Computation and visualization of photonic quasicrystal spectra via Blochs theorem

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.

Published in Physical Review B, 77 104201, 2008

References in corpus (3)

• Photonic quasicrystals for general purpose nonlinear optical frequency conversion
• Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional 5-fold and 8-fold symmetric quasiperiodic photonic crystals
• Non-spiky density of states of an icosahedral quasicrystal

Cited by in corpus (5)

• Synthetic Dimension in Photonics
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Graded quasiperiodic metamaterials perform fractal rainbow trapping
• Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate Systems
• Elastodynamical properties of Sturmian structured media