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 $\pi$ 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.

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• Metamaterials
• Nonlinear optics
• Photonic crystals
• Photonics
• Plasmonics