Clarification of Floquet-enhanced thermal emission through the nonequilibrium Green's function formalism

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.