Temporal Evolution of Blackbody Radiation in a One-Dimensional Photonic Time-Crystal
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 exclusively on PTC-based amplification of coherent light. Here, we theoretically investigate the PTC-based amplification of thermal radiation, specifically blackbody radiation. Such amplification is not only fundamentally intriguing due to the thermal radiation's stochastic nature, but also technologically relevant because thermal radiation's ubiquity, which implies that its amplification generally accompanies that of coherent radiation. For simplicity, and due to the experimental relevance of PTC amplification in transmission lines, we consider amplification in a one-dimensional medium. To analyze the amplification of blackbody radiation in a PTC, we examine the electromagnetic fields' spatial correlations and spatial spectra. We show that the spatial spectra of initially blackbody radiation converge periodically toward Gaussian profiles with progressively increasing amplitudes, coherence lengths, and spatial- and wavenumber-domain purities. We demonstrate that these asymptotic behaviors are governed by the PTC momentum band structure and can be understood using a rotating-wave approximation for the pseudo-Hermitian dynamics of the electromagnetic field in a PTC. Beyond revealing the fundamental evolution of thermal radiation in time-varying media, our numerical framework provides a general approach for analyzing the dynamics of stochastic electromagnetic fields in PTCs and time-varying media, in general. The results also provide physical insight and practical guidance for the design of PTC-based amplifiers, where the concurrent amplification of parasitic thermal radiation may occur.