, Volume 37, Issue 1-3, pp 37-61

Analytic approach to dielectric optical bent slab waveguides

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Abstract

A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise 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 order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.

1Partly these notions originate from the use of a ray picture for the description of bent waveguides, or from approximate models in terms of “equivalent” leaky straight waveguide profiles. We will avoid these viewpoints in the present paper.