Clarification of Floquet--Enhanced Thermal Emission Through the Nonequilibrium Green's Function Formalism

TL;DR

This work addresses the problem of how a time-periodically modulated permittivity drives Floquet-enhanced thermal emission. It develops and cross-validates two rigorous quantum frameworks—nonequilibrium Green's function (NEGF) and macroscopic quantum electrodynamics (MQED)—and demonstrates their formal compatibility via a common Lippmann-Schwinger equation. By analyzing positive- and negative-frequency decompositions and performing second-order perturbation theory, the study shows that a physically meaningful spectrum is finite and that Floquet-induced enhancements are modest. The findings provide a unified theoretical foundation for modeling time-dependent media and reinforce Floquet engineering as a versatile approach to tailor emission dynamics in nanophotonic systems.

Abstract

Floquet engineering offers a powerful route to enhance emission in time-modulated media. Here, we investigate the influence of time-modulated permittivity in silicon carbide on its intensity spectrum. We consider both the nonequilibrium Green's function approach and the macroscopic quantum electrodynamics approach, and establish their formal compatibility by deriving the Lippmann-Schwinger equation in both cases. To analyze spectral features, we propose several methods for decomposing the electric field into positive- and negative-frequency components, along with the criteria required for physical consistency. Our analytical and numerical results show that, when defined appropriately, the intensity spectrum avoids divergence, though the resulting enhancement remains modest. These findings provide a unified theoretical foundation for modeling time-dependent media, and reinforce the utility of Floquet engineering as a versatile platform for tailoring emission dynamics.

Figures (1)

• Figure 1: Frequency spectra of the electric field correlation measured at three distances from the slab. The blue solid curves correspond to the equilibrium value $\mathcal{S}_0$, while the purple dashed curves represent $\mathcal{S}_2$, the leading order correction due to the time modulation. To facilitate comparison, we adopt the same parameters as those used in Fig. 5 of Ref. vazquez-lozano_incandescent_2023.