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Optics Letters

Phase-modulation-induced two-wave mixing in semiconductors

Robert Frey, J. Frey, Christos Flytzanis

Published Feb 15, 1997• 1 citation
Publisher

Abstract

Two-wave mixing amplification of a weak probe beam interfering with a powerful pump beam of the same linear polarization is demonstrated when the probe beam enters the semiconductor sample before the pump pulse. This mixing of two beams of the same frequency is made possible by the difference between self-phase modulation and cross-phase modulation, which modify differently the instantaneous frequencies of both beams. Net gain coefficients up to 5.5 cm (-1) are obtained for experiments performed in CdTe. Theoretical calculations quantitatively confirm this interpretation and predict much higher gain for more resonant configurations or higher pump energies, making this process of potential interest for optical processing.

DOI
10.1364/ol.22.000218

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It is demonstrated that, by modulating a semiconductor optical amplifier at a frequency determined by the detuning between the pump and probe in a collinear four wave mixing geometry, the enhancements in gain and reflectivity of two to three orders of magnitude are possible for remarkably small modulation depths (m=10/sup -2/). The mechanism of frequency mixing using population pulsations in semiconductor laser amplifiers is summarized. In particular, the modification to the standard geometry to achieve enhancements is discussed. The appropriate four wave mixing equations including current modulation terms are solved analytically in the undepleted pump approximation. The analytic forms for transmission gain and phase conjugate reflectivity in several cases of interest are computed. In particular, the case in which four wave mixing is absent and energy transfer occurs solely as a result of the current modulation is examined.>
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Nondegenerate four-wave mixing (FWM) of picosecond optical pulses in semiconductor optical amplifiers is investigated theoretically, taking into account various carrier processes, probe depletion, and cross-gain modulation effects. Analytical solutions for greatly simplified coupled-wave mixing equations are obtained from which conditions where probe depletion and cross-gain modulation effects cannot be neglected are found. On the other hand, the frequency detuning dependence of optimum input pump pulse energy and shaping of output conjugate pulses are observed from numerical simulations. In particular, calculations show that the frequency symmetry of conjugate and probe pulses with respect to the pump pulse does not hold for optical pulse FWM. Two-photon absorption and ultrafast nonlinear refraction effects are shown to decrease the FWM conversion efficiency.
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The theory of probe beam amplification via degenerate optical wave mixing in a Kerr medium is presented. This theory includes consideration of the self-phase modulation, two-wave mixing, and multiwave mixing terms in the coupled-wave equations. Both analytical solutions, under the assumptions of a nondepleted pump beam and a transparent Kerr medium, and numerical solutions with these assumptions removed are presented. Our solutions show that under certain conditions, phase matching can be satisfied and a high probe beam gain is possible, even for a zero phase shift between the refractive index and the intensity gratings.