Highly directional surface emission from concentric-circle gratings on planar optical waveguides: the field expansion method

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Abstract
We describe the azimuthally polarized radiation field surface emitted by a shallow, 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.