Optical properties of 1D photonic time quasicrystals

Photonic time crystals are materials in which the refractive index varies periodically and suddenly in time. This material exhibits unusual properties, such as momentum bands separated by gaps. Because of the sudden change in the optical properties, the light propagating in these materials experiences time refraction and time reflection, analogous to refraction and reflection in conventional photonic crystals. Interference between time-refracted and time-reflected waves gives rise to Floquet–Bloch states and dispersion bands, which are momentum gapped. In this paper, we employ a transfer-matrix treatment to study the propagation of light waves in photonic time quasicrystals composed of two alternating building slabs, A and B , constructed according to Fibonacci, Thue–Morse, and Double-Period sequences. We present numerical results for the photonic band structure in terms of the dimensionless wave-vector k ¯= k / k 0 and the normalized dimensionless Bloch’s angular frequency Ω T / π . Our numerical results show the bandgap behavior as a function of the ratio between refractive indices n BA = n B / n A and layer thicknesses t BA = t B / t A . We also studied the localization and self-similar behavior of the band structures, whose fractality can be described by a power law. We show that the power law scaling index δ , which can be identified as being a diffusion constant of the spectra, presents a non-monotonic dependence on n BA and t BA . Finally, plots of the transmission/reflection spectra, also calculated via the transfer-matrix method, in terms of the dimensionless wave-vector k ¯= k / k 0 , are shown for different values of refractive indices n BA and layer thicknesses t BA .