Controlling Optical Beam Thermalization via Band-Gap Engineering

TL;DR

This paper develops dispersion engineering rules for controlling the thermalization process of optical beams in multimode nonlinear photonic circuits, enabling manipulation of thermal states through band-gap engineering.

Contribution

It introduces a kinetic equation approach to predict non-conventional thermal states based on band-gap structures in photonic systems, validated on the SSH model.

Findings

Stationary solutions differ from Rayleigh-Jeans distribution when gap-to-band width ratio exceeds a critical value.

Relaxation times for non-conventional thermal states are predicted by the theory.

Spectral engineering rules can be extended to complex, non-periodic photonic networks.

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 between 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 (RJ) distribution. The theory also predicts the relaxation times above which such non-conventional thermal states occur. We have tested the validity of our results for the prototype SSH model whose connectivity between the composite elements allows to control 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.