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Can optical phase conjugators produce a very short conjugate pulse

B. R. Suydam

Published Jan 1, 1980• 2 citations
OpenAlex

Abstract

In studying the transient behavior of phase conjugation via four wave mixing, it has been noted that very short probe pulses invariably produce considerably broadened conjugate pulses unless the conjugator is inordinately short. The present investigation was therefore undertaken to determine whether a short conjugate pulse might be produced by judicious programming of the probe. It was found that the probe can indeed be tailored to produce an arbitrarily short conjugate signal and, if the conjugating medium exhibits linear absorption, then the total energy in the probe signal is finite. The required probe programming can be determined by numerical evaluation of a Fourier transform.

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In earlier work, the transient response of a four-wave optical phase conjugator was studied. Here we study the inverse problem, namely: How must we tailor the input pulse in order to obtain a prescribed conjugator output? We find that an arbitrarily short output pulse can be obtained and show how the input, or probe, must be programmed in order to achieve this result.

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It is shown that noise from light-scattering fluctuations inherent in an optical Kerr medium sets a lower limit on the incident probe power required to achieve meaningful phase conjugation by four-wave mixing. For visible wavelengths and room temperatures, we determine that about 10 μW of probe power is needed to obtain a signal-to-noise ratio of unity in the conjugate wave for reflectivities that are less than or near the first oscillation condition.

Applied Physics Letters•Jan 16, 1989•18 citations
In studying the transient behavior of phase conjugation via four wave mixing, it has been noted that very short probe pulses invariably produce considerably broadened conjugate pulses unless the conjugator is inordinately short. The present investigation was therefore undertaken to determine whether a short conjugate pulse might be produced by judicious programming of the probe. It was found that the probe can indeed be tailored to produce an arbitrarily short conjugate signal and, if the conjugating medium exhibits linear absorption, then the total energy in the probe signal is finite. The required probe programming can be determined by numerical evaluation of a Fourier transform.
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].
The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.
We have measured the conjugation fidelity produced by four-wave mixing in sodium vapor using weak probe beams that were aberrated by simulated atmospheric turbulence. Near-diffraction-limited (1.3 times the diffraction limit) return beams were obtained for both moderate (D/r(0) approximately 10) and strong (D/r(0) approximately 25) simulated turbulence, down to probe-beam pulse energies of 200 pJ. We believe this to be the first systematic study of conjugation fidelity as a function of probe energy.
The characteristic features of the conjugate wave's formation under transient four-wave mixing in a two-level medium are investigated. The phase modulations of the signal and conjugate waves induced in the four-wave mixing are not mutually conjugate and have the same sign. The fulfillment of the phase-conjugation for the phase modulated signal has been shown in particular to be connected with the envelope's deformation and the spectrum's change of signal pulses. The transient optical bistability connected with the nonlinear absorption's saturation in the quasi-cw four-wave mixing and with the inertia in the short pulse's regime is observed.