@article{1061,
  author = {Alejandro Rodriguez and Alexander McCauley and Yehuda Avniel and Steven Johnson},
  title = {Computation and visualization of photonic quasicrystal spectra via Bloch s 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 Maxwell s equations in higher dimensions for any PQC defined by the 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 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.},
  year = {2008},
  journal = {PRB},
  volume = {77},
  number = {10},
  pages = {104201},
  url = {http://link.aps.org/abstract/PRB/v77/e104201},
}