# Brillouin Scattering

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## Brillouin scattering

(solid-state physics)
Light scattering by acoustic phonons.

## Brillouin Scattering

(in Russian, Mandel’shtam-Brillouin scattering), the scattering of optical radiation by condensed media (solids and liquids) as a result of their interaction with the natural elastic oscillations of the media. It is accompanied by a change in the set of frequencies (or wavelengths) that characterize the radiation—that is, its spectral composition. For example, Brillouin scattering of monochromatic light leads to the appearance of six frequency components of the scattered light in crystals and three components in liquids (one component is of unchanged frequency).

The comparatively strong interaction between the particles of condensed media, which in crystals binds them into an ordered spatial lattice, leads to a situation in which the particles cannot move independently—any perturbation of them propagates in the medium in the form of a wave. However, at any temperature other than absolute zero the particles are in thermal motion. As a result, elastic waves of various frequencies are propagating in the medium in all possible directions. The superposition of such waves causes the appearance of density fluctuations of the medium (small local deviations of the density from its average value), which scatter light. Brillouin scattering shows that light waves interact directly with elastic waves, which usually are not observed by themselves. The physical picture of the phenomenon is especially graphic in the case of crystals, in which elastic waves of the same frequency but traveling in opposite directions (also called Debye waves, after P. Debye, who first examined them) form standing waves of the same frequency. The scattering of light by the standing waves takes place in all directions, but because of interference of light, an elastic wave of one specific frequency is responsible for the scattering in a given direction. Let the rays of incident light of frequency v and wavelength λ (λ = c*/v, where c* is the speed of light in the crystal) be reflected from a plane wave front, changing their direction by the angle θ (see Figure 1). In order for the reflected rays to produce maximum intensity in a given direction upon interference, the optical path difference CB + BD of the rays 1-1′ and 2-2′, reflected from adjacent wave fronts, must be equal to λ:

(1) 2Λ · sinθ/2 = λ

where Λ = AB is the length of the scattering elastic (hypersonic) wave. The reflection of a light wave from a sound wave is equiva-lent to modulation of the light of the incident ray at the frequency of the sound wave. Condition (1) leads to an expression for the change in frequency Δv of the scattered light:

(2) Δv/v = ±2v/c*·sinθ/2

where v is the speed of sound in the crystal.

Figure 1

The shift in the frequency of light in Brillouin scattering is relatively small, since the speed of sound in the medium is much less than the speed of light (v/c* is small). For example, for a quartz crystal v = 5 X 105 cm/sec and c* = 2 X 1010 cm/sec, and for scattering at an angle θ = 90°, Δv/v = 0.003 percent. However, these quantities can be measured reliably by interferometry.

L. I. MandePshtam, who theoretically predicted L. I. Mandel’shtam, who theoretically predicted Brillouin scattering (his article, written in 1918, was not published until 1926), proceeded from the concept of standing waves, or compressions and rarefactions of density that modulate a light wave. In 1922, L. Brillouin obtained the same results independently while examining the scattering of light by elastic waves traveling in opposite directions in a medium. In his approach to the phenomenon, the Doppler effect appeared as the physical cause of the “splitting” of monochromatic lines.

Brillouin scattering was first observed experimentally by L. I. Mandel’shtam and G. S. Landsberg in 1930. It was investigated in detail by E. F. Gross. In particular, he observed in 1938 that Brillouin scattering in crystals splits a monochromatic line into six components (this is because the speed of sound v in a crystal is different for different directions, as a result of which in the general case there are three sound waves—one longitudinal and two transverse—of the same frequency, each of which propagates with its own v). He also studied Brillouin scattering in liquids and amorphous solids (1930-32), in which an “unshifted” component of the initial frequency v is observed in addition to the two “shifted” components. A theoretical explanation of the phenomenon was given by L. D. Landau and G. Placzek (1934), who showed that temperature fluctuations of the medium must be taken into account in addition to density fluctuations.

The development of lasers not only improved the possibilities for observing Brillouin scattering but also led to the discovery of stimulated Brillouin scattering, which is distinguished by its greater intensity and many qualitative peculiarities. Studies of Brillouin scattering in conjunction with other methods make it possible to obtain valuable information on the properties of the scattering media. Stimulated Brillouin scattering is used to generate powerful hypersonic waves in crystals in a number of technical applications.

### REFERENCES

Vol’kenshtein, M. V. Molekuliarnaia optika. Moscow-Leningrad, 1951.
Fabelinskii, I. L. Molekuliarnoe rasseianie sveta. Moscow, 1965.

IA. S. BOBOVICH

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