Localized modes in nonlinear binary kagome ribbons

Abstract

The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system "binarism" various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.

Localized gap modes in nonlinear dimerized Lieb lattices

“…The influence of nonlinearity in dimerized ("binary") flat band systems have previously been studied for 1D kagome and ladder strips [25]. There, three types of nonlinear ring solutions were found to exist: unstaggered, staggered, and vortex.…”

“…Recently this topic attracted a lot of attention. Light localization effects in 1D nonlinear kagome and ladder ribbons (uniform and binary) [24,25], as well as in 2D kagome lattices [26][27][28][29] were investigated.…”

Simple method to construct flat-band lattices

“…In general, any FB mode possessing a set of N amplitudes (A), but with alternating/staggered sign, has a very simple and compact form [37,38]. As the connector sites amplitudes remain zero, the total power, defined as P = n |A n | 2 , is just given by P = N A 2 .…”

Single and double linear and nonlinear flatband chains: Spectra and modes

“…Obviously, the bifurcation point (24) pertains to symmetric solution (20), while point (25) pertains to symmetric solution (22) with sign minus chosen for ±. The similar analysis for the antisymmetric solution readily demonstrates that it never undergoes an antisymmetrybreaking bifurcation (formally, the bifurcation occurs at an unphysical point, with E 2 = −2).…”

“…[20,25,26], while counterparts of CLSs in nonlinear lattices were discussed in Refs. [16,23,24,[27][28][29]. In this work, we aim to develop the analysis of CLSs and lattice solitons coexisting with them in the nonlinear diamond-chain system.…”