Computation and visualization of photonic quasicrystal spectra via Bloch's theorem

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

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


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. In this paper, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwell's equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Bloch's theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the same higher-dimensional superspace. 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.

Original languageEnglish (US)
Article number104201
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number10
StatePublished - Mar 7 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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