One-dimensional time-Floquet photonic crystal

Abstract

Using the Floquet Hamiltonian derived based on the time-dependent perturbation theory, we investigated the quasienergy bands of a one-dimensional time-Floquet photonic crystal (PC). The PC contains two alternating layers with different permittivies in the static case which are labeled as A and B. The permittivity of layer A is modulated periodically in time. We considered two cases, first the modulation function is a function of time only and second it is a function of both time and space through an unique combination. In the former case, although the permittivity of the whole medium is space-time-modulated, the quasienergy bands are symmetric because inversion symmetry is preserved. Different from the space-time-modulated medium often discussed previously, e.g. a homogeneous medium with the permittivity space-time-modulated according to a wavelike function, where either only exception points (EPs) or only quasienergy gaps generate, the coupling between the positive (negative) and positive (negative) bands in the time-Floquet PC results in quasienergy gaps, while the coupling between the positive and negative bands leads to pairs of EPs, enabling the coexistence of quasienergy gaps and EPs, when the modulation is on the real part of the permittivity. In the latter case, the quasienergy bands become asymmetric since time-reversal and inversion symmetries are simultaneously broken. The coupling between the positive (negative) and positive (negative) bands still results in quasienergy gaps, while the coupling between the positive and negative bands leads to quasienergy gaps at a small modulation speed and pairs of EPs at a high modulation speed.