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Technical Physics

Self-reflection in a naive model of nonlinear media

K. D. Lyakhomskaya, P. I. Khadzhi

Published Nov 1, 2000• 9 citations
Publisher

Abstract

The optical self-reflection in a naive model of a semi-infinite nonlinear medium is studied theoretically. It is demonstrated that a Fabry-Perot resonator is induced by a propagating wave in the medium if the incident intensity exceeds a critical value. Hysteresis dependences of the reflectivity and the resonator length on the incident intensity are predicted.

DOI
10.1134/1.1325030

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The optical self-reflection in a naive model of a semi-infinite nonlinear medium is studied theoretically. It is demonstrated that a Fabry-Perot resonator is induced by a propagating wave in the medium if the incident intensity exceeds a critical value. Hysteresis dependences of the reflectivity and the resonator length on the incident intensity are predicted.
An analysis is made of the propagation of an optical wave parallel to reflecting planes in an extended nonlinear Fabry-Perot interferometer pumped by a strong wave of the same intensity. It is shown that the nonlinear-optics self-interaction of the first wave changes drastically near certain parts of the main experimental characteristic of the interferometer, which is the dependence of the intensity of the transmitted light on the intensity of the pump wave. The acoustooptic interaction can change similarly in this interferometer.
Mode superradiance (i.e. superfluorescence) in an open Fabry—Perot resonator is characterised by simultaneous emission of counterpropagating coherent pulses even when the mirrors have very low (but finite) reflection coefficients, beginning from R cr ≪ 1. It is shown that for any value of the resonator Q factor, even when R ≫ R cr or R ~ 1, a self-matched λ /2 grating of the population inversion in a two-level medium does not result in significant Bragg reflection which would exceed the reflection from the mirrors. A consistent allowance for the interference of inhomogeneous conterpropagating waves significantly alters the spatial and temporal dynamics of depletion of the population inversion and, consequently, greatly changes he profile of collective spontaneous radiation pulses, compared with the predictions of the mean field and unidirectional superradiance theories. A new nonlinear equation for superradiance in an open resonator is derived.
We consider a Fabry-Perot filled with a nonlinear medium. The transmitted (It) and reflected (Ir) intensities are related to the holding or input beam intensity Ih by the Airy formulae: It is assumed that the angle of incidence is sufficiently small (i.e., near normal incidence) to neglect the angular dependence in the Airy function. Two situations have been analysed, depending on whether the reflected beam is fed back into the Fabry-Perot with the same angle of incidence as the holding beam or not. In both cases the reflected beam goes through an attenuator which reduces the intensity by a coefficient α. The coefficient α varies from 0 (no attenuation) to 1 (complete attenuation).
A theoretical investigation is made of the polarization characteristics of the optical polarization and amplitude multistability of a Fabry?Perot interferometer filled with a nonlinear resonant medium. In the case of linear polarization of the incident radiation it is shown that an amplitude hysteresis differs considerably from a hysteresis predicted by a scalar theory; moreover, the degree of polarization exhibits a hysteresis. A calculation is made of the critical input intensity of elliptically polarized radiation for which the ellipticity at the output rises strongly even when it is negligible at the input.