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Modern Physics Letters B

ENERGY TRANSFER BETWEEN LIGHT WAVES IN NONLINEAR MEDIA WITH TWO DIFFERENT RESPONSE TIMES

C. W. A. Paschoal, J.C. Penaforte, I. Guedes

Published Jul 10, 1999• 0 citations
Publisher

Abstract

In this work we extend the conventional theory of the two-wave mixing in Kerr-like media, in order to take into account two different contributions to nonlinear gain. To this end, we use a modified Debye relaxation relation to obtain the dynamical behavior of the nonlinearity and consequently, derive the expressions for pump and probe wave intensities. The two-wave mixing gain coefficient Γ1 is calculated as a function of several parameters.

DOI
10.1142/s0217984999000695

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In this work we extend the conventional theory of the two-wave mixing in Kerr-like media, in order to take into account two different contributions to nonlinear gain. To this end, we use a modified Debye relaxation relation to obtain the dynamical behavior of the nonlinearity and consequently, derive the expressions for pump and probe wave intensities. The two-wave mixing gain coefficient Γ1 is calculated as a function of several parameters.
The solution of the nondegenerate two-wave-mixing problem in an absorptive Kerr medium including the contribution from nonlinear absorption is obtained for the first time to our knowledge. This solution enables us to analyze the influence of nonlinear absorption on the two-wave-mixing gain and account for previously unexplained results reported for ruby and Cr3+:YAlO3. The effect of nonlinear absorption of a pump beam on the gain of a probe beam is shown to be minimized when incident intensities of the interacting beams are equal. The intensity dependence of the two-wave-mixing gain for dispersive (ruby and Cr3+:YAlO3) media and the gain measurements for absorptive (fluorescein-doped glass) media are also in agreement with the new theory.
A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.
We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.
This paper presents an examination of power dissipation in a nonlinear optical medium during the coherent transfer of energy from a pump to a signal beam, and quantitatively relates this dissipation (through the fluctuation-dissipation theorem) to the spectrum of thermal fluctuations that give rise to light-scattering noise. Calculations are presented for two-wave mixing in an artificial Kerr media using a powerful stochastic model for computer simulation of amplitude, phase, and intensity fluctuations due to light-scattering noise.