Computation and visualization of photonic quasicrystal spectra via Blochs theorem

TL;DR

This paper introduces a novel method to compute the spectra and eigenstates of photonic quasicrystals using higher-dimensional Bloch's theorem, avoiding large supercell calculations and enabling efficient analysis of defect states.

Contribution

The authors develop a general approach applying Bloch's theorem in higher dimensions to analyze photonic quasicrystals, simplifying spectrum computation and defect state analysis.

Findings

Successfully applied to 1D quasicrystals as proof of concept.

Allows computation of spectra and defect states without large supercells.

Provides a unified framework for analyzing PQCs using higher-dimensional methods.

Abstract

Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwells equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Blochs theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.