The boundary value techniques in vector–field diffraction theories are generalized to describe electromagnetic scattering of plane waves by a finite number of parallel, rectangular grooves corrugated on a metallic (infinitely conducting) ground plane. Each of the grooves has its own feature size and location for representing a general grating structure in multilevel binary optics. The multiple-scattering matrix is derived for determining the scattering coefficients that lead to a fast convergence in the Bessel-function series representation of the scattered-field angular spectrum. The solution remains stable from the long-wavelength (the Rayleigh limit) to the short-wavelength region (the geometrical optics limit). It is found that any N-groove scattered field can be treated as the sum of N single-groove radiation fields and the cross-groove coupling fields. A coupling index is introduced to measure the coupling effect. Numerical examples of two, six, and twelve grooves are examined in different spectral regions. Plots of the coupling index are generated to show the feasibility of using pattern superposition for an approximate solution.
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