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Nondegenerate two-wave mixing in ruby

Ian C. McMichael, Pochi Yeh

Published Apr 26, 1987• 0 citations
OpenAlex

Abstract

We demonstrate energy exchange by nondegenerate two-wave mixing (NDTWM) in ruby. Our results are in agreement with the theory ot NDTWM in Kerr media,1 when the theory is generalized to take into account a complex nonlinear index. NDTWM provides a method for determining the complex nonlinear index and the response time of the medium. NDTWM gain exceeding the absorption and reflection losses is demonstrated.

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Annual Meeting Optical Society of America•Jan 1, 1987•1 citation
We demonstrate energy exchange by nondegenerate two-wave mixing (NDTWM) in ruby. Our results are in agreement with the theory ot NDTWM in Kerr media,1 when the theory is generalized to take into account a complex nonlinear index. NDTWM provides a method for determining the complex nonlinear index and the response time of the medium. NDTWM gain exceeding the absorption and reflection losses is demonstrated.
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.
Two-waving mixing is a process in which the interference of two waves in a medium with a third-order susceptibility modulates the index of refraction of the medium, causing energy exchange between the two beams. The effect has been used to study the resonance enhanced nonlinear index of refraction in pink ruby.1,2 In Ref. 1, the sign of the real part of the nonlinear index was shown to be the same on both sides of line center at 488 and 580 nm. This is contrary to a prediction one would make using a two-level model for the nonlinear index of refraction. We present the results from a series of experiments aimed at determining the origin of the nonlinear index of refraction in ruby.
According to the theory of two-beam coupling in a thick Kerr medium, which is based on the firstorder coupled-wave method,1 the energy exchange between the two incident beams is forbidden because the phase shift between the intensity grating and refractive-index grating is zero in the Kerr media. The energy exchange must be achieved by artificially creating a phase shift, e.g., by moving the intensity grating with respect to the medium at a speed of the order of one fringe per response time of the medium.
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.
Our semiclassical theory of two-photon multiwave mixing1 is a generalization of the degenerate four-wave mixing case2 to treat nondegenerate pump/signal/conjugate frequencies. We apply that theory to four-wave mixing in two-photon media. We present explicit formulas for the nondegenerate signal/conjugate absorption and coupling coefficients for cases for which the two-photon Stark shifts are sufficiently small compared to the homogeneous linewidths. More general cases require that the spatial hole burning averages be performed numerically. We find intricate dependencies of the transmission and reflection spectra on the pump intensity and on dynamic Stark shifts. In particular, the reflection coefficients do not necessarily bleach to zero as the pump intensity is increased indefinitely, and interferences occur between pure index and mixed absorption/index contributions