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Optics Letters

Impulse-response function of photorefractive phase conjugation

George C. Papen, Bahaa E. A. Saleh, J. A. Tataronis

Published Jan 15, 1989• 8 citations
Publisher

Abstract

Explicit expressions for the impulse-response function of a photorefractive phase conjugator are derived. The expressions are in the form of an infinite series of Bessel functions. The results are derived by using the undepleted pump approximation and are therefore valid at least for small time intervals, even when the conjugator is unstable.

DOI
10.1364/ol.14.000287

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IEEE Journal of Quantum Electronics•Apr 1, 1990•2 citations
Explicit expressions for the impulse-response function of a photorefractive phase conjugator are derived. The expressions are in the form of an infinite series of Bessel functions. The results are derived by using the undepleted pump approximation and are therefore valid at least for small time intervals, even when the conjugator is unstable.
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.>
Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω j = ω p + Ω j , wavevectors k j , and complex amplitudes A j (Ω j , k j ), where ω p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω l −k l is H(Ω l , k l ) is the linearized response, ρ(Ω l , k l ; Ω j , k j ) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.
Using perturbation theory, an examination is made of the fidelity of the photorefractive degenerate four-wave mixing phase conjugator. The general case is considered in which the probe is spatially varying (a beam) and temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane-wave components. Carrying out the perturbation procedure up to the third order, the authors found that the components of the probe interact in pairs, so that the reflectance of each component of the conjugate wave is a combination of a linear term, a self-nonlinear term, and a term representing crosstalk with all other components of the probe. The crosstalk effect as a function of the frequency difference exhibits resonance behavior.>