We present a rigorous analytical approach to diffraction problems posed by multilayered grating structures that incorporate metallic and dielectric elements having arbitrary shapes. The dielectric media can be either transparent or absorbing and may exhibit biaxial anisotropy, while the metallic materials may have finite or infinite conductivities. Our approach uses a modal formulation that describes each layer of the grating configuration in terms of an electrical transmission-line unit. The boundary conditions between adjacent layers are generally expressed by an interface transformer whose properties are dictated by the modal characteristics of the two layers. The electromagnetic behavior of a complex grating configuration can thus be represented by an equivalent network that has simple canonic constituents. Such a formulation of the wave scattering problem serves to systematically derive the diffracted fields everywhere. In addition, it provides a convenient scheme for stable numerical evaluations that have good convergence properties. We demonstrate the accuracy and effectiveness of this approach by examples that include comparisons with situations having exact solutions for the diffracted fields.
© 2001 Optical Society of America
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(230.5160) Optical devices : Photodetectors
(260.2110) Physical optics : Electromagnetic optics
Mingming Jiang, Theodor Tamir, and Shuzhang Zhang, "Modal theory of diffraction by multilayered gratings containing dielectric and metallic components," J. Opt. Soc. Am. A 18, 807-820 (2001)