Dispersion effects in thermal emission from temporal metamaterials: High-frequency cut-offs

The latest breakthroughs in time-varying photonics are fueling novel thermal emission phenomena, for example, showing that the dynamic amplification of quantum vacuum fluctuations, induced by the time-modulation of material properties, enables a mechanism to surpass the black-body spectrum. So far, this issue has only been investigated under the assumption of non-dispersive time-modulations. In this work, we identify the existence of a non-physical diverging behavior in the time-modulated emission spectra at high frequencies, and prove that it is actually attributed to the simplistic assumption of a non-dispersive (temporally local) response of the time-modulation associated with memory-less systems. Accordingly, we upgrade the theoretical formalism by introducing a dispersive response function, showing that it leads to a high-frequency cut-off, thereby eliminating the divergence and hence allowing for the proper computation of the emission spectra of time-modulated materials.