Theory of curved diffraction gratings

A coupled-mode theory is presented for the curved diffraction grating. In general, a numerical analysis is required but it is shown that, for the circularly curved grating, the coupled-mode equations are linearly tapered and can be solved analytically. It is shown that, by curving a grating, both the input acceptance angle and the fractional bandwidth can be increased very substantially. The analysis is essentially two dimensional and has direct application to thin-film integrated optics.