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Journal of the Optical Society of America

Transient behavior of Kerr-like phase conjugators: the inverse problem

B. R. Suydam

Published May 1, 1983• 7 citations
Publisher

Abstract

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.

DOI
10.1364/josa.73.000539

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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.
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.
We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1
In this paper we develop the interrelationships between the steady-state and transient behavior for cw-pumped Kerr-like conjugators in which the optical Kerr effect is considered to respond instantaneously. We use Laplace-transform techniques to develop an expression for the conjugate response to input pulses of arbitrary form. For stable conjugator operation (in which the cw conjugate reflectivity is finite for all input frequencies), the expression reduces to an antilinear Fourier-transform relationship, which is readily adaptable to computer simulation. The cw filter function of Pepper and Abrams [Opt. Lett. 3, 312 (1978)] is found to play a central role. We show, both numerically and analytically, that our calculated delta-function response agrees with that previously published. We numerically demonstrate temporal spreading and reshaping when the conjugator transit time becomes equal to or longer than the duration of the input pulse, and we show numerically the perfect chirp reversal for sufficiently thin conjugators and the deviations from perfect chirp reversal upon increasing the thickness of the conjugator. These numerical results can be understood in terms of the bandwidth of the associated cw filter function.
A general solution to a linearized transient problem is presented and is shown to be valid for Kerr materials, photorefractive materials, and plasmas. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Using this solution, the parameters that govern the overall time behavior are identified and compared. These parameters are then used to discuss the distortion characteristics of the conjugate signal for each of the three materials.>