Generalized Time-Varying Drude Model for Dispersive and Lossy Modulations

We develop a generalization of the time-varying Drude model, treating carrier density, effective mass, and collision rate as explicit functions of time. We derive expressions for polarization, susceptibility, displacement, and permittivity in different domains. Our analysis reveals that non-adiabatic modulations and time-dependent losses induce rich and distinct behaviors, leading to temporal blurring, selective gating and suppression, and low-frequency spectral reshaping. Besides underpinning and upgrading the current framework on photonics of time-varying media, this model may be useful in the design and fitting theoretical models with experimental realizations.