228 |
4.3.3 Individual scattering processes |
[Ref. p. 232 |
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frequency ωo = ωL − ωS (see (4.3.4) for backward scattering, θ = 180◦ ). The parameters in (4.3.15) are the absorption coe cient of the laser intensity α and the relative volume expansion coe cient βT . The half-width ΓB = π δν of the corresponding spontaneous Brillouin line that displays an approximately quadratic frequency dependence also enters the expressions above. For liquids one can write:
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4 |
η S + Λ |
1 |
1 |
+ η V |
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= |
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− |
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, |
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ΓB |
3 |
CV |
Cp |
(4.3.16) |
ωo2 |
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2 ρo v2 |
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where η S and η V, respectively, denote the shear and volume viscosity; the latter is to some extent frequency-dependent via relaxation phenomena. Λ is the thermal conductivity. CV and Cp are
the specific heat per unit mass at constant volume and pressure, respectively. The phonon lifetime τ of the involved acoustic phonons with circular frequency ωo is related to the linewidth by τ = T2/2 = 1/(2 ΓB) . The peak gain value gBa increases proportional to α and is of same order of magnitude as gBe for α ≈ 1 cm−1 .
The total frequency-dependent gain factor for the (first-order) Stokes component of SBS in-
cluding STBS is given by |
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g(ω |
) = |
gBe ΓB2 |
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gBa 2 ΓB (ωS − ωL + ωo) |
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(4.3.17) |
(ωS − ωL + ωo)2 + ΓB2 − |
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S |
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(ωS − ωL + ωo)2 + ΓB2 |
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The maximum contribution of STBS is red-shifted relative to the Brillouin line and occurs at ωS = ωL −ωo −ΓB . In the blue wing of the Brillouin Stokes line the mechanism produces stimulated loss. Equation (4.3.17) states that the Stokes shift observed in the stimulated Brillouin scattering of absorbing media in the generator or oscillator setup – occurring at the peak value of g(ωS) – is modified compared to the spontaneous Brillouin line.
A list of frequency shifts observed in SBS of transparent media is presented in Table 4.3.3 where values for the Brillouin linewidth δν and the gain parameters gBa /α and gBe are also compiled. The relaxation time T2 (= 1/π δν) in condensed matter is in the order of 10−9 s so that SBS is close to steady state for giant laser pulses with tp ≈ 10−8 s (if self-focusing is avoided), but is of transient character in the subnanosecond time domain.
4.3.3.3Stimulated Rayleigh scattering processes, SRLS, STRS, and SRWS
Three mechanisms can be distinguished:
1.Stimulated Rayleigh Line Scattering in transparent substances, SRLS, by electrostrictive coupling to non-propagating density changes,
2.Stimulated Thermal Rayleigh Scattering, STRS, by absorptive coupling similar to the STBS case, and
3.Stimulated Rayleigh Wing Scattering, SRWS, in liquids by orientational changes of anisotropic molecules.
The frequency shifts of the Stokes component of the first two cases are considerably smaller than for SBS. SRLS is di cult to observe because of the small gain factor and the relatively long relaxation time T2 ≈ 10−8 s for backward scattering leading to transient scattering for nanosecond pulses.