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IEEE Journal of Quantum Electronics

Enhanced multiwave mixing interactions in semiconductor optical amplifiers via pump modulation

Martin W. McCall

Published Jan 1, 1992• 4 citations
Publisher

Abstract

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.>

DOI
10.1109/3.119486

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

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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. >

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Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers

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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.

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A theory of four-wave mixing in semiconductor laser media is developed by considering the contributions of both the gain and index gratings created by the carrier-density modulation occurring at the beat frequency of the pump and the probe waves. The general formalism can be applied to semiconductor lasers operating below or above threshold. As an illustration, we consider the case in which the semiconductor laser is operated as a traveling-wave amplifier. The results show that the dominant contribution to the four-wave mixing process comes from the index grating. Further, the index grating makes the probe transmission asymmetric with respect to the pump-probe detuning.

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Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers

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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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Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

Kazuro Kikuchi, Motoki KAKUI, Chung-En Zah +1 more

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.>

IEEE Journal of Quantum Electronics•Jan 1, 1992•132 citations
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.>
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. >
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.
A theory of four-wave mixing in semiconductor laser media is developed by considering the contributions of both the gain and index gratings created by the carrier-density modulation occurring at the beat frequency of the pump and the probe waves. The general formalism can be applied to semiconductor lasers operating below or above threshold. As an illustration, we consider the case in which the semiconductor laser is operated as a traveling-wave amplifier. The results show that the dominant contribution to the four-wave mixing process comes from the index grating. Further, the index grating makes the probe transmission asymmetric with respect to the pump-probe detuning.
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.
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.>