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IEEE Journal of Quantum Electronics

Collinear nearly degenerate four-wave mixing in intracavity amplifying media

Haruto Nakajima, Robert Frey

Published Aug 1, 1986• 60 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1986.1073116

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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.
Nearly degenerate four wave mixing (NDFWM) in semiconductor laser amplifiers has received attention recently as a means of efficiently generating phase conjugate beams. The high efficiency is due to two factors: (i) intracavity geometry enhances pump efficiency; (ii) an amplifying nonlinear medium results in high coupling efficiency. These factors have combined to give observed conjugate reflectivities of approximately 30/40 dB. The NDFWM process in semiconductor lasers is also very fast ( tau approximately 10/sup -9/s) being limited primarily by the interband relaxation time. Recent theoretical studies, however, have suggested that temporal gratings with THz frequencies may be supportable. It should be noted that NDFWM in semiconductor lasers is quite different from four wave mixing in most other media in that to a first approximation the gratings formed are purely temporal. Spatial effects are normally neglected, both for computational convenience and because carrier diffusion tends to wash out spatial holes. Previously, the authors demonstrated how the temporal nature of the wave mixing process could be exploited to produce a resonant enhancement in a two wave mixing geometry. In this paper, they examine a novel scheme for enhancing the phase conjugate reflectivity via pumping the device resonantly at the detuning frequency. They demonstrate that on resonance, conjugate reflectivities several orders of magnitude greater than those previously reported are possible. >
On-axis intracavity nearly degenerate four-wave mixing performed inside a laser composed of inverted two-level systems is studied theoretically using analytical solutions for the propagation equations obtained in the case in which the undepleted pump laser is operating near threshold. Reflectivities up to 103–106 are predicted, together with bandwidths that make such a setup usable for practical applications. The influence of the ac Stark effect and cavity mistuning on the reflectivity is also considered.
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.
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.
Spectral hole burning in semiconductor lasers manifests as a nonlinear suppression of the mode gain by a few percent. In the presence of a probe wave, the same mechanism can lead to highly nondegenerate four-wave mixing (NDFWM) by creating the dynamic gain and index gratings at the beat frequency of the pump and probe waves. Since the grating efficiency is governed by the intraband relaxation time (typically <1 ps), significant NDFWM can occur even for a pump-probe detuning ∼100 GHz. We present the results for the conjugate reflectivity and the probe transmittivity when an InGaAsP laser is used as a traveling-wave amplifier.