Band structure calculations of 2D photonic pseudoquasicrystals obtainable by holographic lithography

The most interesting phenomena in photonic crystals stipulate the presence of omnidirectional band gap, i.e. overlapping of stop bands in all directions. Higher rotational symmetry and isotropy of quasicrystals in comparison with ordinary crystal give a hope to achieve a gap opening at lower dielectric contrasts. But nonperiodic nature of quasicrystals makes the size of stop bands lower than in the case of ordinary periodic crystal. We study transition from periodic structure to nonperiodic one by considering pseudoquasicrystals - quasicrystal approximants with growing period to weigh advantages and disadvantages of quasicrystals. We consider the structures that can be obtained by multiple exposure holographic lithography for the case of 2, 3, 4, and 6-fold exposure by two wave interference pattern, corresponding square, hexagonal, 8-fold and 12-fold symmetry lattice.