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IEEE Journal of Quantum Electronics

An experimental method for identifying nonlinear phenomena intervening in a FWM process developed in a semiconductor optical amplifier

Horacio Soto, Didier Erasme

Published Jan 1, 1998• 8 citations
Publisher

Abstract

The new experimental research on the four-wave mixing (FWM) phenomena described here consists in launching three optical waves (pump, probe, and test) into a semiconductor optical amplifier and measuring the test beam transmission and the conversion efficiency of the new wave generated to one side of the test beam. It allows for an excellent identification of the nonlinear phenomena involved in the FWM process. The analysis principle is based on the modulation of the gain curve for each of the three effects considered: spectral hole burning, carrier heating, and carrier density pulsation. Experimental and theoretical results are presented.

DOI
10.1109/3.726616

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The new experimental research on the four-wave mixing (FWM) phenomena described here consists in launching three optical waves (pump, probe, and test) into a semiconductor optical amplifier and measuring the test beam transmission and the conversion efficiency of the new wave generated to one side of the test beam. It allows for an excellent identification of the nonlinear phenomena involved in the FWM process. The analysis principle is based on the modulation of the gain curve for each of the three effects considered: spectral hole burning, carrier heating, and carrier density pulsation. Experimental and theoretical results are presented.
The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.
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.>
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.
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.