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Pure and Applied Optics Journal of the European Optical Society Part A

Dynamics of two-dimensional high-transmission domains in non-linear planar resonators

J Kohrell, Thomas Peschel, Ulf Peschel, F. Lederer

Published Sep 1, 1994• 0 citations
Publisher

Abstract

Using the modal theory the optical response of a non-linear planar resonator illuminated by a genuine two-dimensional, pulsed beam is studied. We consider a defocusing Kerr-like non-linearity appearing well below the fundamental band-gap of direct semiconductors due to two-photon processes. Optical bistability is identified for normal incidence whereas it disappears if the angle of incidence of the input beam becomes comparable to the width of the resonance. No evidence for symmetry breaking could be found, whereas a pronounced beam shaping arises in the high-transmission state.

DOI
10.1088/0963-9659/3/5/011

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Using the modal theory the optical response of a non-linear planar resonator illuminated by a genuine two-dimensional, pulsed beam is studied. We consider a defocusing Kerr-like non-linearity appearing well below the fundamental band-gap of direct semiconductors due to two-photon processes. Optical bistability is identified for normal incidence whereas it disappears if the angle of incidence of the input beam becomes comparable to the width of the resonance. No evidence for symmetry breaking could be found, whereas a pronounced beam shaping arises in the high-transmission state.
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A comprehensive analysis of the interaction of pulsed light beams with nonlinear planar resonators is presented, covering both arbitrary types of nonlinearity and arbitrary states of polarization of the incident field. The characteristic of the optical response is discussed in its dependence on the crucial parameters of the resonator system as well as of the input pulse. Numerical results are given for the transmission response of a multiple-film configuration under oblique incidence, which is endowed with a dynamic, saturable nonlinearity. In particular, conditions for optical bistability to occur are derived.
We present an analysis of the steady state optical response of two-dimensional optical superlattices with Kerr nonlinearity. We consider the effects of the modification of the refractive index modulation strengths in the superlattices and the angular deviation of incoming radiation from Bragg conditions. We find that under Bragg incidence the system displays optical bistability only when the modulation ratio exceeds a certain threshold. We also predict that optical bistability can disappear under non-Bragg incidence. Physical considerations are presented and discussed on how to optimize the chances for observing optical bistability in such a superlattice.
The dynamical evolution of a two transverse dimensional laser beam profile is monitored as it switches from a low to a high transmission state in a bistable optical resonator. Sharp gradients appearing at the edge of the switched-on central portion of the beam initiate a train of solitary waves which grow inwards towards the beam center. In a high finesse resonator, strong saturation of the beam in the on state tends to stabilize the solitary waves as concentric rings. Unlike earlier one transverse dimensional studies, the central part of the beam undergoes a slow periodic oscillation, but the shapes of the outer rings are consistent with earlier one transverse dimensional predictions. Numerical evidence is provided for filamentation of lower amplitude rings.
A unified nonlinear modal theory that is valid not only for waveguide couplers but also for nonlinear Fabry–Perot resonators has recently been proposed. The validity of this new approach is numerically demonstrated by comparison with the well-known bidimensional theory. The unified modal theory appears to be a powerful tool for studying transverse effects in a broad class of nonlinear resonators. It has been used to derive the main characteristics of the stationary behavior of the optical resonators in the case of a local nonlinearity. In particular, the disappearance of optical bistability when the resonator is tilted is predicted. Optical bistability at nearly normal incidence is interpreted by the coupling between two resonantly excited counterpropagating modes that are at the origin of the required transverse feedback.