Controlling optical beam thermalization via band-gap engineering

Abstract

We establish dispersion engineering rules that allow us to control the thermalization process and the thermal state of an initial beam propagating in a multimode nonlinear photonic circuit. To this end, we have implemented a kinetic equation (KE) approach in systems whose Bloch dispersion relation exhibits bands and gaps. When the ratio of the gap width to the band width is larger than a critical value, the KE has stationary solutions which differ from the standard Rayleigh-Jeans distribution. The theory also predicts the relaxation times above which such nonconventional thermal states occur. We have tested the validity of our results for the prototype Su-Schrieffer-Heeger model whose connectivity between the composite elements allows control of the band-gap structure. These spectral engineering rules can be extended to more complex photonic networks that lack periodicity but their spectra consist of groups of modes that are separated by spectral gaps.