Coupled contradirectional mode equations are derived to describe Hermite-Gaussian beam interactions in corrugated thin-film waveguides when the grating teeth are curved and/or tilted. Coupling coefficients are evaluated for identical and hybrid modes. The problem of focusing a guided Gaussian beam by reflection from a curved grating is considered. It is shown that the grating curvature should serve to match the phase fronts of the contradirectional Gaussians and the grating should extend axially to include the region where the two beam widths are approximately equal.
© 1979 Optical Society of America
Amos Hardy and William Streifer, "Analysis of waveguided Gaussian beams coupled by misaligned or curved gratings," J. Opt. Soc. Am. 69, 1235-1242 (1979)