Highly Directional Surface Emission from Concentric-Circle Gratings on PlanarOptical Waveguides: The Field Expansion Method

摘要

We describe the azimuthally polarized radiation field surface emitted by ashallow, concentric circle grating located at the film cover interface of a step index, three layer optical waveguide. We employ the field expansion boundary perturbation method to obtain an integral expression, correct to first order, for the radiation field produced when the surface perturbation scatters a transverse electric, circularly symmetric, azimuthally polarized guided wave. We apply the method of stationary phase to the radiation integral to generate an algebraic expression for the far field radiation. Plots of the radiation field are shown for waveguides with annular and full (extending from the origin) sets of concentric circular gratings that scatter incoming, outgoing, and standing circular guided waves.