Extreme photonic time crystals: coexisting momentum and frequency bandgaps and Floquet optical response

Periodic variation in the constitutive parameters of a propagating bulk medium over time, while uniform in space, referred to as periodically modulated photonic time crystals, provides a new control modality for wave-matter interaction. Following this, a step-like (square profile) modulation of permittivity and permeability has been utilized to achieve momentum bandgaps (MBGs) in the dispersion diagrams, whereas the modulation of conductivity has been overlooked. In this work, in the beginning, underlying photonic time crystals are extremely modulated with a square profile of permittivity ε(t), permeability μ(t), and conductivity σ(t)—opening simultaneously momentum and frequency bandgaps, which has not been developed to date. The dispersion relation yielding photonic band structure is established with the virtue of the Bloch-Floquet theorem and by exploiting the continuity of electric displacement D(t) and magnetic flux B(t) across simultaneous discontinuities of ε(t), μ(t), and σ(t)—leading to the Krönig-Penney methodology. Furthermore, the amplification of eigenmodes within an MBG is controlled by the conductivity modulation strength mσ and the temporal duty cycle. In addition, the amplitude distribution of higher-order eigenmodes generated by temporal modulation, namely, a frequency comb, is tailored with mσ in a specific band. Moreover, the engineering of the electric field E(t) propagation over time(and its frequency-domain spectrum) under multiple modulation strength schemes is presented. Subsequently, the optical response for a spatially finite temporal slab is studied under normal and oblique (s- and p-polarization) incidence of plane waves. The frequency comb in reflection and transmission spectra against operating frequency and incidence angle is analyzed. Finally, the total absorptance for s- and p-polarization is also discussed. Additionally, the modulation strength of the temporal variation ranges between −1 < mε,μ,σ < 1, whereas earlier studies restricted it to 0 < mε,μ,σ < 1.