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InTech eBooks

Two-Wave Mixing in Broad-Area Semiconductor Amplifier

Mingjun Chi, Jean‐Pierre Huignard, Paul Michael

Published Apr 1, 2010• 1 citation
Publisher

Abstract

In conclusion, the TWM in broad-area semiconductor amplifier in nondegenerate condition is investigated theoretically. The coupled-wave equations are derived and analytical solutions are obtained when the intensity of the pump is much larger than that of the signal, but much less than the saturation intensity of the amplifier. A special case of TWM, degenerate TWM, is investigated experimentally in a GaAlAs broad-area semiconductor amplifier. The experimental results show good agreement with the theory, and the validity of the theory for this experiment is discussed. A diffusion length of 2.0 m is determined from the experiment. The TWM gain in broad-area semiconductor amplifier is calculated as a function of the frequency difference between the pump and the signal based on the data obtained from the degenerate TWM experiment; and the calculated results are discussed based on the different contributions from the refractive index grating and the gain grating to the TWM gain. Depending on and , the TWM gain in semiconductor broad-area amplifier can be positive or negative. The energy exchange between the pump and signal beams occurs when 0.

DOI
10.5772/8665

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In conclusion, the TWM in broad-area semiconductor amplifier in nondegenerate condition is investigated theoretically. The coupled-wave equations are derived and analytical solutions are obtained when the intensity of the pump is much larger than that of the signal, but much less than the saturation intensity of the amplifier. A special case of TWM, degenerate TWM, is investigated experimentally in a GaAlAs broad-area semiconductor amplifier. The experimental results show good agreement with the theory, and the validity of the theory for this experiment is discussed. A diffusion length of 2.0 m is determined from the experiment. The TWM gain in broad-area semiconductor amplifier is calculated as a function of the frequency difference between the pump and the signal based on the data obtained from the degenerate TWM experiment; and the calculated results are discussed based on the different contributions from the refractive index grating and the gain grating to the TWM gain. Depending on and , the TWM gain in semiconductor broad-area amplifier can be positive or negative. The energy exchange between the pump and signal beams occurs when 0.
A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.
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 (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.
Two-wave mixing at λ = 1.06 μm in the saturable gain of a flash-lamp-pumped Nd:YAG amplifier was investigated, both experimentally and theoretically, by development of a transient analysis. Despite the local response of the inverted medium, it is shown that energy redistribution can occur, thus leading to the depletion of a low-intensity signal beam. Finally we measured a diffraction efficiency of 20% of the transmission-gain grating by diffracting a probe beam at λ = 1.06 μm under the Bragg condition.
A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
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.