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 electric field waveforms and propagation constants) of a single dielectric slab waveguide are considered to be known, and tight-binding is used to compute the propagation constants of several multi-waveguide structures. Analytical solutions are derived for linear and circular arrays of adjacent waveguides. The problem of two similar adjacent waveguides is treated in detail for two cases of similar and different propagation constants of the two waveguides. For this case, the proposed method is verified using the beam propagation method (BPM). Optical band formation and effect of introducing defects is also illustrated by further examples.