Modeling of fully etched waveguiding photonic bandgap structures

Modeling of a 1-D finite-height, finite-length fully etched waveguiding photonic bandgap structures, based on the leaky mode propagation method, is proposed for the first time. So far only infinitely long gratings have been modeled by this approach. Finite extension structures having deep grooves, high refractive index contrast, and an arbitrary profile of the etched region can be modeled in very short computer time, starting from the infinitely-long photonic bandgap structure. Useful analytical and closed-form expressions for the reflection and transmission coefficients and out-of-plane losses are derived, which are valid for any operating conditions. One of the most important applications of the model relevant to 1-D photonic bandgap devices is to determine the losses occurring also in 2-D devices. Comparisons of results in terms of transmittance, losses, bandgap position and complex propagation constant with those obtained by the bi-directional mode expansion and propagation method and an exact vectorial method show an excellent agreement together with a strongly reduced CPU time for our method. Full investigations of three different etching profiles (i.e., rectangular, triangular and saw-tooth) are carried out. Particular attention is paid to the physical behavior around the first and second Bragg interaction regions. We demonstrate that the rectangular shape exhibits the highest losses and the widest bandgap, while the saw-tooth grating exhibits the lowest losses and the narrowest bandgap. Quick and accurate determination of the out-of-plane losses in a large variety of photonic bandgap devices is also demonstrated