Propagating Beam Analysis of Bent Optical Waveguides

Abstract

We employ the propagating beam method to analyze mode coupling in both bent waveguides with a periodic structure and circularly bent waveguides. Our results illustrate the physical origin of and provide error estimates for the often-employed method of transforming a circular fiber into an equivalent straight fiber with a modified refractive index profile.

Beam-propagation method for analysis of z-dependent structures that uses a local oblique coordinate system

“…This problem can be solved by use of the conformal transformation from the curved waveguide to a straight one or by rotation of the coordinate system such that the propagation direction always coincides with the tangent to the waveguide axis at each propagation step. 7 However, the interfaces of the waveguide are required to be parallel to the new propagation direction. If the curved waveguide were tapered, the coupling would still arise because of nonparallel interfaces and could not be treated by simple rotation of the coordinate system.…”