Effects of Blazing Through a Lamellar Grating

Abstract

The lamellar grating, with grooves having rectangular profile, if examined from a purely geometrical-optics point of view, is seen to produce backscatter for wave lengths λ_m= (—2d/m) sin θ_i, where d is the period of grating, θ_i being the angle between the incident wave and the surface normal to the grating, and λ_m is the wave length of m^th back-scattered wave. A grating is said to be idealized whenever it is perfectly reflecting of infinite spatial extent. In the present paper, an attempt has been made to determine the groove field ψ_g (P) as a wedge solution of Helmholtz's wave equation subject to general boundary condition on the groove surfaces. The results of Double Fourier series and the Complex Fourier Double Transforms have been used for finding the groove field co-efficients. Moreover, the principle of Conservation of Power in the groove has been used for finding the relative powers of the groove fields. Finally, the relative groove dimensions have been formulated under various conditions of blazing. Conditions of blazing for a Comb grating have been obtained as a limiting case when the grating period approaches the groove-width.

Indexing terms:

• Lamellar grating
• Grating period
• Groove-width and Groove field