Brillouin Spectroscopy

Brillouin Scattering

Brillouin scattering (BLS) is defined as inelastic scattering of light in a physical medium by thermally excited acoustical phonons. Prediction of the BLS became possible with the development of the theory of thermal fluctuations in condensed matter at the beginning of the 20th century. Brillouin scattering belongs to statistical phenomena, when scattering of the light occurs in a physical medium due to interaction of light with medium inhomogeneities. Such inhomogeneities can be thermal fluctuations of the density in the medium.

History: With the studies conducted by Smoluchovskii, Einstein and Debye (W. Hayes, R. Loudon, Scattering of Light by Crystals, 1978), it became obvious that the thermal fluctuations of density can be considered as a superposition of the acoustic waves (thermal phonons), propagating in all directions in condensed media (L. Landau, E. Lifshits, L. Pitaevskii, Electrodynamics of Continuous Media, 1984; Einstein, Ann. Physik, 33, 1275, 1910; I. L. Fabelinskii, in Progress in Optics, XXXVII, E. Wolf, Ed. 1997, 95). The first theoretical study of the light scattering by thermal phonons was done by Mandelstam in 1918 (see Fabelinskii, 1968; Landau et al,1984), however, the correspondent paper was published only in 1926 (Mandelstam, Zh. Russ. Fiz-Khim. Ova., 58, 381, 1926). Brillouin independently predicted light scattering from thermally excited acoustic waves (Brillouin, Ann. Phys. (Paris), 17, 88, 1922). Later Gross (Gross, Nature, 126, 400, 1930) gave experimental confirmation of such a prediction in liquids and crystals.

Spectrometer: In almost all Brillouin experiments, the Fabry-Perrot interferometer has been instrument of choice (Grimsditch, 2001). However, conventional Fabry Perot interferometers do not achieve the contrast needed to resolve the weak Brillouin doublets. Sandercock first showed that the contrast can be significantly improved by multipassing (Sandercock, Opt. Commun. 2 73-76 (1970). The usefulness of coupling two synchronized Fabry-Perot, thus avoiding the overlapping of different orders of interference, was also recognized .

John Sandercock and Li Chung Ming (Hawaii 2003)

Principles

Elasto-optical scattering mechanism: The scattering in this case is mediated by the elasto-optic scattering mechanism, in which dynamic fluctuations in the strain field bring about fluctuations in the dielectric constant, and these in turn translate into fluctuations in the refractive index. These fluctuating optical inhomogeneities result in inelastic scattering of the light as it passes through the solid. The phonons present inside a solid move in thermal equilibrium with very small amplitudes creating fluctuations in the dielectric constant, which is viewed as a moving diffraction grating by an incident light wave. Therefore Brillouin scattering can be explained by the two concepts of Braggs reflection and Doppler shiftIn the case of a transparent solid, most of the scattered light emanates from the refracted beam in a region well away from the surface, and the kinematic conditions relating wave vector and frequency shift of the light pertain to bulk acoustic wave scattering (Fabelinskii, Molecular Scattering of Light, 1968).

a. SLS can be viewed as a Braggs reflection of the incident wave by the diffraction grating created by thermal phonons. According to the Braggs law, the grating spacing d can be expressed in terms of Braggs angle (φ/2)and wavelength of the laser light inside solid λ = λ_o/n, λ_o where λ_o is the laser wavelength in vacuum, and n is the index of refraction in the solid.

2d sin (φ/2) = λ_o/n

b. The moving grating scatters the incident light with a Doppler effect, giving scattered photons with shifted frequencies Δƒ. Brillouin spectrum gives frequency shift (Δƒ) of the thermal phonon, and its wavelength (d space) can be determined from the experiment geometry (see expression above). Then the velocity of the phonon V_l has a form

V_l = λ_oΔƒ /(2 n sin φ/2)

For back scattering configuration, φ = π, this equation yealds: V_l = λ_oΔƒ /(2 n)

Ripple mechanism: Unlike the elasto-optic effect, this mechanism does not occur in the bulk but at the surface of the specimen (Mutti, Bottani et al., in Advances in Acoustic Microscopy. A. Briggs, ed., I, 249 1995).. The phonons present at the surface of the sample move in thermal equilibrium with very small amplitudes creating corrugation of the surface, which can diffract incident light.

Kinetics of a light scattering from a surface: The moving corrugating surface scatters the incident light with a Doppler effect, giving scattered photons with shifted frequencies. For backscattering from surface acoustic phonons, the phase velocity (V_SAW) of surface acoustic wave can be written as

V_SAW = λ_o Δƒ /(2 sin θ )

where θ is the angle between the incident laser beam and the normal to the surface.

Applications: The main application of Brillouin scattering is to measure elastic properties (acoustic velocities) of micron size samples. Materials Science: BLS is widely used in material sciences for measuring the elastic properties of submicron films and specimens (Beghi, Every, Zinin, in T. Kundu ed., Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization, chpt. 10, 581, 2003). The films and materials that have been studied to date are many and diverse, and include inorganic materials like silicon and silicides, superhard materials, C₆₀, cubic BN, cubic BC₂N, a variety of carbonaceous materials like diamond, CVD diamond and diamond-like films, various types of hard coatings like carbides and nitrides, Langmuir-Blodgett films, and various types of multilayers. SBS can probe acoustic waves of frequencies up to 100 GHz and characterize films of thickness as thin as a few tens of nanometers (Comins, Handbook of Elastic Properties of Solids, Liquids, and Gases. Vol. I. in M. Levy et al., eds. 349, 2001). Geophysics: BLS is one of the main tools in studying the elastic properties of Earth interior (Grimsditch, Handbook of Elastic Properties of Solids, Liquids, and Gases, Vol. I, in Levy, Bass, et al., eds., 331, 2001). Understanding of the elastic behavior of minerals under high pressure is a crucial factor for developing a model of the Earth's structure because most information about the Earth's interior comes mainly from seismological data. Brillouin scattering can be used for measuring elastic properties of transparent materials at pressures up to 172 GPa (Murakami, Sinogeikin, et al., Earth Planet. Sci. Lett. 259, 18, 2007).

Brillouin Scattering
Brillouin scattering (BLS) is defined as inelastic scattering of light in a physical medium by thermally excited acoustical phonons. Prediction of the BLS became possible with the development of the theory of thermal fluctuations in condensed matter at the beginning of the 20th century. Brillouin scattering belongs to statistical phenomena, when scattering of the light occurs in a physical medium due to interaction of light with medium inhomogeneities. Such inhomogeneities can be thermal fluctuations of the density in the medium.
	History: With the studies conducted by Smoluchovskii, Einstein and Debye (W. Hayes, R. Loudon, Scattering of Light by Crystals, 1978), it became obvious that the thermal fluctuations of density can be considered as a superposition of the acoustic waves (thermal phonons), propagating in all directions in condensed media (L. Landau, E. Lifshits, L. Pitaevskii, Electrodynamics of Continuous Media, 1984; Einstein, Ann. Physik, 33, 1275, 1910; I. L. Fabelinskii, in Progress in Optics, XXXVII, E. Wolf, Ed. 1997, 95). The first theoretical study of the light scattering by thermal phonons was done by Mandelstam in 1918 (see Fabelinskii, 1968; Landau et al,1984), however, the correspondent paper was published only in 1926 (Mandelstam, Zh. Russ. Fiz-Khim. Ova., 58, 381, 1926). Brillouin independently predicted light scattering from thermally excited acoustic waves (Brillouin, Ann. Phys. (Paris), 17, 88, 1922). Later Gross (Gross, Nature, 126, 400, 1930) gave experimental confirmation of such a prediction in liquids and crystals.
Spectrometer: In almost all Brillouin experiments, the Fabry-Perrot interferometer has been instrument of choice (Grimsditch, 2001). However, conventional Fabry Perot interferometers do not achieve the contrast needed to resolve the weak Brillouin doublets. Sandercock first showed that the contrast can be significantly improved by multipassing (Sandercock, Opt. Commun. 2 73-76 (1970). The usefulness of coupling two synchronized Fabry-Perot, thus avoiding the overlapping of different orders of interference, was also recognized . John Sandercock and Li Chung Ming (Hawaii 2003)
Principles
Elasto-optical scattering mechanism: The scattering in this case is mediated by the elasto-optic scattering mechanism, in which dynamic fluctuations in the strain field bring about fluctuations in the dielectric constant, and these in turn translate into fluctuations in the refractive index. These fluctuating optical inhomogeneities result in inelastic scattering of the light as it passes through the solid. The phonons present inside a solid move in thermal equilibrium with very small amplitudes creating fluctuations in the dielectric constant, which is viewed as a moving diffraction grating by an incident light wave. Therefore Brillouin scattering can be explained by the two concepts of Braggs reflection and Doppler shiftIn the case of a transparent solid, most of the scattered light emanates from the refracted beam in a region well away from the surface, and the kinematic conditions relating wave vector and frequency shift of the light pertain to bulk acoustic wave scattering (Fabelinskii, Molecular Scattering of Light, 1968).
a. SLS can be viewed as a Braggs reflection of the incident wave by the diffraction grating created by thermal phonons. According to the Braggs law, the grating spacing d can be expressed in terms of Braggs angle (φ/2)and wavelength of the laser light inside solid λ = λ_o/n, λ_o where λ_o is the laser wavelength in vacuum, and n is the index of refraction in the solid. *2d sin* (φ/2) = λ_o/n**
b. The moving grating scatters the incident light with a Doppler effect, giving scattered photons with shifted frequencies Δƒ. Brillouin spectrum gives frequency shift (Δƒ) of the thermal phonon, and its wavelength (d space) can be determined from the experiment geometry (see expression above). Then the velocity of the phonon V_l has a form V_l = λ_oΔƒ /(2 n sin φ/2) For back scattering configuration, φ = π, this equation yealds: V_l = λ_oΔƒ /(2 n)
Ripple mechanism: Unlike the elasto-optic effect, this mechanism does not occur in the bulk but at the surface of the specimen (Mutti, Bottani et al., in Advances in Acoustic Microscopy. A. Briggs, ed., I, 249 1995).. The phonons present at the surface of the sample move in thermal equilibrium with very small amplitudes creating corrugation of the surface, which can diffract incident light.
	Kinetics of a light scattering from a surface: The moving corrugating surface scatters the incident light with a Doppler effect, giving scattered photons with shifted frequencies. For backscattering from surface acoustic phonons, the phase velocity (V_SAW) of surface acoustic wave can be written as V_SAW = λ_o Δƒ /(2 sin θ ) where θ is the angle between the incident laser beam and the normal to the surface.
Applications: The main application of Brillouin scattering is to measure elastic properties (acoustic velocities) of micron size samples. Materials Science: BLS is widely used in material sciences for measuring the elastic properties of submicron films and specimens (Beghi, Every, Zinin, in T. Kundu ed., Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization, chpt. 10, 581, 2003). The films and materials that have been studied to date are many and diverse, and include inorganic materials like silicon and silicides, superhard materials, C₆₀, cubic BN, cubic BC₂N, a variety of carbonaceous materials like diamond, CVD diamond and diamond-like films, various types of hard coatings like carbides and nitrides, Langmuir-Blodgett films, and various types of multilayers. SBS can probe acoustic waves of frequencies up to 100 GHz and characterize films of thickness as thin as a few tens of nanometers (Comins, Handbook of Elastic Properties of Solids, Liquids, and Gases. Vol. I. in M. Levy et al., eds. 349, 2001). Geophysics: BLS is one of the main tools in studying the elastic properties of Earth interior (Grimsditch, Handbook of Elastic Properties of Solids, Liquids, and Gases, Vol. I, in Levy, Bass, et al., eds., 331, 2001). Understanding of the elastic behavior of minerals under high pressure is a crucial factor for developing a model of the Earth's structure because most information about the Earth's interior comes mainly from seismological data. Brillouin scattering can be used for measuring elastic properties of transparent materials at pressures up to 172 GPa (Murakami, Sinogeikin, et al., Earth Planet. Sci. Lett. 259, 18, 2007).