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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical Logic Functions Using Nearly Degenerate Four-Wave Mixing In Laser Diodes

Bruno J. Thedrez, Hisao Nakajima, Robert Frey

Published Jan 8, 1987• 0 citations
Publisher

Abstract

Optical logic functions can be obtained through nearly-degenerate four-wave mixing in laser diodes operating above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laser oscillation or by amplification of an external pump signal. The conjugate frequency w + δw is then obtained by intracavity nearly-degenerate four-wave mixing when a probe beam of frequency w - δw is injected through the laser diode colinearly with the pump beam. Several examples using this technique are discussed including high contrast bistable memory, AND, OR, and INV gates.

DOI
10.1117/12.936979

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Optical logic functions can be obtained through nearly-degenerate four-wave mixing in laser diodes operating above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laser oscillation or by amplification of an external pump signal. The conjugate frequency w + δw is then obtained by intracavity nearly-degenerate four-wave mixing when a probe beam of frequency w - δw is injected through the laser diode colinearly with the pump beam. Several examples using this technique are discussed including high contrast bistable memory, AND, OR, and INV gates.
Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (\omega- \delta\omega), or conjugated (\omega + \delta\omega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 103-104) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.
Experimental results are presented regarding the generation and bistable behavior of a conjugated signal obtained through intracavity nearly degenerate four-wave mixing in a semiconductor laser amplifier injected with both pump ($\ensuremath{\omega}$) and probe ($\ensuremath{\omega}\ensuremath{-}\ensuremath{\delta}\ensuremath{\omega}$) frequencies. Conjugated reflectivities at $\ensuremath{\omega}+\ensuremath{\delta}\ensuremath{\omega}$ larger than 500% with 35% efficiency together with bistable behavior in the three signals (pump, probe, and conjugated) are reported.
Optical phase conjugation through nearly degenerate four-wave mixing (NDFWM) in semiconductor lasers has attracted considerable attention in recent years since being first demonstrated by Nakajima and Frey[ 1 ]. Such interest arises due to the very high conjugate reflectivity of order 30-40dB which can be achieved owing to the amplifying effect of the semiconductor gain medium and cavity enhancement of mixing process. However, most previous experimental and theoretical work has placed emphasis on the weak signal case, where the injection signal acts only as a small perturbation of free-running laser diode. It is only very recently that a theoretical analysis of NDFWM in a semiconductor laser subject to strong probe injection power has been presented[2].
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.
Generation of phase conjugated optical waves within an active medium of a semiconductor diode laser has been demonstrated recently based on the intracavity four-wave mixing1-4). The methods employed for generation and detect ion of the phase conjugated optical waves are briefly summarized as follows: a probe beam with an angular frequency ω0+ δω is injected into an active waveguide of a semiconductor diode laser, where the standing waves of the oscillating fields serve as the two counter-propagating pumping waves for the four-wave mixing at the angular frequency of ω0. The phase conjugated wave in the frequency domain has to possess the frequency component of ω0−δω, so that this frequency component was detected as an evidence of the generation of the phase conjugated wave.
In this paper, nearly degenerate four-wave mixing created by pump-probe structure with small frequency spacing and enough high power is demonstrated and discussed by introducing single optical beam into single-mode Fabry-Pérot laser diode, in which the injected beam is called the probe wave, whose frequency detuning is controlled within ±50 GHz, and lasing resonance mode such as dominant mode or arbitrarily residual side mode is selected as the pump wave. In the case of dominant mode like the pump wave, conjugate signals around the pump-probe wave are easily observed for positive and negative probe detuning by judiciously tuning injected probe power. While external injection mode is moved towards the side mode selected as the pump wave, newly generated signals only occurred with small positive probe detuning. As the probe wave with positive frequency detuning is close to the pump wave, higher order conjugate signals are gradually grown. Under the condition of side mode as the pump wave, the strongly nonlinear mixing of the pump-probe wave also gives rise to new frequency signals on both sides of the dominant mode with enough high peak level. Against the change of correspondingly initial power and frequency detuning of the probe wave, outcome spectrum, output power, and conversion efficiency of conjugate signals are analyzed in detail, while dominant or one side mode is, respectively, selected as the pump wave.