Nonlinear Bloch modes, optical switching and Bragg solitons in tightly coupled micro-ring resonator chains

Abstract

We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching behavior of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input.

Dynamical analysis of double-ring resonator with non-instantaneous Kerr response and effect of loss

“…For such systems, even the instantaneous Kerr response leads to SP and chaos (Morichetti et al 2006;Petráček et al 2011); detailed classification of the states in short chains of coupled microcavities was presented in (Maes et al 2009). The behavior of the coupled structures is similar to those observed in one-dimensional nonlinear photonic crystals (Lidorikis and Soukoulis 2000) and thus SP can be attributed to generation of gap solitons (Maes et al 2009); for long, tightly coupled, microring chains, such generation was studied in (Chamorro-Posada et al 2012). Alternatively, SP in two coupled nonlinear microcavities can be explained as a combined result of beating of modes and nonlinear switching (Grigoriev and Biancalana 2011).…”

Gap solitons and symmetry breaking in parity-time symmetric microring coupled resonator optical waveguides

“…Since the system response is frequency-periodic, Ω can be considered as a frequency detuning parameter from one reference resonance. For the analysis in terms of linear and nonlinear Bloch modes, a continuous-wave input signal with frequency ω is assumed [23] that has stationary solutions of the form…”

“…When this ansatz is plugged into (1), the nonlinear dispersion relation obtained is The stationary evanescent solutions within the bandgaps can be shown to fulfill the condition f = 1 [23].…”

“…is recovered. A particularly interesting regime is found in the tight-binding limit |θ| → 1 [23]. It has been shown that, for certain parameter values, a oscillatory response is obtained within the bandgap that corresponds to the self-structuring of the microring CROW field into spontaneously generated soliton trains.…”

Simulation of self-pulsing in Kerr-nonlinear coupled ring resonators

“…For long microring chains, spontaneous generation of gap solitons from cw input was studied in Ref. [21].…”