Mode behaviour on bent planar dielectric waveguides

A nonperturbative analysis of the field and propagation constant changes in a bent step index planar waveguide is presented, with the aim of investigating limitations on standard perturbation theory. Mode behaviour for two extreme regimes in which perturbation theory is no longer valid are demonstrated: single-mode guides with very small bend radius (~1 mm), in which the field in the cladding becomes oscillatory, and large multimode structures bent with a constant radius of curvature. Equations are derived for the dispersion relation whose solutions give the real propagation constant of the bent waveguide