Brillouin frequency shift

Brillouin scattering occurs as a result of an interaction between the propagating optical signal and thermally acoustic waves present in the silica fibre giving rise to frequency-shifted components, similar to a Doppler effect. The acoustic velocity is directly related to the medium density and depends on both temperature and strain. As a result, the so-called Brillouin frequency shift carries information about the local temperature and strain of the fibre. Furthermore, Briflouin-based sensing techniques rely on the measurement of a frequency as opposed to Raman-based techniques that are intensity based. 

The working principle of BOTDA is based on the Stimulated Brillouin Scattering (SBS) elFect, which is depicted in Figure 1. The Brillouin frequency shift has a linear relationship with strain and temperature applied on a single-mode optical liber, which can be expressed by (Bernini et al. 2002)... 

Figure 1. A schematic diagram showing the relative positions of Rayleigh and Brillouin scattering peaks. The incident light has frequency cOq the Brillouin frequency shift is cOg. The widths of the Brillouin and Rayleigh peaks (Tg and Tp.) are also shown.

Figure 5. Hypersound velocities (a) and Brillouin frequency shifts (b) as a function of temperature for 8CB, redrawn from [16]. The notation of [16] is also used L refers to the director perpendicular to and k, ...

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

Brillouin scattering provides information about the acoustic branches of the dispersion curves of the material under study. The measured frequency shift of the radiation is equal to that of the phonon under consideration (EQN (1)), and its wave vector is deduced from EQN (2), so the sound velocity may be calculated by ... 

If Ar,r( >) and Tr r(w) do not vary much with a>, they may be interpreted as the frequency shift, i.e., the resonance shifts from cor(q) to Brillouin zone [see Eq. (71), for instance]. Some simplification may arise from the lattice... 

T ight scattering in dense media is caused by fluctuations in the local " dielectric tensor c (i). In 1922 Brillouin (2) predicted that thermal acoustic phonons would lead to such fluctuations and hence to light scattering. In addition, the scattered light should be shifted in frequency because the phonons are moving. The frequency shift is given by ... 

The next two terms define Mandelshtam-Brillouin s doublet with the frequency shift rktjj(q) = Vq and the halfwidth... 

Near the critical point, an increase in the scattered light intensity (critical opalescence) is observed. The Rayleigh (non-frequency-shifted) line chiefly contributes to this increase, its intensity being proportional to c/> — cy (see Equation 53) and exceeding that of Mandelshtam-Brillouin s (MB) components (proportional to cylcy, see Equation 53) by several orders of magnitude (Swinney, 1978). 

Brillouin scattering in essence a Doppler effect, which yields small frequency shifts. 

The phonon dispersion relation (kph) of the bulk modes is usually taken. For most crystalline solids, the phonon dispersion relation has a maximum at the center of the Brillouin zone, and one observes a low-frequency shift of the Raman line with decreasing crystalline size, but the opposite behavior can also occiu (Nemanich, 1981). 

Fig. 7. Typical diagram of the spectrum of scattered light as measured by a Fabry Perot interferometer showing the Rayleigh line (center) and the Brillouin doublet. From the frequency shift and the width of the Brillouin bands one can obtain the storage and loss moduli fin- compresacHKil waves exxuring at hypersonic frequencies...

Brillouin scattering is the inelastic scattering of light on propagating elementary excitations. For acoustic phonons considered here, the relation between the measured frequency shift of the scattered light Av, the sound velocity Y, (he sound frequency/, and the sound wave length A is... 

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