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Previous methods for determining photonic quasicrystal (PQC) spectra haverelied on the use of large supercells to compute the eigenfrequencies and/orlocal density of states (LDOS). In this manuscript, we present a method bywhich the energy spectrum and the eigenstates of a PQC can be obtained bysolving Maxwells equations in higher dimensions for any PQC defined by thestandard cut-and-project construction, to which a generalization of Blochstheorem applies. In addition, we demonstrate how one can compute bandstructures with defect states in the higher-dimensional superspace with noadditional computational cost. As a proof of concept, these general ideas aredemonstrated for the simple case of one-dimensional quasicrystals, which canalso be solved by simple transfer-matrix techniques.

Computation and visualization of photonic quasicrystal spectra via Blochs theorem