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Physical Review A

Transient analysis of Kerr-like phase conjugators using frequency-domain techniques

Robert A. Fisher, B. R. Suydam, B. J. Feldman

Published Jun 1, 1981• 40 citations

Abstract

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.

DOI: 10.1103/physreva.23.3071

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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.

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We study the dynamics of a stable Fabry–Perot resonator in which one mirror is a phase-conjugate mirror (PCM) with instantaneous response. The temporal variations in the model are caused by round-trip effects. An exact solution is given in a form of an infinite series. The step-function response is summed exactly. Numerical studies with Gaussian input pulses and PCM reflectivity variations are presented, and their behavior is explained. Approximate formulas for responses to slowly varying pulses are derived. Noise effects are simulated with a model in which the phases of the probe and the amplitude reflection coefficient of the PCM make uncorrelated jumps with Poissonian statistics. The theoretical model is aimed for optimizing experiments on phase-conjugate resonators involving transients and fluctuating fields.

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