Fast modelling of deeply and fully etched gratings based on the Bloch-Floquet theorem

A model of deeply and fully etched gratings (also identified as one-dimensional waveguide photonic bandgap structures), based on the Bloch-Floquet theorem, has been developed to perform a complete analysis of the electromagnetic (e.m.) wave propagation in the structure, assumed of finite extension, i.e. to determine mode propagation constants, electromagnetic field harmonics and total field distribution, transmission and reflection coefficients, total forward and backward power flow in the structure, guided power and total losses. Comparisons with other accurate numerical methods confirm the accuracy of the new one, whose main advantages are the quickness and the possibility to determine a great amount of information and figures of merit in a few seconds (for each operating wavelength). Moreover, the model allows the designer a complete view of the physical and geometrical device features, so it permits to draw design rules for optimization of photonic bandgap (PBG) waveguide device design.