Periodic corrugated dielectric waveguides

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Abstract
Grating coupled radiation and distributed feedback are analyzed in periodically corrugated dielectric waveguides. Several results are derived. First it is shown that gratings (periodic corrugations) have nonzero radiation Fourier coefficients and nonzero distributed feedback Fourier coefficients for all Bragg scattering orders regardless of gating tooth shape—even for sinusoidal and other symmetrical grating teeth. The single exception can occur for rectangularly shaped teeth. Second, an equation for coupling coefficients of hybrid modes is derived. Third, Fourier coefficients of multiple periodic gratings are obtained for rectangular modulation of an arbitrarily shaped grating and for arbitrary modulation of a rectangular shaped grating. Both expansions contain all sum and difference spatial frequencies of the two periods. Finally, a waveguide with two different grating periods on opposite surfaces is studied. To first order the sum and difference spatial frequency Fourier coefficients are zero.

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