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.Comment: Published in Physical Review B, 77 104201, 200