Tight-Binding Analysis of Coupled Dielectric Waveguide Structures

 Based on the mathematical similarity of the Schrödinger and Helmholtz equations, the tight-binding method has been employed for solving optical waveguide problems, in a manner similar to the methods commonly used in solid state physics. The solutions (TE mode waveforms and propagation constants) of a single dielectric waveguide are considered to be known, and tight-binding is used to compute the propagation constants of several multiwaveguide structures. Analytical solutions are derived for linear and circular arrays of adjacent waveguides The problem of two similar adjacent waveguides is treated in detail with the propagation modes of the waveguides being similar or different. For this case computer simulation is used to compare the proposed method to BPM (Beam Propagation Method) to test its validity. The results of the two approaches agree satisfactorily. Three examples further illustrate the proposed method and clarify the effect of defects in the waveguide array on the obtained band diagram

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