Research on the irreducible Brillouin zone and band structure of two-dimensional photonic crystals

Abstract

It is generally considered that the irreducible Brillouin zone (IBZ) of crystals will not be changed for a given lattice in solid state physics. In fact, for different crystals (crystal = lattice + basis) with the same lattice, the basis’s symmetry, orientation and configuration may make the symmetry of crystal different from lattice. Here, the IBZ of crystal will be changed. This paper, through a specific example of two-dimensional photonic crystals, illuminates that the IBZ of crystal will be changed with the change of bases orientation. The IBZ of crystal expand into the whole first Brillouin zone when the symmetry of crystal is far below its lattice.