FDTD modeling of a grating-assisted coupler integrated with a photonic bandgap resonant cavity

The finite-difference time-domain approach (FDTD) has been selected to model grating structures because of its ability to model complex structures and materials. Some of the many grating applications studied with the FDTD approach include gratings that can be used in waveguide environments as directional couplers to transfer energy into radiating modes which propagate in predefined directions or as mode converters to convert energy between various modes in the same waveguide, and that can be used as diffraction components to transfer energy between waves propagating in different directions. While analytical methods can handle infinite, periodic gratings well, numerical methods usually are needed for general finite, aperiodic gratings. We first examine the scattering of a guided wave from a finite grating to achieve a directional coupler to transfer energy into a predefined direction. We then propose a new grating configuration which incorporates a photonic bandgap structure (PBS) to enhance that output coupling. Furthermore, it is shown that by virtue of the resonant cavity formed by the PBS and the grating that the relative amounts of the output scattered and the transmitted guided wave power can be significantly modified. The potential applications for optical switches and wavelength demultiplexers based on this new configuration are also discussed.