Brillouin doublet frequency

All these studies treated only the intensities of the scattered light. There was, however, a parallel development in light scattering which started with the work of Leon Brillouin (1914, 1922), who predicted a doublet in the frequency distribution of the scattered light due to scattering from thermal sound waves in a solid. This doublet is now known as the Brillouin doublet. 

In viscous fluids, however, a coupling occurs between internal and external modes of freedom and translational motions. This structural relaxation process, characterized by a frequency >e, influences both the central line as well as the Brillouin doublet, depending on the frequency of this relaxation relative to the frequency of the hypersonic waves. In principal three different cases must be considered ... 

The simple theory given above shows the origin of the Brillouin doublet which is the Stokes and anti-Stokes components of the scattered light each shifted from the frequency of the incident light by an amount given by Eq. (81). However what is observed experimentally is a triplet -three distinct bands. One of these is centered about the laser line itself and is called the Rayliegh line while the others constitute the Brillouin doublet. A schematic spectrum of the Rayliegh line and the Brillouin doublet is shown in Fig. 7. 

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...

The next two temis (Lorentzians) arise from the mechanical part of the density fluctuations, the pressure fluctuations at constant entropy. These are the adiabatic sound modes (l/y)exp[-FA t ]cos[co(A) t ] with (D(k) = ck, and lead to the two spectral lines (Lorentzians) which are shifted in frequency by -ck (Stokes line) and +ck (anti-Stokes line). These are known as the Brillouin-Mandehtarn, doublet. The half-width at... 

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... 

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

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