The impedance boundary conditions and effective surface impedance of inhomogeneous metals

I.M. Kaganova

Institute for High Pressure Physics
Russian Academy of Sciences
142190 Troitsk, Moscow Region, Russia

We present the nonperturbative results for the effective impedance of strongly inhomogeneous metals valid in the frequency region of the impedance (the Leontovich) boundary conditions applicability [1,2]. The inhomogeneity is due to the properties of the metal or/and the surface roughness.

If the surface of an inhomogeneous metal is flat, the effective surface impedance associated with the reflection of an averaged electromagnetic wave is equal the value of the local impedance tensor averaged over the surface inhomogeneities (Ref.[1]). This result is exact within the accuracy of the impedance boundary conditions. It is suitable both under the conditions of normal and anomalous skin effect.

As an example, we examine strongly anisotropic polycrystalline metals (the inhomogeneity is due to the misorientation of discrete single crystal grains). Under the conditions of normal skin effect the effective impedance is expressed in terms of the principle values of the static conductivity tensor of single crystal grains (Ref.[1]).

Under the conditions of extremely anomalous skin effect the relation between the current and the electric field strength is non-local. With regard to the spatial dispersion the elements of the impedance tensor of a single crystal metal are expressed in terms of integrals over the Fermi surface. The Fermi surfaces of the majority of real metals are extremely complex. On the other hand, it is usual to think of a polycrystal as of an effective isotropic metal with a spherical Fermi surface.

We present the general expression allowing us to calculate the effective impedance of a polycrystalline metal when the equation of the Fermi surface is known. Some model Fermi surfaces are examined. In the vicinity of the electronic topological transition the singularities of the effective impedance related to the change of the topology of the Fermi surface are calculated (Ref.[3]). Our results show that though a polycrystal is an isotropic medium in average, it is not sufficient to consider it as a metal with an effective spherical Fermi surface.

A similar approach for calculation of the effective impedance of metals with rough surfaces is proposed in Ref.[2]. For strongly rough surfaces it allows us to calculate the ohmic losses and the shift of the reflected wave, if we know the magnetic vector in the vicinity of the perfect conductor of the same geometry. One-dimension rough surfaces are examined. Particular attention is paid to the influence of the generated evanescent waves and the difference of the values of the components of the effective impedance tensor relating to different polarizations of the incident wave. We show that when the roughness of the surface is rather strong, the element of the effective impedance tensor relating to the p-polarization state is much greater than the input local impedance. As an example, the effective impedance tensor associated with one-dimensional lamellar grating is calculated.


1. A.M.Dykhne, I.M.Kaganova, Phys. Rep. 288 (1997) 263-290
2. A.M.Dykhne, I.M.Kaganova (to be published)
3. I.M.Kaganova, M.I.Kaganov, Phys.Rev.B 63 (2001) 054202