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IEEE Journal of Quantum Electronics

Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold

Antonio Mecozzi, Alessandro D’Ottavi, Rongqing Hui

Published Jun 1, 1993• 45 citations
Publisher

Abstract

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.>

DOI
10.1109/3.234398

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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.>
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.
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.
We present both theoretical and experimental studies of four-wave mixing in a distributed-feedback (DFB) laser. The measured amplified spontaneous emission and probe gain spectra are also used to extract the DFB laser parameters. We use mean-field theory to investigate both nearly degenerate and non-degenerate four-wave mixings. For small pump-probe detunings, the dependence of multiple conjugate waves on the pump and probe powers is measured. For larger detunings, the gain of the probe signal and the conversion efficiency are measured in great detail up to a detuning of /spl plusmn/550 GHz. The measured conversion efficiencies as a function of the pump-probe detuning and the power scaling laws are compared with those of the theoretical results. We also demonstrate the DFB cavity effects on the conversion efficiency spectrum.
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 in Fabry–Perot semiconductor lasers is studied for pump–probe detunings that range from a few hundred megahertz to as high as 20 GHz. It is observed that the conjugate reflectivity and probe amplification decrease with slopes of −60 and −20 dB per frequency decade, respectively, when the detuning exceeds the relaxation-oscillation frequency. A resonance enhancement of the four-wave mixing signal is observed at both the relaxation-oscillation frequency and twice the relaxation-oscillation frequency. Cascade four-wave mixing signals are observed under a very weak (−37-dBm) input probe beam. A quantitative fit to the nearly degenerate four-wave mixing data is obtained, permitting the extraction of basic semiconductor-laser parameters by use of this technique.
Degenerate Four Wave Mixing (DFWM) and Nearly Degenerate Four Wave Mixing (NDFWM) have attracted a considerable attention in non-linear optics. DFWM has found several applications in phase conjugation, used in real time holography and adaptive optics. To realize a higher amplification of the conjugate wave, semiconductor amplifiers have been used. A theoretical analysis of the NDFWM process has been presented by Agrawal [1]. Here, an experimental and theoretical analysis of NDFWM in Distributed Feedback (DFB) lasers is proposed, where the FWM efficiency is enhanced by the cavity feedback mechanism.