Symmetric and asymmetric localized modes in linear lattices with an embedded pair of χ(2)-nonlinear sites

摘要

We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensionalnbichromatic lattices with the second-harmonic-generating (χ(2)) nonlinearity concentrated at a pair of sitesnplaced at distance l. The lattice can be built as an array of optical waveguides. Solutions are obtained in annimplicit analytical form, which is made explicit in the case of adjacent nonlinear sites, l = 1. The stability isnanalyzed through the computation of eigenvalues for small perturbations and verified by direct simulations. Innthe cascading limit, which corresponds to a large mismatch q, the system becomes tantamount to the recentlynstudied single-component lattice with two embedded sites carrying the cubic nonlinearity. The modes undergonqualitative changes with the variation of q. In particular, at l u0002 2, the symmetry-breaking bifurcation, whichncreates asymmetric states from symmetric ones, is supercritical and subcritical for small and large values of q,nrespectively, while the bifurcation is always supercritical at l = 1. In the experiment, the corresponding changenof the phase transition between the second and first kinds may be implemented by varying the mismatch, via thenwavelength of the input beam. The existence threshold (minimum total power) for the symmetric modes vanishesnexactly at q = 0, which suggests a possibility to create the solitary mode using low-power beams. The stabilitynof solution families also changes with q.