Brillouin Spectroscopy

Magdalena Fuchs, winter semester 2021/22

Brillouin spectroscopy is a spectroscopy technology that uses the inelastic scattering of light by thermally generated or coherently excited elementary excitations such as phonons ^[1]. It was named after the French scientist Léon Brillouin, who predicted the interactions between light and thermally excited phonons in solids at the beginning of the 20th century ^[1].

Fundamentals of Brillouin Spectroscopy

The Brillouin scattering process involves scattering light, e.g. into an optical fibre ^[2]. In contrast to Raman scattering, Brillouin scattering does not involve the excitation of optical phonons, but of acoustic phonons ^[1]. The interaction between the light and sound waves leads to Brillouin scattering ^[2], which consists of forward-propagating and backward-propagating phonons ^[3]. The former produce a positive frequency shift (anti-Stokes peak) and the latter a negative frequency shift of the original light (Stokes peak) ^[3]. Brillouin spectroscopy uses two different mechanisms to scatter this light ^[1]. One is the scattering of light by bulk phonons and the other is the scattering of light by surface phonons ^[1]. In each case, the extent to which the two mechanisms occur depends on the size, thickness, optical properties, transparency and opacity of the material ^[1].

Scattering by bulk phonons occurs preferentially in transparent or semi-transparent materials, since the wavelength of the incident laser light is sufficiently large there ^[1]. Figure 1 shows the light scattering process by bulk phonons. In the scattering process, a photon with wavevector k_i and frequency ω_i is scattered into the state k_s, ω_s ^[1]. This is done by either creating (Stokes process) or annihilating (anti-Stokes process) a phonon with wavevector q and frequency ω_q ^[1]. Since both the law of conservation of momentum and the law of conservation of energy apply, the following two equations must be observed ^[1]:

conservation of momentum: $//<![CDATA[ \begin{array}{l}k_{s}-k_{i}=\pm q\end{array} //]]>$

conservation of energy:        $//<![CDATA[ \begin{array}{l}\omega_{ s }-\omega_{ i }=\pm \omega_{ q }\end{array} //]]>$

The angle Φ is called scattering angle and is defined as the angle between k_i and k_s ^[1]. In light scattering processes by acoustic phonons, the energy change is negligible compared to the energy of the incident light, which means that k_i ≈ k_s can be assumed ^[1]. By adding the variables n as the refractive index of the material and λ as the wavelength of the exciting laser light, the phonon wave vector q can be defined as followed ^[1]:

The scattering of light by surface phonons, shown in Figure 2, occurs predominantly in opaque and semi-transparent materials via the ripple mechanism ^[1]. In (mostly) opaque materials, the penetration depth of light into the surface is limited, which means that only the component of the phonon momentum conservation law that lies parallel to the surface in the scattering plane is fulfilled ^[1]. As a result, only phonons with the wavevector component lying in the plane can contribute to light scattering ^[1]. This is defined as followed ^[1]:

θ_i and θ_s are the angles between incident or scattered light and the normal to the surface ^[1]. For a complete backscattering geometry θ_i = θ_s = θ and $//<![CDATA[ \begin{array}{l}q_{\parallel}=\left( \frac{4\pi}{\lambda} \right)sin\left( \theta \right)\end{array} //]]>$ results, so that the phonon wave vector depends exclusively on the angle of incidence and the wavelength of the excitation laser ^[1]. If this is the case, phonons with different wavevectors can be investigated by changing the angle of incidence of the laser light and the energy (frequency) of the phonons is obtained as a function of the wavevector ^[1].

Brillouin vs. Raman spectroscopy

Brillouin spectroscopy has many similarities with Raman spectroscopy, such as the above-mentioned momentum and energy conservation laws that apply to both spectroscopies ^[4]. The major difference is the excitation of the phonons. While the Brillouin spectrometer measures the effect of acoustic phonons, Raman spectroscopy measures the effect of optical phonons ^[1]. By comparing the two spectra, it becomes clear that the Brillouin shift is much smaller than the Raman shift because the speed of sound waves is lower than the speed of light ^[5]. The underlying wavenumbers used in Brillouin spectroscopy are of the order of 0.1-6cm^-1, while those used by Raman spectroscopy are usually between 10-1000cm^{-1 [4]}. Due to the lower order of the wavenumber and the vicinity to the elastically scattered Rayleigh line, Brillouin scattering requires the use of instruments with higher resolution than Raman scattering, such as the Fabry-Pérot interferometer ^[4]. Brillouin spectroscopy can often be more informative than Raman spectroscopy because it not only measures the energy of the phonons near the Γ-point (Brillouin zone centre), but also provides data to determine phonon dispersion ^[1].

Application

Brillouin spectroscopy is a versatile non-destructive technology used in many optical systems, such as advanced high-power lasers, sensors, microwave signal processors, scientific instrumentation and optomechanical systems ^[5]. Since there are countless research papers on this subject, Garmire has divided the applications in [5] with regards to the following optical parameters through which the Brillouin spectroscopy process interacts with the medium:

1. Spatial dependence
2. Time dependence
3. Frequency dependence
4. Linewidth dependence
5. Background noise
6. The physical hypersonic waves
7. Amplitude of stimulated Brillouin scattering signal
8. Micro-devices
9. Nanostructures

The subdivision illustrates on the one hand that there are numerous fields of application and approaches in which Brillouin spectroscopy is used and on the other hand that many additional fields of application can be expected due to modern research. For example, Kargar and Balandin write in [1] that Brillouin spectroscopy is becoming increasingly important with further research in investigations with small samples and the detection of elementary excitations with small energies, as other non-optical methods may fail either due to the limited sample size or the complicated nanofabrication required to implement other measurement methods.

Brillouin microscopy

One application of Brillouin spectroscopy is Brillouin microscopy, which is used to determine viscoelastic properties of materials on a microscopic level ^[5]. It is used in many areas, such as the investigation of intracellular biomechanics in whole living cells, the analysis of liquid-to-solid phase transitions in individual subcellular structures, or the biomechanical assessment of regenerating tissues in living zebrafish, to name a few ^[6]. Brillouin microscopy could also be used in medicine in the future, as it would enable the early detection of various diseases such as atherosclerosis, cancer, keratoconus, meningitis, Alzheimer's and amyotrophic lateral sclerosis ^[6].

Literature

1. Kargar, F. and Balandin, A., 2021. Advances in Brillouin–Mandelstam light-scattering spectroscopy. Nature Photonics, 15(10), pp.720-731.

2. Kluth, R.J., Watley, D., Farhadiroushan, M., Park, D., Lee, S.U., Kim, J.Y., & Kim, Y.S., 2006. Case Studies on Distributed Temperature and Strain Sensing (DTSS) by using optic fibre.

3. Lainović, T., Margueritat, J., Martinet, Q., Dagany, X., Blažić, L., Pantelić, D., Rabasović, M., Krmpot, A. and Dehoux, T., 2020. Micromechanical imaging of dentin with Brillouin microscopy. Acta Biomaterialia, 105, pp.214-222.
4. Polian, A., 2003. Brillouin scattering at high pressure: an overview. Journal of Raman Spectroscopy, 34(7-8), pp.633-637.
5. Garmire, E., 2018. Stimulated Brillouin Review: Invented 50 Years Ago and Applied Today. International Journal of Optics, 2018, pp.1-17.

6. Prevedel, R., Diz-Muñoz, A., Ruocco, G. and Antonacci, G., 2019. Brillouin microscopy: an emerging tool for mechanobiology. Nature Methods, 16(10), pp.969-977.