Circuits for light in holographically defined photonic-band-gap materials

We present a theoretical roadmap for three-dimensional optical waveguide networks in holographically defined, diamondlike photonic band gap (PBG) materials. A fully 3D waveguide network is demonstrated through broadband (100-200 nm), single-mode waveguiding in air, coupled with sharp bends in three dimensions with minimal backscattering. Optimal waveguides in the in-plane x and y directions are shown to exhibit nearly 250 nm of single-mode bandwidth for light of wavelengths near 1.5 mu m. Vertical waveguide channels are formed by introducing air defects in a zigzag pattern. Realization of these circuit designs may be achieved through the combination of direct laser writing of defects within the holographically defined photoresist and the subsequent replication of the microchip template with a high refractive index semiconductor such as silicon.