EVANESCENT WAVES AND COMPLEX RAYS FOR MODAL PROPAGATION IN CURVED OPEN WAVEGUIDES.

Evanescent wave tracking (EWT) has provided a new and effective method for analyzing high-frequency trapped mode propagation in longitudinally open dielectric waveguides. It has therefore been suggestive to extend EWT so as to account for mode field leakage when the waveguide is curved. A circularly bent two-dimensional guiding structure has served as a prototype in the present study. Even in this canonical configuration, direct generalization of the EWT procedure, attempted first, has not been achieved so as to bridge the transition from the predominantly evanescent to the predominantly radiating regime as the observer moves away from the guide axis on the convex side. Therefore, the problem has been analyzed alternatively by complex ray tracing (CRT) that involves continuation of initial conditions, boundaries, etc. , into a complex coordinate space. This approach, structured around the complex ray congruences generated by a complex caustic, has been successful. By self-consistent closure of the complex ray system, it has been possible to describe all of the various types of guided modes that may arise on a circular guiding structure. When waveguide axis deviates weakly from circularity, local closure of CRT defines the properties of local modes that adapt continuously to the changing guiding environment. The CRT procedure therefore provides a unified and systematic treatment of a broad class of high-frequency guiding problems which can then be physically interpreted in terms of EWT.