Two-dimensional Green's functions for a rotationally invariant anisotropic medium

A coordinate transformation is introduced to map the anisotropic region into a fictitious isotropic region of finite angular extent where the field equations can be easily solved. This results in an infinite series representation which is not convenient for numerical calculations. An alternative representation is found by introduction of an apparently new integral form for the product of two-cylinder functions. The new representation provides physical insight as to the nature of the solution and is attractive from the computational standpoint. The results are analyzed, and a new corner-reflector-type effect is found for certain kinds of materials, which is in agreement with independent calculations. The analysis is of special importance for the derivation of a mathematical statement of a Huygen's principle for this type of material.<
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