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Physical Review A

Transient behavior of the amplification of the Stokes field by thermal Rayleigh and Brillouin effects

Arturo Bambini, R. Vallauri, M. Zoppi

Published Oct 1, 1975• 6 citations
Publisher

Abstract

We derive analytical solution for a signal field amplified by stimulated Rayleigh and Brillouin effects. The presence of light absorption is taken into account. The solution describes the transient behavior at all frequency differences between the pump and the signal waves. The validity is demonstrated for the simple case of no absorption, and the particular time behavior at $\ensuremath{\omega}=0$ is stressed.

DOI
10.1103/physreva.12.1713

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Journal of the Optical Society of America B•Jan 1, 2001•13 citations
We derive analytical solution for a signal field amplified by stimulated Rayleigh and Brillouin effects. The presence of light absorption is taken into account. The solution describes the transient behavior at all frequency differences between the pump and the signal waves. The validity is demonstrated for the simple case of no absorption, and the particular time behavior at \ensuremathω=0\ensuremath{\omega}=0\ensuremathω=0 is stressed.
A general transient theory of light amplification in absorbing media is developed for small amplification and for small signal. The amplification by stimulated thermal Rayleigh scattering has been studied in detail for various shapes of the laser pulse. A transient gain is predicted when the frequencies of the pump and signal pulse are the same. The dependence of the amplification from the scattering angle was investigated. For narrow angles (Θ < 2 x 10-2 rad) scattering of higher order in angle was calculated. A method of measuring the Rayleigh linewidth with one laser pulse is proposed
Using well defined input pulses the amplification by stimulated thermal Rayleigh scattering was investigated experimentally as a function of time (within the pulse), of absorption coefficient, and of interaction length. The frequency difference between the two interacting light pulses was varied with an accuracy better than Δν/ν = 10-8. Amplification was measured in the backward direction and at several degrees from the forward direction. The various experimental observations are in good agreement with theory. The possibility of determining material parameters in this amplifier system is discussed
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.
The stochastic nature of initial stimulated Brillouin scattering (SBS) can lead to a deep modulation of Stokes intensity in fibers, even under conditions of strong pump depletion. It is known that at a moderate pump depletion, when parameter T1/T2 ≫ 1 (T1 is the light propagation time through the effective amplification length and T2 is the hypersound relaxation time), fluctuations correspond to the Gaussian statistics of temporal field distribution. As T1/T2 → 1 the statistics of fluctuations can change. Gaeta and Boyd1 were the first to show that at a sufficient pump depletion (by our estimate, parameter T1/T2 in Ref. 1 was ~4) the correlation function of the Stokes intensity c(τ) = (〈I(t)I(t + τ)〉 - 〈I(t))2)/(/(t)〉2 differs from the Gaussian by a more rapid initial fall and the presence of the region in which it is negative.
We numerically investigate the transient interaction between optical Kerr bistability and stimulated Brillouin scattering (SBS) when an intense optical pulse is incident in a short fiber ring resonator. An initial phase detuning of the ring resonator and the difference in the phase shift between the pump wave and the created Stokes wave are taken into account in the three-wave SBS model. The ratio of the Brillouin gain coefficient to the nonlinear refractive index of the fiber, which is termed the relative Brillouin gain coefficient, is used as a key parameter for examining the conditions for obtaining optical Kerr bistability in a fiber ring resonator. The numerical results show that optical Kerr bistability cannot be obtained in a ring resonator made from a conventional fused-silica fiber because of the generation of SBS. However, if other fibers with relative Brillouin gain coefficients at least 1 order smaller than that of fused-silica fibers are used, we can suppress SBS and hence obtain optical Kerr bistability. Moreover, we investigate theoretically and experimentally the dynamics of SBS in a fused-silica fiber ring resonator irradiated by a Gaussian pulse. The relaxation and pulsation in the Stokes signal depend strongly on the initial phase detuning of the ring resonator. The experimental results obtained with a single-frequency pulsed YAG laser agree qualitatively with theoretical predictions.