Three-dimensional field representation in a ten-parameter cylindrically symmetric anisotropic material

A vector-field representation of the electromagnetic field in a cylindrically symmetric anisotropic region is derived and discussed in terms of its usefulness as an analytical tool for studying basic wave processes in anisotropic materials. The field representation clearly displays the polarization coupling nature of an electromagnetic field in a cylindrically symmetric anisotropic material. The representation is also attractive from the practical standpoint, since the mathematical model of absolute (i.e. not relative to free-space) permeability and permittivity tensors is ideal for representing general anisotropically coated cylindrical structures. The vector problem is reduced to a scalar problem for the axial fields. In the solution of the set of second-order partial differential equations for the axial fields, a type of generalized vector cylinder function encountered when a contour representation of the Barnes type is employed for the two unknown scalars is discussed. The special case for which polarization decoupling occurs is described