Dynamical Equivalent Circuit for 1-D Periodic Compound Gratings


Metallic compound gratings are studied in this work by suggests that of an analytical equivalent circuit approach so as to get its transmission and reflection properties when illuminated by a TM-polarized plane wave. A compound grating consists of the periodic repetition of a finite number of slits carved out of a thick metal slab (reflection grating) or connecting 2 separated open regions through teams of slits within the metal slab (transmission grating). The equivalent circuit is rigorously obtained beginning from a simplified version of the integral equation for the electrical field at the slits apertures. That equivalent circuit involves transmission-line sections that account for the basic and lowest order diffracted modes (that will offer the “dynamical” nature to this equivalent circuit), and lumped parts to model the result of all the upper order diffracted modes. All the relevant and complex features of the spectra can be satisfactorily explained in terms of the topology and characteristics of the equivalent circuit. In contrast with some previously reported circuit models, all the dynamical and quasi-static circuit elements are analytically and explicitly obtained in terms of the geometric and electrical parameters of the grating. The accuracy of the approximate circuit model is very smart over a terribly wide band, as it's demonstrated by comparison with full-wave data computed with commercial electromagnetic solvers.

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