Diffraction by surface-relief gratings with conic cross-sectional grating shapes

Diffraction of plane waves by dielectric surface-relief gratings with conic (elliptic, hyperbolic, parabolic) cross-sectional grating shapes is analyzed, using a simple transmittance theory. Integral expressions for the complex amplitudes of the diffracted waves are given for these structures. The calculated results indicate new types of diffraction behavior compared with corresponding results for the commonly studied grating shapes (sinusoidal, rectangular, triangular). In particular, these structures are shown to exhibit a large number of diffracted waves with similar intensities. It is also shown that a bandpasslike behavior (a variable number of fairly even-intensity orders with reasonably sharp cutoff) is obtainable.