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Applied Physics Letters

Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier

Kyo Inoue, Takaaki Mukai, Tadashi Saitoh

Published Oct 5, 1987• 94 citations
Publisher

Abstract

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.

DOI
10.1063/1.99004

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1998•0 citations
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.
The optical nonlinearity in a semiconductor laser gain medium is investigated through copropagating nearly degenerate four-wave mixing (NDFWM) in a 1.5- mu m InGaAsP traveling-wave laser amplifier (TWA). The FWM signal output powers vary symmetrically with the sign of probe detuning with respect to the pump frequency, while the pump and probe output powers vary asymmetrically. The NDFWM conversion efficiency from the probe input to the FWM signal output is a maximum of 8.3 dB around zero detuning and has positive gain in the range of +or-6 GHz. This demonstrates highly efficient nonlinear interaction due to both large optical gain and large third-order susceptibility. The NDFWM efficiency is also investigated in connection with the TWA gain saturation characteristics and is found to be a maximum for operation around the saturation intensity of the TWA.>
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 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.>
Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect.>
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.
Optical phase conjugation through nearly degenerate four-wave mixing (NDFWM) in semiconductor lasers has attracted considerable attention in recent years since being first demonstrated by Nakajima and Frey[ 1 ]. Such interest arises due to the very high conjugate reflectivity of order 30-40dB which can be achieved owing to the amplifying effect of the semiconductor gain medium and cavity enhancement of mixing process. However, most previous experimental and theoretical work has placed emphasis on the weak signal case, where the injection signal acts only as a small perturbation of free-running laser diode. It is only very recently that a theoretical analysis of NDFWM in a semiconductor laser subject to strong probe injection power has been presented[2].