Abstract

The symmetry properties of the diffracted orders of gratings in the resonance domain are frequently used in diffractive optics [1]. For example, a beam-splitter element or star coupler (fan-out to N) is obtained with a grating that produces N equal-efficiencies diffraction orders. In general, those gratings are synthesized by using a parametric optimization algorithm combined to rigorous electromagnetic theory. Their shape is then precisely defined. However, in certain cases, the identity of the values of the transmitted efficiencies stems from simple considerations on the symmetry of the field at the bottom of the grid and it does not require drastic specifications on the motif of the grating. It is shown in [2] that lamellar perfectly conducting gratings produce two symmetric transmitted orders with equal amplitude if they are illuminated under -1 Littrow mounting and if the width a of the groove satisfies λ/2<n_ga<λ in s-polarization and n_ga <λ/2 in p-polarization, (where λ is the wavelength of the incident beam, n_g is the refractive index of the material filling the groove, n₁ and n₂ are the refractive indices of the superstrate and substrate, respectively, see Fig. 1).

© 1998 Optical Society of America