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In the context of coupled periodic waveguides, "couplonics" refers to the rigorous equivalence between continuous wave coupling and localized interactions. We extend it here to a cyclic ternary system, looked upon as the simplest discrete photonic crystal with actual periodic boundary conditions. A linear decomposition on a supermode basis enables one to reduce the original six-wave problem to three independent two-wave distributed Bragg reflectors (or 1D PC).

Photonic Crystals, Couplonics, Coupled Mode Theory