Thermal Emission Effects in Time-Varying Dispersive Media

In the last few years, temporal metamaterials have emerged as a powerful platform for dynamically controlling optical properties and light-matter interactions, becoming one of the most active research areas in optics and nanophotonics.This concept has recently been extended to thermal emission, establishing a theoretical framework for incandescence in time-varying media and showing extraordinary thermal emission effects.However, for simplicity, that analysis has been restricted to non-dispersive (instantaneous) time modulations.In this work, we extend this framework to include dispersion effects, a fundamental aspect gaining increasing attention in the field.The main contribution is the identification of a non-physical divergence at high frequencies in the emission spectra -a feature attributed to the non-dispersive approach-which is resolved by incorporating dispersion, naturally leading to high-frequency spectral cutoffs.Beyond enabling more accurate emission spectra and the possibility to calculate total radiated power calculations, our findings provide key theoretical insights that could aid experimental research on thermal emission in time-varying media.