On leaky-wave approach of rigorous modes coupled in multilayered periodic waveguides

The field supported by multilayered periodic waveguides is well characteriz ed by only one or two discrete leaky waves, rather than by a more complicat ed field representation that includes continuous spectra. The rigorous leak y-modes coupled in multilayered geometry can be then treated by relatively simpler and analytic model that describes the operation of practical optoel ectronic devices in terms of leakage effects. To complement our modeling, w e discuss and emphasize novel mathematical formulations based on the field orthogonality conditions of TE and TM modes coupled in multilayered periodi c structures. In addition, to show the validity of our approach we numerica lly evaluate new physical meaning to illustrate quantitatively and rigorous ly the coupling efficiency of grating-assisted directional couplers (GADCs) . The results reveal that the systematic and effective technique yields phe nomenolgically useful interpretations.