Octonacci Photonic Quasicrystals

TL;DR

This paper theoretically investigates the transmission spectra of one-dimensional Octonacci photonic quasicrystals, revealing fractal, self-similar spectral features, omnidirectional band gaps for TE waves, and mode localization due to quasiperiodicity.

Contribution

It introduces a theoretical analysis of Octonacci photonic quasicrystals, highlighting their fractal spectra, omnidirectional band gaps, and mode localization, which were not previously characterized.

Findings

Transmission spectra exhibit self-similarity and fractal behavior.

Omnidirectional band gaps appear for specific generations in TE waves.

Modes are localized due to quasiperiodic structure.

Abstract

We study theoretically the transmission spectra in one-dimensional photonic quasicrystals, made up of SiO$_2$($A$) and TiO$_2$($B$) materials, organized following the Octonacci sequence, where the $n$th-stage of the multilayer $S_{n}$ is given by the rule $S_{n}=S_{n-1}S_{n-2}S_{n-1}$, for $n\geq 3$ and with $S_{1}=A$ and $S_{2}=B$. The expression for transmittance was obtained by employing a theoretical calculation based in the transfer-matrix method. To normally incident waves, we observe that, for a same generation, the transmission spectra for TE and TM waves are equal, at least qualitatively, and they present a scaling property where a self-similar behavior is obtained, as an evidence that these spectra are fractals. The spectra show regions where the omnidirectional band gaps emerges for specific generations of Octonacci photonic structure, except to TM waves. For TE waves, we note that all of them have the almost same width, for different generations. We also report the localization of modes as a consequence of the quasiperiodicity of the heterostructure