Formulation of Dispersive and Dissipative Time-Varying Media as a Floquet Matrix Eigenproblem

Dispersion is ubiquitous in nature as a result of causality, and dispersive time-varying materials have been widely used in the experimental realization of photonic time-varying media. Here, we derive the Floquet Hamiltonian and formulate Maxwell's equations of dispersive time-varying media as a Floquet matrix eigenproblem. The derived Floquet Hamiltonian allows us to investigate the band structures and eigenmodes of the system. Using the eigenmodes, we identify the Floquet π exceptional points by tracking the variation of Aharonov-Anandan phase. Our theory rigorously reformulates existing models and facilitates the development of Floquet Green's function and resonant mode expansion in open photonic time-varying systems.