Complex conjugation of fields in stimulated Brillouin scattering

Bel'dyugin, Igor' M; Galushkin, M. G.; Zemskov, E M; Mandrosov, Valery I.

doi:10.1070/qe1976v006n11abeh012060

Cited by 52 publications

(3 citation statements)

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“…(2), ignoring the small d z 2 R and d z 2 R r terms (where the differential operators d z n ==d n /dZ n ), and assuming paraxial ray conditions k \z -k lZ -k lf one obtains d z R-aR = j>, d z R'-(a + iy)R' = j>aR 9 (5) where y = {k 2 -k 1 ,2 )/2k 1 =Ksin{9 l -6) ~K 2 /2k l (Fig. 1) is a dephasing factor, which can, in general, be nonzero because of Eq.…”

Section: Theory Of Optical Ray Retracing In Laser-plasma Backscattermentioning

confidence: 98%

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Theory of Optical Ray Retracing in Laser-Plasma Backscatter

Lehmberg

1978

Phys. Rev. Lett.

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It is suggested that the optical ray-retracing effects observed in laser-produced plasmas originate from the same mechanism believed to cause phase conjugation from backward stimulated processes in liquids. .This mechanism is elucidated with the aid of a simple model, and generalized to include plasma inhomogeneity. A comparison is made with a recent experiment.Optical ray retracing, in which the transverse spatial structure of an incident beam is reproduced by its backscatter, is a well-known property of the Brillouin instability in high-power laser-plasma interaction, 1 ' 2 Attempts have been made to relate this phenomenon to the curvature of the critical surface, to channeling effects in the long focal region, or simply to the inherent preference of stimulated Brillouin scattering, (SBS) to radiate in the local backward direction, 1 Such explanations, however, fail to account for the reproduction of detailed spatial structure 1 (including even hot spots) in the beam 0 Consider the local-backscatter argument, for example, One can apply the usual dispersion relations and frequency-and phase-matching conditions to obtain the Brillouin gain coefficient aeos(A0/2), where A6 is the angle between the (locally) incident and backscattered rays 0 3 The resulting gain has an angular distribution exp[2aZcos(A#/2)] -exp(2aZ-4A0 2 /6# LB 2 ) that does indeed favor the exact backward direction A# = 0, but its angular divergence 66 LB = (l §/aZ)^2 is far too large to account for the observed phenomena.In this Letter, it is suggested that the ray-retracing effects arise from Bragg diffraction. For simplicity, consider the incident pump radiation at the focusing lens to consist to two or more isolated beams, which may be created by an apertured mask in front of the lens, When these beams are focused into a Brillouin-active medium, such as a plasma, their interference pattern produces an identical pattern in the gain coefficient. (The medium is assumed to operate in the strongly damped steady-state limit. 4 ) If this focal region is many wavelengths long, then it behaves essentially as an active volume hologram; i,e,, a small plane-wave noise field propagating through the region oppositely to any one of the pump beams will grow rapidly while Bragg diffracting into those directions opposite the other pump beams. Waves that do not propagate initially along any of these favored directions will simply not grow as rapidly. This effect has not been found in the standard treatments of SBS in plasmas 3 because these theories have not pursued the case where the pump consists of two or more nonparall el plane -wave components that can interfere,The Bragg-diffraction mechanism has also been suggested 5 to account for similar ray-tracing behavior (the so-called phase conjugation) of backward SBS 6 and stimulated Raman scattering 7 (SRS) from liquids, in which the Stokes amplitude S X (R) is approximately proportional to the pumpwave conjugate amplitude < § 0 *(R), The present analysis differs from the theoretical treatments of phase conjuga...

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Section: Theory Of Optical Ray Retracing In Laser-plasma Backscattermentioning

confidence: 98%

“…(5) to obtain a new pair of coupled equations d z P ± + ±((3±iy)p ± = ^aP?, where /3(Z) = a~1d 2 a. These can then be combined to give d z 2 P, -\{a 2 -y 2 + P 2 -2d z p±2iy0)P ± =O.…”

Section: Duces Tomentioning

confidence: 99%