Realization of Impedance Boundary in Terms of a Slab of Wave-guiding Medium

Abstract

Introducing a class of metamaterial, labeled as wave-guiding anisotropic media, it shown that given impedance boundary conditions can be exactly realized by a slab of such a material when backed by a PEC plane. An analytic relation is derived between the surface admittance dyadic of the boundary and the parameters of the material slab and verifled with non-trivial special cases of the theory. DOI: 10.2529/PIERS060904062925 The impedance boundary condition (IBC) deflnes a linear relation between the time-harmonic electric and magnetic fleld components tangential to the boundary surface. Denoting by Ys the surface-admittance dyadic and by n the outer normal, the reation can be expressed as n £ H = Ys ¢ E: The admittance dyadic is two-dimensional satisfying n ¢ Ys = Ys ¢ n = 0: The IBC is required to make the solution of an electromagnetic boundary-value problem unique. Physically, IBCs are generally approximate when they replace real interface conditions at a surface separating two regions. Mathematically IBCs make the problem easier to handle in restricting the region of solution to one side of the surface, only. The basic form of the IBC with scalar surface impedance was introduced by Shchukin and Leontovich in the 1940's (1). Its use in solving electromagnetic problems is, however, limited when applied to physical interface problems. Basically, to be exact, Shchukin-Leontovich IBC requires that the fleld be constant along the boundary. For a planar boundary this is satisfled for a normally incident plane wave, while for oblique incidence the IBC introduces some error. During the last couple of decades, modiflcations to the basic IBC have been made by treating the surface impedance as an operator. Taking care of the lowest-order derivatives of the fleld along the boundary surface, numerical procedures based on the generalized IBC have been generated. In contrast to the view that IBC's are approximative in nature one can point out that there exist problems where the IBC is exact. Of course it is known that a PEC obstacle can be exactly represented by the surface impedance Zs = 0 and the PMC obstacle by the surface admittance Ys = 0. Also, certain tuned corrugated structures can be represented by an impedance dyadic with zero and inflnite components along two orthogonal directions on the surface, as the soft-and-hard surface. Actually these correspond to physical realizations for some special cases of the impedance surface. An idea on how to construct a realization for the general surface admittance dyadic Ys was obtained when a realization for another special case, the perfect electromagnetic (PEMC) boundary, was recently found (2,3). The realization was based on a certain metamaterial, labeled as gyrotropic wave-guiding medium. In the present case the wave-guiding medium is deflned more generally as an anisotropic medium with permittivity and permeability dyadics consisting of components normal and transverse to the guiding z axis,