Fundamentals of Couplonics

摘要

We call COUPLONICS the systematic extension of analytical Coupled-Wave Equations to two-dimensional Photonic Crystals, most specifically in the context of its application to coupled Photonic Crystal Waveguides. The present work is chiefly devoted to the generic study of a pair of mutually coupled periodic waveguides. Thoroughly investigating the cases where both co- and contra-directional coupling mechanisms are either distributed or localized, we prove the formally rigorous equivalence between the two configurations. By working in the basis of the eigenmodes, the general 2D problem of a periodic array of mutually coupled periodic waveguides can be reduced to a finite set of strictly 1D sub-problems. We use a normalization procedure that gives universal responses, in dimensionless parameters, whatever the dimensions - or even the physical nature - of the waves under consideration. These results illustrate once more the well-known deep behavioral analogies between electromagnetic, sonic or electronic waves in their respective "crystals".