Higher-order beyond-band discrete solitons in binary waveguide arrays

Abstract

We study higher-order beyond-band discrete solitons (HOBBDSs) and quasi-HOBBDSs, which can be constructed by multiplying the solutions of fundamental single-peaked beyond-band discrete solitons by a soliton order parameter larger than unity. In the quasi-continuous regime when the HOBBDS peak amplitude is low (thus its width is large) and the soliton order parameter is a small integer number, HOBBDSs periodically evolve during propagation and their dynamics are similar to those of higher-order solitons governed by the nonlinear Schrödinger equation in an optical fiber, including the periodicity, pattern evolution, and independence of the period length on the soliton order parameter. If the soliton order parameter is still small but not an integer, then one can obtain the quasi-HOBBDSs whose profiles almost periodically evolve during propagation. The breathing length of quasi-HOBBDSs decreases if the soliton order parameter increases. Moreover, the breathing length of quasi-HOBBDSs is approximately inversely proportional to the square values of the peak amplitude of the fundamental beyond-band discrete solitons, just like what happens with the period length of the higher-order solitons governed by the nonlinear Schrödinger equation. If the fundamental beyond-band discrete solitons are intense enough and/or the soliton order parameter is large enough, then most of the energy of the beams is eventually trapped in a single waveguide.