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Physical Review A

Time-resolved nondegenerate four-wave mixing in a semiconductor amplifier

Chi‐Wai Chow, Robert A. Indik, A. Knorr, S. W. Koch, Jerome V. Moloney

Published Sep 1, 1995• 7 citations
Publisher

Abstract

The dynamics of copropagating femtosecond pulses with different carrier frequencies is modeled for a semiconductor amplifier. The propagation induced four-wave mixing signal is studied as a function of the pulse intensity and the spectral detuning between the pulses.
DOI
10.1103/physreva.52.2479

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The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.
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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