Impact of lattice-shape moduli on band structure of photonic crystals

We conduct a comprehensive study of the effect of the Bravais lattice-shape moduli on the band structure and in particular the band gap of photonic crystals. Unlike the conventional comparisons between triangular and rectangular photonic crystals, where the effect of the volume modulus is not separated, we rigorously decouple the volume modulus and determine the differences that can be attributed only to the shape of the lattice. We observe that the triangular lattice enjoys the largest band gap owing to its unique symmetry properties. We also show that the band gap decreases when the ratio of the lattice constants differs from unity. The use of an appropriate parametrization of the lattice-shape moduli combined with the inherent scaling invariance in the Maxwell equations allows us to cover Bravais lattices of all shape and volume moduli completely and without redundancy.