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Abstract
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two-dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries.
Highlights
Dual-core couplers represent one of the basic types of optical waveguides [1]
The objective of the present paper is to report a new result for the ordinary and double symmetry breakings in dual-core systems, in which the additional symmetry in each core is introduced by assuming that its intrinsic nonlinearity is subject to the spatial modulation, being concentrated at two mutually symmetric spatially separated points
The purpose of our study is to investigate the interplay of inter- and intra-channel symmetry breaking of soliton modes in a pair of linearly-coupled planar nonlinear optical waveguides, as well as in a Bose-Einstein condensate (BEC) loaded into a dual-cigar-shaped potential trap, with two parallel cores coupled by tunneling of atoms
Summary
Dual-core couplers represent one of the basic types of optical waveguides [1]. In most cases, the couplers are realized as twin-core optical fibers [2,3] (i.e., in the temporal domain), as well as in double-layer planar waveguides (see, e.g., Reference [4]), i.e., in the spatial domain. The intra-channel symmetry breaking is considered with respect to a symmetric pair of spots at which the local nonlinearity is concentrated The model of this setting is based on a system of linearly-coupled nonlinear Schrödinger equations, alias Gross-Pitaevskii equations (GPEs), in terms of the BEC realization [9]. Before addressing the model with the double delta function, as defined by Equation (4), we first consider the profile of g( x ) with a single delta function
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