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Journal of Modern Optics

Two-dimensional solitons in a Kerr cavity

W. J. Firth, Angus Lord

Published May 1, 1996• 51 citations
Publisher

Abstract

We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.

DOI
10.1080/09500349608233267

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We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.
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This thesis presents the theory of the driven optical ring cavity containing a nonlinear material. First, an overview of the history of bistability and spatial solitons in driven nonlinear cavities is outlined. Then, the basic theory of the optical Kerr effect is presented and two of its consequences are outlined: optical bistability and spatial solitons. Within this background, the mirror feedback model is derived from the Maxwell-Bloch equations and considerations of the classical optics of the cavity. This model is analytically shown to exhibit bistability in the plane wave case. The mean-field model is subsequently derived by applying the mean-field limit to the Maxwell-Bloch equations and the cavity optics. In addition, the mean-field model is analytically shown to exhibit bistability in the plane wave case. Numerical simulations are performed on the mean-field model demonstrating the existence of: (i) plane wave bistability, (ii) transverse modulational bistability, (iii) the ability to “switch†between bistable states in both the plane wave and modulated case, (iv) instabilities in the modulated case and (v) the possibility for optimization of the switching process. Finally, an application of bistable driven cavities is explored: an all-optical digital information processor and storage device.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
In this communication, the authors investigate numerically and analytically the influence of delayed feedback on the mobility properties of 2D cavity solitons. The authors consider a passive cavity filled with a two-level medium and driven by a coherent injection beam. The authors report on a new type of instability leading to a spontaneous drift of dissipative solitons. The authors show that when the product of the delay time and the feedback amplitude exceeds a certain threshold, a single circularly symmetric localized structure starts to move in an arbitrary direction.
Light propagation in a 2-D array of coupled optical cavities with Kerr nonlinearity driven by a plane holding beam is numerically studied. Optical bistability together with its modulational instability (MI) are investigated, and 2-D discrete cavity solitons are simulated. These simulations revealed the switching on/off of the solitons along with the ability of a proper Gaussian beam (GB) to control their positions. Soliton-soliton and soliton-GB interactions are considered, and finally, all-optical NOR , XNOR, and NAND gates are proposed as realized by this device.