The Temporal Evolution of Blackbody Radiation in a One-Dimensional Photonic Time-Crystal

Abstract

Perhaps one of the most intriguing phenomena in time-varying-media photonics is the amplification of light in a photonic time crystal (PTC). However, studies to date have focused only on the PTC-based amplification of coherent light. In this work, we theoretically examine the PTC-based amplification of thermal radiation, specifically blackbody radiation. Such amplification is fundamentally intriguing because of the inherently stochastic nature of thermal radiation, and technologically relevant because of its ubiquity. For simplicity, and because of the experimental relevance of transmission lines, we consider a one-dimensional medium. To analyze the PTC-based amplification of blackbody radiation, we examine the spatial correlations and spatial spectra of the electromagnetic fields. We show that the initially blackbody radiation periodically converges to Gaussian spatial correlations and spectra, with gradually increasing amplitudes, coherence lengths, and both spatial- and wavenumber-domain purities. We further demonstrate that these asymptotic behaviors are governed by the momentum band structure of the PTC and can be understood using a rotating-wave approximation for the pseudo-Hermitian dynamics of an electromagnetic field in a PTC.