The uniaxial chiral medium. which is a modification of well-studied reciprocal chiral material, can be created by embedding microscopic metal helices in an isotropic host medium in such a way that the axes of all helices are oriented parallel to a fixed direction but distributed in random locations. Based on the concept of characteristic waves and the method of angular spectral expansion, cylindrical vector wave functions are rigorously developed to represent the electromagnetic fields in a source-free uniaxial chiral medium. Analysis reveals that the solutions of the source-free vector wave equation for uniaxial chiral medium, which are composed of two transverse waves and a longitudinal wave, can be represented in sum-integral forms of the cylindrical vector wave functions. The addition theorem of the vector wave functions for a uniaxial chiral medium can be directly obtained from its counterpart for the isotropic medium. To widen the application scope of the present cylindrical vector wave functions in a uniaxial chiral medium, a generalized mode-matching method is also proposed to study the two-dimensional electromagnetic scattering of a cylinder with an arbitrary cross section, and a conducting circular cylinder with an inhomogeneous coating thickness. To check the convergence of the present cylindrical vector wave functions for the multiple-body problem, electromagnetic scattering of two circular cylinders of uniaxial chiral media is also investigated. Excellent convergence properties of the cylindrical vector wave functions in these application examples are numerically verified, which establishes the reliability and applicability of the present cylindrical vector wave functions.
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