In the plane wave scattering from a periodic grating high order diffracted plane waves disappear at a low grazing angle limit of incidence. In this paper the scattering of a beam wave by the end-face of an ordered waveguide system composed of identical cores of equal space is treated by the perturbation method and the scattered field is analytically derived. The possibility that high order diffracted beam waves remain at a low grazing angle limit of incidence is shown.

We describe a geometrical optics approach for the analysis of dielectric tapered waveguides. The method is based on the ray-optical treatment for wave-normal rays defined newly to waves of light in open structures. Geometrical optics fields are represented in terms of two kinds of wave-normal rays: leaky rays and guided rays. Since the behavior of these rays is different in the two regions separated at critical incidence, the geometrical optics fields have certain classes of discontinuity in a transition region between leaky and guided regions. Guided wave solutions are given as a superposition of guided rays that zigzag along the guides, all of which are totally reflected upon the interfaces. By including some leaky rays adjacent to the guided rays, we obtain more accurate guided wave solutions. Calculated results are in excellent agreement with wave optics solutions.