Highly Stable and Rigorous Numerical Model to Design quasi 3D PBG-based Devices

In this chapter we review a very accurate and fast model of Photonic Band-Gap (PBG) structure characterized by a two-dimensional (2D) periodic change of the refractive index and finite height, therefore named quasi 3D PBG. The model is based on the Floquet-Bloch formalism and allows to find all the propagation characteristics, including the space harmonics and the total field distribution, the propagation constants, the guided and radiated power and modal loss induced by the 2D grating. A clear explanation of the physical phenomena occurring when a wave propagates inside the 2D periodic structure is presented, including the photonic band gap formation and the radiation effects. The approach does not require any theoretical approximation, and can be applied to rigorously study any PBG-based multilayer structures. We have applied the model to investigate several structures for both optical and microwave applications.