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

The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators

F. Lederer, Thomas Peschel, Ulf Peschel

Published Nov 1, 1993• 8 citations
Publisher

Abstract

The optically non-linear response of arbitrary planar semiconductor resonators (microresonators) is studied theoretically. We use a versatile approach that takes into account the finite beam width as well as pulse length of the incident light, and incorporates the non-linearity consistently. The intensity-dependent non-linearity of semiconductors is described by appropriate phenomenological models. We show that the propagation characteristic of the leaky waves excited controls the response behaviour of the resonators. Conditions for switching and optical bistability are identified. The effect of various parameters on the response is studied numerically.

DOI
10.1088/0963-9659/2/6/009

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The optically non-linear response of arbitrary planar semiconductor resonators (microresonators) is studied theoretically. We use a versatile approach that takes into account the finite beam width as well as pulse length of the incident light, and incorporates the non-linearity consistently. The intensity-dependent non-linearity of semiconductors is described by appropriate phenomenological models. We show that the propagation characteristic of the leaky waves excited controls the response behaviour of the resonators. Conditions for switching and optical bistability are identified. The effect of various parameters on the response is studied numerically.
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.
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.
By using a modal approach, the distributed coupling of two inhomogeneous, transient waves with opposite angles of incidence into nonlinear waveguides is studied. We show that cross modulation and the coherent interaction via a dynamic grating, nonlinearily induced by the excited counterpropagating leaky waves, provide a longitudinal feedback. This feedback is the necessary prerequisite for bistability to occur. We show that bistability may even appear when one incident beam is weak. Consequently, modulation of the strong signal beam by a weak control pulse can be achieved. Furthermore, we demonstrate that the symmetry of the input signal can be broken beyond a certain intensity and that set-reset flip-flop operation with finite beams is feasible. We demonstrate that the mechanism responsible for this flip-flop operation differs considerably from that acting in the plane-wave case. The optical nonlinearities may be caused by either virtual or real carrier excitation, which models the behavior of semiconductors as well as nonlinear polymers or organic dyes well below or close to a resonance, respectively. For real carrier excitation the interplay of carrier relaxation, diffusion, and the propagation of the excited fields is taken into account.