2D Jackiw–Rebbi and trivial localized states in square interfaced binary waveguide lattices

Abstract

We investigate optical analogs of two-dimensional (2D) Jackiw–Rebbi (JR) states and 2D trivial localized states in square interfaced binary waveguide lattices in the linear and nonlinear regimes of Kerr type. The 2D JR states can be formed in the square interfaced binary lattice during propagation of optical beams and turn out to be quite robust, especially in the linear and defocusing nonlinearity regime where established 2D JR state profiles are well conserved during propagation. The established profiles of nonlinear 2D JR states formed during propagation agree well with exact solutions obtained by using the Newton–Raphson method. The 2D nonlinear trivial localized states found by the successive approximation method are much broader than 2D JR states with the same peak amplitudes. The 2D JR states can also be well trapped within the central interface of the lattices even in the presence of an initial tilt of the input beam which can easily displace 2D trivial localized states in square interfaced binary waveguide lattices, 2D Dirac solitons in perfectly periodic binary waveguide lattices and other solitonic structures in the continuous media.