Interleaving two-dimensional lattices to create three-dimensional photonicbandgap structures

A two-dimensional lattice consists of an inhomogeneous dielectric medium wh ich has periodic variations of permittivity along two linear directions, an d is uniform in the third dimension. The paper considers a class of three-d imensional photonic bandgap materials formed by the interleaving of a pair of two-dimensional lattices whose uniform directions are mutually orthogona l, the so-called 'woodpile' geometry. It is shown by numerical calculations that the strong polarisation discrimination exhibited by the constituent t wo-dimensional sublattices in their respective stopbands leads to a complet ely three-dimensional photonic bandgap crystal in all polarisations when th e two sublattices are interleaved. For a general class of such synthetic cr ystals having arbitrary two-dimensional distributions in the sublattices, m any properties of the three-dimensional interleaved crystal can be predicte d directly from a knowledge of the properties of the sublattices, thereby r adically the computational cost of their inhomogeneous dielectric medium wh ich periodic variations of permittivity along properties reducing me determ ination.