Bandgap engineering and amplification in photonic time crystals

Abstract

Lately, there has been a growing interest in time-varying photonic media
owing to its 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 independent amplification in 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 to offer
new opportunities to manipulate and control the amplification of light for applications
including highly tunable PTC lasers and devices.