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Optics Letters

Nondegenerate two-wave mixing in ruby

Ian C. McMichael, Pochi Yeh, Paul H. Beckwith

Published Jun 1, 1988• 60 citations
Publisher

Abstract

We demonstrate energy exchange by nondegenerate two-wave mixing in ruby. Our results are in agreement with the theory of nondegenerate two-wave mixing when the theory is generalized to take into account a complex nonlinear index. Two-wave mixing gain exceeding the absorption and reflection losses is demonstrated, and we show that these experiments provide a simple and accurate method for determining the complex nonlinear index, response time, and saturation intensity of the medium.

DOI
10.1364/ol.13.000500

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We demonstrate energy exchange by nondegenerate two-wave mixing in ruby. Our results are in agreement with the theory of nondegenerate two-wave mixing when the theory is generalized to take into account a complex nonlinear index. Two-wave mixing gain exceeding the absorption and reflection losses is demonstrated, and we show that these experiments provide a simple and accurate method for determining the complex nonlinear index, response time, and saturation intensity of the medium.
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.
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.
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
We have studied two-wave mixing in resonant media. Illumination with two beams of the same frequency leads to the formation of a spatially local volume grating with no exchange of energy between the writing beams, each beam merely reducing the absorption experienced by the other beam. Nondegenerate two-wave mixing leads to gain for one beam and additional absorption for the other beam as they propagate through the medium. Starting from first principles, the explicit forms of the two-beam coupling constants are derived using third-order perturbation theory, and their dependence on material and experimental factors is examined.