Theoretical Characterization of Multilayer Photonic Crystals having a 2D periodicity

We present a new, 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 new 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 occuring when a wave propagates inside the 2D periodic structure is presented, including the photonic bandgap formation and the radiation effects. The approach does not require any theoretical approximation, and can be applied to study rigorously manner any PBG-based multilayer structures. We have applied the model to investigate several structures for both optical and microwave applications.