Thermalization dynamics in photonic lattices of different geometries

TL;DR

This study numerically compares thermalization dynamics in honeycomb and triangular photonic lattices, revealing that lattice geometry, temperature, and nonlinearity sign significantly influence thermalization speed and behavior.

Contribution

It provides the first detailed numerical analysis of how lattice geometry and nonlinear effects impact thermalization in photonic lattices.

Findings

Honeycomb lattices thermalize faster than triangular lattices.

Spectrum differences explain the variation in thermalization speeds.

Temperature and nonlinearity sign significantly affect thermalization dynamics.

Abstract

The statistical mechanical behavior of weakly nonlinear multimoded optical settings is attracting increased interest during the last few years. The main purpose of this work is to numerically investigate the main factors that affect the thermalization process in photonic lattices. In particular, we find that lattices with identically selected properties (such as temperature, coupling coefficient, lattice size, and excitation conditions) can exhibit very different thermalization dynamics and thus thermalization distances. Our investigation is focused on two different two-dimensional lattices: the honeycomb lattice and the triangular lattice. Our numerical results show that, independently of the excitation conditions, the honeycomb lattice always thermalizes faster than the triangular lattice. We mainly explain this behavior to the quasilinear spectrum that promotes wave-mixing in the honeycomb lattice in comparison to the power-like spectrum of the triangular lattice. In addition, we investigate the combined effects of temperature as well as the sign and magnitude of the nonlinearity. Switching either the sign of the Kerr nonlinear coefficient or the sign of the temperature can lead to significant differences in the thermalization dynamics, a phenomenon that can be physically explained in terms of wave instabilities. Larger absolute values of the temperature |T| result in more uniform distributions for the power occupation numbers and faster thermalization speeds. Finally, as expected, increasing the magnitude of the nonlinearity results in accelerated thermalization. Our findings provide valuable insights into optical thermalization in discrete systems where experimental realization may bring about new possibilities for light manipulation and applications.