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IEEE Journal of Quantum Electronics

Four-wave mixing in traveling-wave semiconductor amplifiers

Antonio Mecozzi, S. Scotti, Alessandro D’Ottavi, Eugenio Iannone, P. Spanò

Published Apr 1, 1995• 124 citations
Publisher

Abstract

The traveling-wave equations of four-wave mixing in semiconductor amplifiers are solved analytically including saturation of the amplifier. Excellent agreement is obtained with numerical solutions of the traveling-wave equations. The analytical model is used to analyze a highly nondegenerate four-wave mixing experiment in a bulk semiconductor amplifier.>

DOI
10.1109/3.371944

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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
The traveling-wave equations of four-wave mixing in semiconductor amplifiers are solved analytically including saturation of the amplifier. Excellent agreement is obtained with numerical solutions of the traveling-wave equations. The analytical model is used to analyze a highly nondegenerate four-wave mixing experiment in a bulk semiconductor amplifier.>
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.
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.
We present a formalism and a technique for analyzing the propagation of optical signals through semiconductor traveling-wave amplifiers. The formalism retains, in particular, the spontaneous recombination term, and the newly developed technique permits analytic, real-time solutions to be obtained, so that both the transient and the steady-state regimes are characterized. This end has been achieved by iteratively applying the method of in order to solve the set of coupled differential equations that result from the formulation of the characteristics physical problem. From the real-time solutions so obtained it is also possible easily to recognize the amplitude and phase-modulation effects that occur not only in the steady state but also in the transient regime.
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.>