Temporal transfer matrix method for Lorentzian dispersive time-varying media

Incorporating dispersion into time-varying media not only holds practical significance but also profoundly transforms the electromagnetic characteristics of such dynamic media. In this work, we have developed a temporal transfer matrix method (TTMM) tailored for time-varying media exhibiting a specific type of dispersion, namely, Lorentzian dispersion. The conventional TTMM for nondispersive time-varying media can be regarded as an approximation of this developed TTMM in the nondispersive limit by ignoring the unobservable infinite-frequency modes. By using this developed TTMM, we have investigated the Floquet bands of Lorentzian dispersive media with time-periodic plasmon frequencies or resonant frequencies. Under temporal modulations, certain degenerate points of the Floquet bands will be lifted, creating bandgaps, while others will give rise to two types of exceptional point (EP) pairs. This sharply contrasts with the well-known Floquet bands of nondispersive time-varying media, where only one type of EP pair exists. Our developed TTMM serves as a powerful tool for investigating the phenomena within the realm of dispersive time-varying media.