On a surface integral representation for homogeneous anisotropic regions: two-dimensional case

A mathematical statement of the Huygen´s principle for an electromagnetic field in an anisotropic region is obtained by a linear mapping of the original anisotropic region into a complex isotropic region using the material permeability and permittivity tensors. The original field equations are reduced to canonical form so that they resemble Helmholtz equations in transform space. This allows the use Huygen´s principle in the transform space, after which the result is mapped back into real space; here the resulting contour quantities can be expressed in terms of tangential field quantities, using Maxwell´s equations. The field representation is found to be polarization-dependent. In this two-dimensional analysis, each polarization has a different representation and is therefore treated both separately and using duality. Some elementary applications to scattering are presented and discussed in detail