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 / k₀ and the normalized dimensionless Bloch’s angular frequency T/. Our numerical results show the band-gap behavior as a function of the ratio between refraction indices n₁₀ = n₁/n₀ and layer thicknesses t₁₀ = t₁/t₀. 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, which can be identified as being a diffusion constant of the spectra, presents a non-monotonic dependence on n₁₀ and t₁₀. Finally, plots of the transmission/reflection spectra, also calculated via transfer-matrix method, in terms of the dimensionless wave-vector k = k / k₀, are shown for different values of refraction indices n₁₀ and layer thicknesses t₁₀.