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arXiv · 0711.2052

Computation and visualization of photonic quasicrystal spectra via Blochs theorem

Alejandro W. Rodriguez·Alexander P. McCauley·Yehuda Avniel·Steven G. Johnson
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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.

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Alejandro W. Rodriguez, Alexander P. McCauley, Yehuda Avniel, Steven G. Johnson. 2008-03-07. Computation and visualization of photonic quasicrystal spectra via Blochs theorem. https://doi.org/10.1103/physrevb.77.104201

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