Bandgap engineering and amplification in photonic time crystals

Abstract Recently, there has been a growing interest in time-varying photonic media owing to their significant potential in the field of wave manipulation. Here, we explore the exotic characteristics of wave amplification in a photonic time crystal (PTC) made of a spatially homogeneous medium where the refractive index varies periodically in time. Based on qualitative and quantitative analysis of the amplification, we show that the amplification not only depends on the choice of wave vector of a propagating light but also attains different values in different bandgaps. Our approach further extends towards achieving the minimum amount of variation of permittivity required to open momentum gaps to facilitate the phase-dependent amplification of PTCs. Further, we investigate the impact of permittivity variation and choice of number of temporal unit cells to truncate a PTC to mimic the properties of infinite PTC and offer new opportunities to manipulate and control the amplification of light for applications including highly tunable PTC lasers and devices.