Multimode network description of a planar periodic metal-strip grating at a dielectric interface-II: small-aperture and small-obstacle solutions

For pt.I see ibid., vol.37, no.3, p.534-41 (1989). Two analytical small-argument solution procedures for integral equations are presented. Explicit expressions for the elements of the coupling matrices in the small-aperture and small-obstacle ranges are derived for both TE and TM polarizations. Simple and useful equivalent network descriptions in which all of the network elements are in very simple analytical form are derived. When the discontinuity is electrically small, the resulting network becomes dramatically simple. The various networks, together with estimates for their ranges of applicability, are discussed. Finally, numerical comparisons with an independent numerical reference solution are presented. These show that the simple networks are indeed very accurate within their ranges of applicability