer thickness. Hence, Raman spectra can provide a convenient and reliable means of determining the layer thickness in two-dimensional crystalline materials with atomic level precision.

Enhanced Raman Scattering Through SERS

Ault et al. [221] were the first to use SERS to enhance the Raman scattering signal of previously undetectable secondary organic aerosol particles on Ag nanoparticle-coated quartz substrates. Fu et al. [96] demonstrated enhancement factors of 6 for the Raman spectra of ammonium sulphate (AS) at the Raman active mode ν∼sν∼s(SO₄²⁻) at 970 cm⁻¹ with Klarite. Figure 5c shows a microscope image of a large AS particle on the surface of Klarite (Fig. 5c i), the corresponding Raman mapping image is in Fig. 5c ii. Figure 5c iii shows another sample of AS particle but on a silicon wafer. The corresponding Raman mapping image is shown in Fig. 5c iv. Aside from the three larger AS particles, small (sub-micron) AS particles are apparent in Fig. 5c iii. However, in the absence of SERS, these smaller particles are undetectable. On the other hand, the SERS Raman mapping image (Fig. 5c ii) shows a vastly enhanced signal intensity, as is evident from the scale bars, to the point where a number of small spots yield a signal at the ν∼sν∼s(SO₄²⁻) Raman mode. Such spots most likely correspond to small AS particles that are observable in Fig. 5c ii but are not apparent in Fig. 5c i.

Insights into Cellular Structure with CARS

CARS microscopy is relevant to the chemical [64, 222,223,224,225], materials [78, 226, 227], biological and medical fields [29, 36, 61, 63, 167, 228] and can provide unparalleled insights into cellular structures [53]. Spontaneous Raman and infrared micro/spectroscopy can provide adequate chemical specificity and sensitivity to delineate a variety of neoplasms [229,230,231,232,233,234,235,236,237] but require long integration times and have a coarse spatial resolution, which may limit accurate tumour-boundary identification and early-stage tumour detection. However, coherent Raman imaging techniques have demonstrated high-speed, high-spatial-resolution imaging, but with contrast limited to single or few Raman peaks [36, 53, 167, 232]. Figure 5d presents images of orthotopic xenograft brain tumours from within a murine brain [167]. Figure 5d i shows a broadband CARS image with nuclei in blue (Δν∼Δν∼ = 730 cm⁻¹), lipid content in red (Δν∼Δν∼ = 2850 cm⁻¹) and red blood cells in green (Δν∼Δν∼ = 1548 cm⁻¹ + 1565 cm⁻¹: C-C stretch from haemoglobin [238]). The large tumour mass and a projection of neoplastic cells within healthy tissue are clearly shown (Fig. 5d i). Figure 5ii shows several small regions of main tumour mass migrating into the healthy brain matter. Figure 5 iii shows the boundary between normal brain tissue, white matter and tumour masses, which contrasts lipids in red (Δν∼Δν∼ = 2850 cm⁻¹); CH₃ stretch-CH₂ stretch (Δν∼Δν∼ = 2944 − 2850 cm⁻¹), a general contrast; and nuclei in blue (Δν∼Δν∼ = 785 cm⁻¹). The image shows the fibrous texture of the white matter and strands of myelination around cancer cell clusters. Figure 5d iv presents a set of single-pixel spectra from an intra-tumoural nucleus, the white matter and normal brain, respectively. The spectra indicate that lipids are most concentrated in the white matter and least in the tumour regions.

Raman Thermography

Advances in electronic and opto-electronic semiconductor devices, such as high electron mobility transistors (HEMTs), have led to thermal management challenges [65]. Conventional thermal characterisation approaches such as infrared thermography are often no longer applicable for the accurate characterisation of high-power density devices due to limited spatial resolution which can result in the underestimation of the device peak temperature [239]. Batten et al. [218] have demonstrated temperature profiling in AlGaN/GaN HEMTs using Raman thermography by exploiting the E₂ and A₁ (LO) phonon modes. Both the E₂ and A₁ (LO) modes shift to lower frequency when operating the device. Figure 5e shows a comparison of the temperature rise in a AlGaN/GaN HEMT on a SiC substrate from Raman thermography and thermal simulations. The device was operated at a source-drain voltage of 40 V and a power density of 25 W/mm and had a thermal resistance of 8 °C/(W/mm).

Measuring Strain on the Nanoscale Using TERS

TERS microscopy is an effective means of imaging nanostructures beyond the spatial resolution of the so-called light diffraction limit [152,153,154, 219]. Nanostructures such as DNA molecules [240], carbon nanotubes (CNTs) [241, 242], silicon devices [101, 243], dye molecules [244] and single molecules [83] can be imaged using TERS. The technique can even be used to measure the local molecular strain in nanostructured materials. For example, AFM can be used to manipulate CNTs with nanoscale precision to develop a local strain [245,246,247,248]. Figure 5f (left) illustrates the process of CNT manipulation using contact-mode AFM. Although local strain in CNTs has previously been studied using AFM and transmission electron microscopy [245], TERS microscopy is the only optical technique that can provide images of such local structural distribution of nanomaterials. When a straight CNT is deformed by manipulation, a local breakdown in symmetry is induced. This causes the selections rules of Raman scattering to become relaxed, allowing forbidden Raman modes to become visible in the vicinity of the local curvature [219]. The position of the characteristic G-mode Raman scattering line in graphene can be used to deduce local strain using TERS [249]. Figure 5f (right) shows a TERS image of a deformed CNT which has been constructed from the peak positions of the G⁺-mode [219]. The image has a spatial resolution better than 20 nm which is about 25 times finer than the diffraction limit of the excitation wavelength of light (488 nm). The colour variation (as indicated by the scale bar) corresponds to the local peak position of the G⁺-mode and represents the variation of strain along the CNT.

Recent Results

Stimulated Raman Scattering Microscopy

Unlike CARS, SRS microscopy does not contain a nonresonant background signal that degrades image contrast. However, SRS can be affected by cross-phase modulation (where light at one wavelength modulates the refractive index in the medium affecting another wavelength of light), transient-absorption (which is characteristic of femtosecond light pulses) and photo-thermal effects which can modify the vibrational energy levels and reduce hyperspectral image contrast [250,251,252]. SRS is quantified by the amount of energy transfer from the pump light to the Stokes light when the difference frequency between the pump and Stokes light matches a specific vibrational frequency, ω_osc. In addition, the resulting signal from SRS is strongly sensitive to the incident polarisations when the orientation of the probed vibrating species is ordered. This polarisation dependence can be exploited to probe the orientational order of vibrational modes in samples. However, currently developed techniques are not able to perform large-field fast time scale dynamics instantaneously due to the requirement of point-wise scanning over the sample space. Conventional polarisation-resolved techniques take minutes because each point of the scanning area must be polarisation tuned sequentially [74, 80, 253, 254].

Multi-lamellar myelin plays a crucial role for efficient transmission of nerve impulses as an electrical insulator [255]. The lipids and proteins in myelin self-assemble into a highly ordered and stable structure to form a tightly packed membrane [256]. In neurological disorders, this compact structure is highly perturbed leading to dysfunctions of the central nervous system [257, 258]. As these biological processes are highly dynamic, researchers seek to observe the dynamics of molecular order with sufficient resolution and frame rate. Hofer et al. [259] have recently demonstrated fast-polar-SRS by exploiting high-speed amplitude- and polarisation modulation with an acousto-optic modulator (AOM) and electro-optical polarisation modulation, respectively, to read out the molecular order and orientation at a fast rate. They therefore obtain both amplitude and phase information. The authors report the ability to retrieve density maps of molecular bonds with the absolute value of molecular order. The linear polarisation direction of the pump beam is rapidly rotated while the Stokes polarisation is circularly polarised to avoid polarisation dependence from the Stokes beam. The polarisation is further modified by a quarter-wave plate. The polarisation modulation leads to an α-dependant response of the signal intensity given by the following:I(α)∝a0+S2cos2(α−φ2)I(α)∝a0+S2cos⁡2(α−φ2)(14)

where α is the rotating pump polarisation direction in the sample plane, a₀ is the total measured intensity, and S₂and φ₂ are the amplitude and phase of the second-order induced modulation [259].

Figure 6a.i shows a comparison of conventional polarisation SRS with that from Hofer’s fast-polarisation SRS on a multi-lamellar lipid vesicle (MLV). The fast-polarisation SRS image in the bottom of Fig. 6a i was obtained in 1 s which is two orders of magnitude faster than the conventional-SRS image (top) using the same incident powers, number of pixels and dwell time per pixel. Figure 6a ii shows sub-second frame-rate imaging of a MLV using double EOM-AOM modulation SRS at two instances in time. The measurement technique was remarked to have little effect on the lipid order properties during the measurement. Hofer et al.[259] were able to observe second-timescale dynamics in thin lipid membranes down to the cell plasma membrane using fast-polarisation-resolved SRS as shown in Fig. 6a iii.

Flow cytometry (FC) is one of the most important technologies for high-throughput single-cell analysis. FC is a technique used to measure physical/chemical characteristics of a population of cells or particles suspended in a fluid [59, 261]. The fluid suspension flows through the instrument detectors for fluorescent labelling which is the primary approach for cellular analysis in FC. Figure 6b i shows an optical FC setup [260]. However, for small molecules, the fluorescent tags can perturb the biological function of the species. In addition, non-specific binding of fluorescent labels as well as cellular autofluorescence can also reduce the clarity of the result. SRS flow cytometry (SRS-FC) non-invasively detects chemical cell content but conventional techniques suffer slow acquisition rates.

Zhang et al. [260] have recently demonstrated label-free high-throughput single-particle SRS-FC with a 32-channel multiplexing technique. Their technique measured single-particle chemistry at a rate of 5 μs per SRS spectrum, approaching that of standard fluorescence-based FC. The SRS-FC technique was based on broadband laser excitation and a multiplex spectral detection system. The systems allowed the acquisition of 200,000 spectra per second, more than 11,000 particles per second. The subpopulations of species, such as mixed polymer beads and 3T3-L1 cells, could be separated and distinguished through compositional principle component analysis (CPCA) of the SRS signals. The principle components were designated according to their Raman spectra. An agglomerative clustering procedure was performed on the resulting CPCA spectral matrix. This procedure assumed the number of cluster groups (κ) was known to separate the clusters of principle components in the CPCA analysis. Figure 6b ii shows the CPCA of the SRS spectra for a mixture of three types of beads: poly-methyl-methacrylate (PMMA), polystyrene (PS) and polycaprolactone (PCL), all with a 10-μm mean diameter, mixed at a 2:1:1 ratio of PMMA:PS:PCL and a final concentration of 2% solids in the fluid. The flow speed was ≈ 0.16 ms⁻¹, the SRS-FC data was acquired in 6 s. The CPCA plot (Fig. 6b ii) shows three distinct clusters of principle components. The agglomerative clustering procedure (κ = 3) allowed the quantification of ~ 7100 PMMA bead (red), ~ 3400 PS beads (blue) and ~ 3600 PCL beads (green) as shown in Fig. 6b ii. Their measurement demonstrated the ratio of ≈ 2:1:1 (PMMA:PS:PCL) at a throughput rate of ~ 2350 particles per second and that their multiplex SRS-FC system, paired with the CPCA analysis, could distinguish different chemical components with small spectral differences. Zhang et al. [260] were able to detect beads as small as 1 μm and were even able to detect single Staphylococcus aureus bacteria flowing through the laser focus highlighting the potential to characterise subcellular organelles with SRS-FC.

Zhang et al. [260] also demonstrated the discrimination of 3T3-L1 cells at different stages of cell differentiation according to their difference in lipid amount using SRS-FC. After insulin-induced differentiation, 3T3-L1 cells acquire an adipocyte-like phenotype with a significantly increased amount of triglycerides which aggregate to form large lipid droplets. This aggregation of triglycerides causes the intensity of the methylene symmetric vibration at Δν∼Δν∼= 2850 cm⁻¹ from fatty-acid acyl chains to become stronger compared to that of non-differentiated cells which provides the means for CPCA analysis. Figure 6b iii shows the CPCA scatter plot of the cell mixture measured by Zhang et al. [260] which were separated using the agglomerative clustering approach. The insert SRS images (Fig. 6b iii, right) show a non-differentiated 3T3-L1 cell and a differentiated cell with the formation of large lipid droplets.

Twisted Laguerre-Gaussian lasers, with orbital angular momentum (OAM) and characterised by doughnut-shaped intensity profiles, are of great interest to a number of growing research fields such as ultra-cold atoms [262,263,264], microscopy and imaging [265, 266], atomic and nanoparticle manipulation [267, 268], ultra-fast optical communication [269, 270], quantum computing [271], astrophysics [272] and plasma accelerators [47]. Spiral phase plates or computer-generated holograms are usually used to generate visible light with OAM [273,274,275,276]. Spiral phase plates can produce light with predefined OAM modes. By using plasma as an optical medium to generate and amplify laser pulses with OAM and relativistic intensities, well above the damage threshold of optical devices, could provide for high-energy-density science and applications. Plasmas also allow for greater flexibility in the level of OAM in the output laser beam than conventional optics. Vieira et al. [46] have shown that SRS in nonlinear optical media with Kerr nonlinearity (e.g. plasmas, optical fibres and nonlinear optical crystals) can be used to generate and amplify OAM light. The authors show that it is possible to generate and amplify light with OAM when no net OAM is initially present. Figure 6a i illustrates the process in which the pump EM fields can have different OAM components in both transverse directions x and y (blue and orange in Fig. 6a i). l_0x is the pump electric field component of OAM in the x direction. Likewise, l_0y is the pump electric field component of OAM in the y direction. The initial seed electric field component has an OAM component l_1x. After interacting with the plasma, the pump is depleted, and a new electric field component appears in the seed with OAM l_1y = l_1x + l_0x − l_0y.

The authors [46] use an analytical theory for arbitrary transverse laser field envelope profiles and particle-in-cell simulations for plasma. Stimulated Raman backscattering in plasma is a three-wave mode coupling process in which a pump pulse decays into an electrostatic (Langmuir) plasma wave as well as a counter-propagating seed laser. The plasma can be viewed as a high-intensity mode converter. The presence of OAM in the pump and/or seed results in additional matching conditions that ensure the conservation of angular momentum of the pump when the pump decays into a scattered electro-magnetic wave and a Langmuir wave [40].

Particular superpositions of Hermite-Gaussian modes TEM modes are mathematically equivalent to Laguerre-Gaussian modes [277]. Vieira et al. [46] therefore explore the use of Stimulated Raman backscattering to generate and amplify light with OAM using TEM laser beams with no initial net OAM. Each Hermite-Gaussian beam in the simulation is described by TEM_m,n, where m and n represent the Hermite-Gaussian mode index. Figure 6c ii and iii show the 3D simulation results from the setup shown in Fig. 6c i. The simulations show that SRS results in a new OAM mode with l₁ = 1 linearly polarised at 45°. The field topology of the seed normalised vector potential changes from plane isosurfaces in Fig. 6c ii, to helical isosurfaces in (Fig. 6c iii). Hence, light with OAM has been generated from light with no net OAM. The authors [46] note that their results could be extended to other nonlinear optical media with Kerr nonlinearity. In the case of plasma, the interaction between the seed light and the pump light occurs via an electron Langmuir wave. This interaction ensures that the frequency, wavenumber and OAM matching conditions are conserved.

Coherent Anti-Stokes Raman Scattering Microscopy

CARS results from an induced anti-Stokes scattering of radiation, ω_AS, which is enhanced when ω_p − ω_S = ω_OSC. One of the main challenges with CARS microscopy is the nonresonant background. The existence of the nonresonant background can either distort or even saturate the resonant signal of Raman peaks, which reduces the image contrast. Qin et al. [278] have recently demonstrated multi-colour background-free coherent anti-Stokes Raman scattering microscopy using an all-fibre, low-cost, multi-wavelength time lens source. A time lens, in analogy to a spatial lens, is simply a quadratic optical phase modulator in time, which can be approximated by a portion of a sinusoidal phase modulator [279,280,281]. Three different wavelength picosecond pulse trains were provided by the time lens source, at 1064.3 nm (stable), 1052–1055 nm (tuneable) and 1040–1050 nm (tuneable). The time lens was used to apply temporal quadratic phase modulation to a continuous-wave laser to broaden its spectral bandwidth [279, 282,283,284,285,286,287,288]. In this instance, the time lens was applied with fibre-integrated electro-optic radio-frequency phase modulators. The phase modulation and pulse synchronisation were derived from a mode-locked Ti:Sapphire laser that provided synchronised multi-colour picosecond pulses with dispersion compensation. Electronic tuning of the pulse delay was used to achieve temporal overlap between the pump and Stokes laser pulse trains, which is a convenient substitution for mechanical optical delay paths. Two of the three wavelengths of light from the time lens source were used for two-colour on-resonance imaging and the third wavelength for off-resonance (nonresonant background subtraction) imaging. Pixel-to-pixel wavelength switching was achieved, which provided simultaneous two-colour CARS imaging with real-time nonresonant background subtraction. Qin et al. [278] demonstrated the technique with an excised fresh tissue sample from a mouse ear and imaged molecular stretching vibrations at 2845 cm⁻¹ (CH₂) and 2940 cm⁻¹ (CH₃) and non-resonance background at Δν∼Δν∼ = 2770 cm⁻¹. Figure 7a i–iii shows the process applied to the Raman peak of CH₃ stretching vibration from the mouse ear tissue sample.

The nonresonant background signal in CARS can also be suppressed by applying an external static electric field to the sample known as electro-CARS. Capitaine et al. [120] demonstrate this electro-optical technique on n-alkanes in solution with broadband multiplex coherent anti-Stokes Raman scattering spectroscopy. The nonresonant background is suppressed due to the orientation response of the molecules to the electric field. The molecular orientation is related to the induced electric dipole moment. The enhancement of the CARS signal-to-noise ratio was achieved in the case of the CH₂ and CH₃ symmetric/asymmetric stretching vibrational modes.

Conventional CARS provides information about the chemical nature but not about the molecular organisation or symmetry in the system. The Cartesian components of the nonlinear susceptibility tensor χ⁽³⁾ represent the vibrational symmetry properties of the material [290, 291]. These tensor elements can be extracted with polarisation-resolved coherent Raman scattering schemes [72, 74, 169, 259, 292,293,294,295]. However, these schemes often involve the acquisition of multiple images from different polarisation angles requiring long acquisition times due to limits imposed by polarisation tuning [259] and time-consuming post-processing [67].

Cleff et al. [289] have recently demonstrated a label-free microscopy technique that uses circularly polarised light to probe the symmetry as well as the chemical fingerprint of the probed sample in a single acquisition. This symmetry-resolved CARS (SR-CARS) depends on both the presence of (ro-)vibrational modes as well as their local organisation. By switching between combinations of left- and right-handed circular polarisation states for the involved fields, the individual symmetry contributions of the sample can be imaged. This technique offers a straightforward means to access the local organisation of (ro-)vibrational bonds with improved image contrasts (with 1 to 2 orders of magnitude) for anisotropic samples, as well as improved chemical selectivity without post-processing and independently of sample orientation in the transverse plane. In addition, SR-CARS provides higher chemical selectivity with the contrast in symmetry characteristics, which are not accessible with conventional spontaneous Raman or SRS microscopy.

Multi-lamellar lipid vesicles (MLVs) are made of a tight packing of lipid layers forming a ring of highly ordered matter with twofold symmetry and a lipid orientation distribution close to a Gaussian angular shape [74].

Figure 7b i shows a conventional CARS image of an aqueous MLV at Δν∼Δν∼ = 1133 cm⁻¹ (C-C stretching vibration) which illustrates the expected poor contrast due to the nonresonant background [289]. Figure 7b ii and iii show the zeroth and second-order mF¯¯¯¯mF¯-value image of the same MLV as in Fig. 7b ii. The mF¯¯¯¯mF¯-value is the summation of the light circular polarisation handedness quantum numbers of the incident light beams:mF¯¯¯¯=mp−ms+mpr−masmF¯=mp−ms+mpr−mas(15)

When light with field tensor F¯¯¯¯F¯ probes matter with nonlinear susceptibility tensor χ⁽³⁾, in a CARS process, the light probes only the parts of the matter with identical rotational invariant symmetries (i.e. identical mF¯¯¯¯mF¯). Hence, by engineering the field tensor of the light, specific sample symmetries can be directly read out, creating a symmetry-based image contrast mechanism [289]. The aqueous solution surrounding the MLV is only visible in the mF¯¯¯¯=0mF¯=0image (Fig. 7b ii) due to its purely isotropic nature. Background-free imaging of the MLV with superior contrast with respect to conventional CARS is shown in Fig. 7b iii at mF¯¯¯¯=2mF¯=2, which results from the symmetric microscopic organisation of the lipids in the MLV. Imaging at mF¯¯¯¯=4mF¯=4 (not shown) lacked sufficient signal strength to provide an image of the MLV due to the lack of anti-symmetry in the lipid organisation.

As with SRS, the CARS signal is sensitive to the polarisation of the incident light when the orientation of the scattering species is ordered. Polarisation-resolved CARS (PR-CARS) requires monitoring of the CARS signal response depending on the relative rotation of the incident light polarisations (pump and Stokes) to the sample, in species with ordered orientations. Provided that the molecular bonds are oriented, the detected intensity of the anti-Stokes signal is maximised when the incident polarisations lie along the averaged direction of the bonds. The ability to monitor lipid order without the need for fluorescent labels can provide information on lipid packing properties. As mentioned, PR-CARS schemes often involve long acquisition times due to limits imposed by polarisation tuning and time-consuming post-processing.

In addition to fast-polar-SRS, Hofer et al. [259] have recently demonstrated fast-polar-CARS imaging with combined electro-optic polarisation and acousto-optic amplitude modulations. Figure 7c shows fast-polarisation CARS with similar sensitivity to that of SRS (shown in Fig. 6a). Despite the requirement of lock-in amplification for the detection of low modulation over a large nonresonant background, the fast-polarisation technique demonstrated by Hofer et al. [259] can considerably improve the signal-to-noise ratio in CARS imaging. Despite the robustness of MLVs, occasional alteration of molecular order in MLVs could be observed at the time scale accessible in Hofer’s experiment (0.25–1 s per image). MLVs could detach from the sample surface, inducing motion (Fig. 7c) or shape change. The modifications observed in Fig. 7c were attributed to a local membrane disruption, followed by its spontaneous reformation. Hofer et al. [259] demonstrated the possibility of visualising local modification during MLV displacement that was not accessible using the minute-time-scale conventional polarisation Raman experiments.

There have also been a number of developments in CARS flow cytometry (CARS-FC) [58, 296, 297]. However, these techniques were shown to be much slower than fluorescence-based FC. Out-of-focus microparticles can randomly impede CARS-FC and the fluid often generates a strong nonresonant background limiting CARS-FC from achieving high-throughput single-cell analysis. Recently, however, O’Dwyer et al. have demonstrated that it is possible to significantly enhance the fraction of unambiguously and instantly recognised in-focus microparticles, in unconstrained flows by co-monitoring CARS-FC with linear scattering of light.

CARS is invariably performed with two synchronised picosecond laser sources owing to the coherence life time of Raman resonance. Ti:Sapphire oscillators [168] or optical parametric oscillators pumped by a picosecond frequency-doubled Nd:Vanadate laser [53] are the instruments of choice, which are generally very expensive and the synchronisation mechanisms can be challenging. In addition, the spectral drift in the pump wavelength can introduce errors in the calculation of ω_osc. Langbein et al. [124] have demonstrated CARS micro-spectroscopy using a single Ti:Sapphire laser oscillator and simple passive optical elements. Vibrational excitation, tuneable over a large spectral range with adjustable spectral resolution, was achieved by spectral selection with dichroic mirrors and linear chirping by glass elements.

Tip-Enhanced Dual Wavelength Coherent Anti-Stokes Raman Scattering Microscopy

TERS offers spatial resolution far beyond the diffraction limit of the probing light. The more conventional technique is to directly illuminate the tip-sample cavity [86]. This technique achieves the desired resolution (beyond the diffraction limit) by forcing the evanescent light into the far field image formation. However, the far field light presence in the tip-sample cavity generates an unfavourable background light source. It is possible to perform TERS by coupling the far-field excitation light to the tip a few tens of micrometres from the tip apex [298]. Femtosecond laser pulses can be coupled to the tip surface by shining the light on a grating fabricated on the tip surface. The SPPs then propagate to the tip apex and generate background-free localised optical excitation [210].

Toma et al. [298] previously demonstrated selective excitation of a single Raman mode and its CARS imaging of CNT using ultra-fast SPP pulse nanofocusing using an Au tapered tip. In a more recent publication, seminal work by Tomita et al. [155] demonstrated simultaneous nanofocusing of ultra-fast SPP pulses at 440 and 800 nm, which were coupled with a common diffraction grating structure. Figure 8a i, illustrates the scheme. The Al-tapered tip had an apex radius of ≈ 35 nm. Selective CARS microscopy that combined an 800 nm (ω) SPP pump pulse and a 440-nm (2ω) SPP probe pulse was achieved. Figure 8a ii illustrates the energy level process of ω– and 2ω-CARS. The pump pulse achieves selective vibrational excitation by spectral focusing [299,300,301,302]. Raman shift intensities with this 2ω-CARS scheme were reported to increase by as much as 4 compared with that of ω-CARS for monolayer graphene. The selectivity of vibration band excitation and background noise suppression were confirmed on the CARS intensity probed by a 2ω-SPP plasmon pulse for a monolayer graphene sample. Venezuela et al. [8] reported the Raman lines in graphene associated with both phonon-defect processes (such as the D line at Δν∼Δν∼ ~ 1350 cm⁻¹) and two-photon processes (such as the 2D line). The 2D-band intensity in graphene was reduced monotonously when the defect concentration was increased, contrary to the D-band. Tomita et al. [155] applied their multi-vibrational-mode 2ω-CARS imaging method to a multi-walled CNT (MWCNT) at the D, G and 2D bands. This dual-wavelength nanofocusing technique could open new nanoscale micro-spectroscopy and optical excitation schemes in SPM, such as sum frequency mixing, two-photon excitation (ω+2ω) and pump-probe schemes.

Figure 8b i shows a topography image of a MWCNT with a diameter of ~ 175 nm measured by the Al-tapered tip. Figure 8b ii shows a composite image of three 2ω-CARS images of the MWCNT using the 2ω-CARS spectrum from D- (red), G- (blue), and 2D- (green) bands. In ref. [155], the D- and 2D-band showed a negative correlation (in agreement with ref. [8]) except for the central part of the MWCNT. The 2D- and G-bands were intense near the central part of the MWCNT. Tomita et al. [155] indirectly estimated the spatial resolution of their technique to be less than 90 nm by taking the profile of the 2D-band signal across the axis of the MWCNT.

Conclusions

This review detailed the numerous applications of Raman spectroscopy and its advanced derivatives: stimulated Raman scattering, coherent anti-Stokes Raman scattering and surface- and tip-enhanced Raman spectroscopy. A description of the fundamental physics that underpins these techniques has been provided. Experimental considerations have been discussed with examples of typical instrumentation used. Examples of the analysis techniques employed to interpret the Raman spectroscopic data were presented and discussed.

The Raman effect now underpins prominent spectroscopic techniques in biology, medicine, crystallography and flow cytometry and has gained interest in plasma physics. It is employed as a non-invasive label-free chemically selective hyperspectral imaging technique with recent advances enabling the probing of molecular orientation and chemical composition. SRS and CARS are used to enrich signal detection at specified wavelengths associated with vibrational modes that are prescribed for spectral-selective imaging. Unlike SRS, CARS carries with it a nonresonant background contribution to the spectrum. This review detailed some of the efforts to suppress this unfavourable contribution.

Surface-enhanced Raman scattering is an ultrasensitive Raman technique that has enabled the detection of trace amounts of molecular species in samples that would otherwise be undetectable in spontaneous- or coherent Raman scattering techniques. The enhancement effect is largely associated with the plasmonic activity of the sample surface, which augments the light-matter interaction. This enhancement effect is optimised by tuning the plasmons associated wavelength with plasmonically active surface nanostructures.

Tip-enhanced Raman scattering spectroscopy is a relatively new technique that can capture hyperspectral images with spatial resolution beyond the diffraction limit of light. As light is fundamental to the Raman effect, the spatial resolution offered by TERS is so far unparalleled by other Raman scattering techniques. The surface plasmon wavelength can also be tuned for TERS techniques and recent advances have exploited surface plasmon polaritons to focus evanescent light at the tip apex with light coupled remotely from the tip apex. This technique has yielded enhanced the signal-to-noise ratio by removing the far-field light from the apex region. Recent advances have demonstrated this technique with dual-wavelength CARS.

Abbreviations

AFM:

Atomic force microscopyAOM:

Acousto-optic modulatorAS:

Ammonium sulphateCARS:

Coherent anti-Stokes Raman scatteringCARS-FC:

CARS flow cytometryCNT:

Carbon nanotubeCPCA:

Compositional principle component analysisCRS:

Coherent Raman scatteringDBR:

Distributed Bragg reflectionDFB:

Distributed feedbackE-CARS:

Epi-scattered CARSEM:

Electro-magneticFC:

Flow cytometryF-CARS:

Forward scattered CARSHEMTs:

High electron mobility transistorsLSPR:

Local surface plasmon resonanceMLV:

Multi-lamellar lipid vesicleMoS₂ :

Molybdenum disulphideMWCNT:

Multi-walled carbon nanotubeNA:

Numerical apertureOAM:

Orbital angular momentumPCL:

PolycaprolactonePMMA:

Poly-methyl-methacrylatePR-CARS:

Polarisation-resolved CARSPS:

PolystyreneSERS:

Surface-enhanced Raman scatteringSFM:

Shear force microscopySLM:

Single-longitudinal modeSPM:

Scanning probe microscopySPP:

Surface plasmon polaritonSR-CARS:

Symmetry-resolved CARSSRS:

Stimulated Raman scatteringSTM:

Scanning tunneling microscopyTEM:

Transverse electro-magnetic modeTERS:

Tip-enhanced Raman scatteringVBG:

Volume Bragg-grating