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IEEE Journal of Quantum Electronics

Two-dimensional transverse solitary waves as asymptotic states of the field in a bistable optical resonator

J. V. Moloney

Published Sep 1, 1985• 18 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1985.1072833

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2 Dimensional Transverse Patterns in Optical Bistability

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Transverse optical bistabilities and instabilities

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A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.

IEEE Journal of Quantum Electronics•Sep 1, 1985•18 citations

Evolution of Two-Dimensional Transverse Solitary Waves and Solitons in an Optical Bistable Resonator

J. V. Moloney

•Jun 18, 1984•2 citations
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.
Transverse beam-profile variations are investigated for a system which shows cavityless optical bistability due to increasing absorption. Coupled transport equations for the light field and the excitation density are derived and solved numerically for the case of an optically thin sample, where longitudinal density variations can be neglected and where diffusion of the excitation is the dominant transverse coupling mechanism. Assuming a Gaussian input beam, the increasing absorption is shown to cause substantial profile modifications when the medium undergoes the transition from low to high absorption. The formation of spatial ring structures is predicted and it is shown that transverse carrier diffusion plays an important role in determining both the steady-state and the temporal response of the system.
Pioneered by Moloney and collaborators [1], transverse effects of nonlinear passive systems in a ring cavity have been the object of extensive study. Analytical investigations with diffractive coupling in one transverse dimension have demonstrated [1] that static and dynamic transverse structures occur in this system. Extension of the mean-field dispersive model developed from optical bistability to include diffraction [2] independently demonstrated qualitatively similar features, again in one transverse dimension. Investigations in two transverse dimensions have been largely confined to numerical studies by the Moloney group [1], showing for gaussian beam illumination ring structures which develop through azimuthal instability to a pattern of spots which typically execute a slow chaotic motion with a progressive loss of symmetries.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.