Modal theory of lamellar gratings in a conical diffraction mount

Abstract

Botten et al.1,2 developed a rigorous modal theory of lamellar gratings of arbitrary refractive indices and groove depth at the classical mount (grating groove perpendicular to the plane of incidence). Later, certain numerical aspects of their work was improved by Suratteau et al.3 In this paper, the results of these two groups of authors are extended to the conical diffraction mount (arbitrary angle of incidence). First, the fields in the grating region are decomposed into the H⊥ and E⊥ components. Then the coupled differential equations and the associated boundary conditions are separated into two sets identical to those for the TE and TM fields in the classical mount, provided that the wavelength is replaced by a reduced wavelength. Hence the completeness and orthogonality of the basis functions are proved, and all the theoretical results and numerical techniques of Refs. 1-3 can be used. The relative merits of different projection schemes in the final step of solving the grating problem using the method of moments are discussed. Computational results of diffraction efficiencies and polarization characteristics of lamellar gratings in conical diffraction mount are included.