Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules, and simulations

We demonstrate on-chip, single-mode, waveguiding of light in air for a variety of 2D-3D photonic band gap (PBG) heterostructures. These include square spiral, woodpile, slanted pore, and inverse opal three-dimensional (3D) photonic crystals intercalated with a 2D (planar) photonic crystal microchip. Design rules are established to yield maximal single-mode waveguiding bandwidths of up to roughly 180 nanometers centered at a wavelength of 1.5 microns. This can be achieved with 3D PBG materials with gaps as small as 15% of the PBG center frequency. Finite-difference time-domain (FDTD) simulations of light flow in optical mirocircuits within such heterostructures reveal tolerance to layer misalignment and other fabrication-related structural disorder. We provide an interpretation of the universal mechanism for diffractionless light propagation in 2D-3D photonic crystal heterostructures. We demonstrate that planar, on-chip, optical microcircuitry similar to that of two-dimensional (2D) photonic crystals is almost universally achievable within the engineered electromagnetic vacuum of 3D PBG materials.