Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors

Abstract

Metallic surface-relief diffractive cylindrical mirrors are designed for on-axis and off-axis focusing and incidence configurations. These diffractive structures are analyzed by both rigorous and scalar integral methods. Two design methods, based on initial assumptions of zero-thickness and finite-thickness structures, are presented for determining the zone-boundary locations and the surface-relief mirror profiles for the general case of an off-axis incident plane wave and off-axis focusing. With the use of these methods, continuous diffractive, multilevel diffractive, and continuous nondiffractive mirrors were designed. Rigorous analysis is performed for both TE and TM polarizations by using an open-region formulation of the boundary element method (BEM) suitable for regions of complex refractive index such as finite-conductivity metals. Three scalar integral methods corresponding to Dirichlet, Neumann, and Kirchhoff boundary conditions are also used to analyze the diffractive mirrors. The diffracted fields from both the rigorous BEM and the scalar methods of analysis are used to calculate a number of performance metrics including diffraction efficiency, sidelobe power, total reflected power, and focal spot size. The performance of the mirrors is evaluated, and the accuracy of the various scalar methods is determined.