A Generalized Floquet Hamiltonian Method for Dispersive Photonic Time Crystals

We present a generalized Floquet Hamiltonian method for dispersive photonic time crystals (PTCs), a class of time-varying media with time-periodic plasma frequencies and damping rates. Using the time-independent Floquet Hamiltonian method, we successfully obtained the quasienergy band dispersions of dispersive PTCs, which show excellent agreement with the temporal transfer matrix method (TTMM) results when applied to temporal multilayers. Furthermore, our approach overcomes the limitations of TTMM by handling arbitrary time interfaces and providing access to both right and left eigenstates, enabling deeper insights into the properties of PTCs. Ultimately, our method significantly advances the analytical and numerical investigations into dispersive time-varying media.