Study Of Band Gap Solitons In Two-dimensional Optical Lattices In Photorefractive Crystals

Spatial optical soliton refers to the transverse wave propagating in the direction perpendicular to the propagation direction can keep its shape unchanged.The reason for this is that the nonlinear effects of the medium material and the diffraction effects of the beam itself can reach a balance when the light wave propagates in the medium material.Because of its unique properties,it has great potential applications in all-optical switching,optical waveguide,optical interconnection,optical communication and optical computing.Photonic lattice is a kind of optical structure with periodic refractive index,the bandgaps of this periodic optical structure can limit the propagation of the light.After the defect is introduced into the lattice,the beam propagates in the bandgap to form defective soliton,which further enhances the possibility of regulating light.In our calculation,we use Plane-Wave Expansion Method,Newton-Conjugate-Gradient Method,Modified Squared-Operator Method and Symmetric Step-Fourier Method.In this paper,we study gap solitons and defect solitons in kagome photonic lattices in centrosymmetric photorefractive crystals,and propose the theory of defect solitons in kagome photonic lattices in centrosymmetric photorefractive crystals.By numerically calculating,we analyze the defect solitons and their stabilities in two dimensional photonic lattices,and discuss in detail the impact of the defect intensity on theregions where solitons can stably exist.When the defect is zero,i.e.,in a uniform lattice,defect solitons exist only in semi-infinite bandgap,and the ones with high power are unstable,but the ones withlow power can stably propagate.The power of the gap solitons decrease as the propagation constant increases.When the defect is positive,defect solitons existonly in the semi-infinite bandgap,and the ones with high power are unstable,but the ones withlow power can stably propagate.When the defect strength is increased,the stable region of defect solitons is extended.When the defect is negative,defect solitons exist in the semi-infinite and first bandgaps.In the semi-infinite bandgap,negative defect solitons can propagate stably inmoderate power regions and areunstable in the high power regions and low power regions.Defect solitons with high power change their shapes and positions and the ones with low power may break up during propagation.Inthe first bandgap,defect solitons with low defect intensities can propagate stably.When defect intensities are large,defect solitons with high power can propagate stably,but low power solitons cannot do it.When the defect strength is increased,the stable region of defect solitons is narrowed.