Analytic approach to dielectric optical bent slab waveguides

A rigorous classical analytic model of confined optical wave propagation along 2-D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise frequency domain ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher oder bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.