Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures

TL;DR

This paper explores the thermodynamic behavior of incoherent multimode optical waves, revealing phase transitions and condensation phenomena at positive and negative temperatures in spatio-temporal regimes, with implications for optical beam control.

Contribution

It introduces a comprehensive analysis of spatio-temporal equilibrium states of optical waves using Bose-Einstein statistics, highlighting novel negative temperature states and phase transitions in multimode fibers.

Findings

Positive temperature equilibrium leads to spatial mode condensation.

Negative temperature states exhibit inverted modal populations.

Spatio-temporal Bose-Einstein condensation predicted at negative temperatures.

Abstract

Optical thermalization has been recently studied theoretically and experimentally in the 2D spatial evolution of (quasi-)monochromatic light waves propagating in multimode fibers. In this work, we investigate the spatio-temporal equilibrium properties of incoherent multimode optical waves through the analysis of the (2+1)D Bose-Einstein thermal distribution and the corresponding classical Rayleigh-Jeans approximation. In the anomalous dispersion regime, the spatio-temporal equilibrium is characterized by positive temperatures. In this regime, we show that as the number of modes of the waveguide increases, the fundamental spatial mode becomes macroscopically populated, while its temporal spectrum undergoes significant narrowing, ultimately leading to complete (2+1)D spatio-temporal condensation in the thermodynamic limit. In the normal dispersion regime, the spatio-temporal equilibrium is characterized by negative temperature states that exhibit a hybrid character: the spatial equilibrium displays an inverted modal population, whereas the temporal spectrum remains peaked around the fundamental (carrier) optical frequency. In this regime, we predict that spatio-temporal light waves exhibit a phase transition to Bose-Einstein condensation at negative temperatures, which occurs by increasing the temperature above a negative critical value. Our work opens new avenues for future research, including the possibility for a dual spatio-temporal beam cleaning through full spatio-temporal light condensation, and lay the groundwork for the development of spatio-temporal optical thermodynamics.