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Electronics Letters

Resonantly enhanced two-wave mixing via population pulsations in semiconductor laser amplifiers

Martin W. McCall, K. Alan Shore

Published May 26, 1988• 4 citations
Publisher

Abstract

We demonstrate theoretically the existence of enhanced probe gain via population pulsations in nearly degenerate two-wave mixing in a semiconductor amplifier. The enhancement arises from the injection current modulation frequency coinciding with the pump/probe detuning. Probe saturation is shown to occur in less than 10 μm cavity length.

DOI
10.1049/el:19880441

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We demonstrate theoretically the existence of enhanced probe gain via population pulsations in nearly degenerate two-wave mixing in a semiconductor amplifier. The enhancement arises from the injection current modulation frequency coinciding with the pump/probe detuning. Probe saturation is shown to occur in less than 10 μm cavity length.
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.>
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.
Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers above threshold in investigated theoretically and experimentally. The experimental results reveal an almost symmetric amplification of probe and conjugate fields versus frequency with respect to zero pump-probe detuning, in contrast with observations in traveling wave amplifiers. The result of the theory, based on the coupled mode formalism, is a set of nonlinear differential equations which are solved in the mean field approximation. The theory is shown to match well with the experimental results when the effect of the nonlinear gain compression is taken into account.>
Nearly degenerate four wave mixing (NDFWM) in semiconductor laser amplifiers has received attention recently as a means of efficiently generating phase conjugate beams. The high efficiency is due to two factors: (i) intracavity geometry enhances pump efficiency; (ii) an amplifying nonlinear medium results in high coupling efficiency. These factors have combined to give observed conjugate reflectivities of approximately 30/40 dB. The NDFWM process in semiconductor lasers is also very fast ( tau approximately 10/sup -9/s) being limited primarily by the interband relaxation time. Recent theoretical studies, however, have suggested that temporal gratings with THz frequencies may be supportable. It should be noted that NDFWM in semiconductor lasers is quite different from four wave mixing in most other media in that to a first approximation the gratings formed are purely temporal. Spatial effects are normally neglected, both for computational convenience and because carrier diffusion tends to wash out spatial holes. Previously, the authors demonstrated how the temporal nature of the wave mixing process could be exploited to produce a resonant enhancement in a two wave mixing geometry. In this paper, they examine a novel scheme for enhancing the phase conjugate reflectivity via pumping the device resonantly at the detuning frequency. They demonstrate that on resonance, conjugate reflectivities several orders of magnitude greater than those previously reported are possible. >
Nearly degenerate four-wave mixing (NDFWM) in a traveling-wave semiconductor laser amplifier is demonstrated by simultaneously injecting two lights of slightly different frequencies in the same direction. A new frequency light at an expected frequency for NDFWM is observed with the same order of output as that of the injected light. The output power ratio of the three beams is strongly dependent on the sign of the frequency detuning. Theoretical analysis, in which the carrier rate equation is coupled with nonlinear Maxwell’s equations, explains the experimental results well. The observed behaviors are attributed to a unique third-order nonlinearity stemming from saturation-induced refractive index change in the semiconductor gain medium.
A theory for the nonlinear properties of optical-frequency conversion using nearly degenerate four-wave mixing in semiconductor lasers is presented for the first time. Because of pump depletion, the converted signal and the conversion efficiency depend on both the injected probe power and the frequency detuning. The relaxation resonance frequency and the damping rate are both related to the probe signal, especially for a high optical injection level. The theory is in good agreement with experiments.