Fig. 1: Band structures of time-varying Lorentzian material.
From: Expanding momentum bandgaps in photonic time crystals through resonances
a, Band structure of a time-modulated bulk material when its plasma frequency is modulated harmonically. b, Dispersion relations of a stationary (unmodulated) bulk material when its plasma frequency is ωp1 (red line) and ωp2 (green line). c, Band structure of a time-modulated bulk material when its resonance frequency is modulated harmonically. d, Dispersion relations of a stationary (not modulated) bulk material when its resonance frequency is ωr1 (red line) and ωr2 (green line). In all of the panels, the wavenumber is normalized by \({k}_{{\rm{r0}}}={\omega }_{{\rm{r0}}}\sqrt{{\epsilon }_{0}{\mu }_{0}}\), and the material parameters are chosen as m = 0.2, ωm/2 = 0.95ωr0, γ = 0 and ωp0 = 3.5ωr0. A time convention of ejωt is considered, with j being the imaginary unit.
