Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides

We investigate coupled-mode theory in designing high index contrast silicon-on-insulator waveguide couplers and arrayed waveguides. We develop and demonstrate a method of solution to the inverse problem of reconstructing the coupling matrix from the modal profiles obtained, in this case, from finite-difference frequency-domain field calculations. We show that whereas supermode theory provides a good approximation of the mode profiles, next-to-nearest-neighbor coupling becomes significant at small separation distances between arrayed waveguides. These distances are quantified for three different silicon-on-insulator material platforms. We also point out the phenomenon of field skewing and deformation at small separations.