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The gyromagnetic uniaxial chiral medium, which is a generalization of the well-studied reciprocal chiral material, can be created by mixing three sets of small metal helices in a host gyromagnetic medium (e.g., magnetically biased ferrite), with the axes of two sets perpendicular and parallel to a fixed direction, respectively, and the other set distributed in random orientations and locations. Based on the concept of characteristic waves and the method of angular spectral expansion, vector wave functions are rigorously developed to represent the electromagnetic fields in a source-free gyromagnetic uniaxial chiral medium. The analysis reveals that the solutions of the source-free vector wave equation for the gyromagnetic 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. Addition theorem of the vector wave functions for gyromagnetic uniaxial chiral medium can be directly obtained from its counterpart for isotropic medium. To apply the present formulations for practical applications, an extended mode-matching method is proposed to study the two-dimensional electromagnetic scattering of a gyromagnetic uniaxial chiral cylinder with 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 multiple-body problem, electromagnetic scattering of two circular cylinders of gyromagnetic uniaxial chiral media is also investigated. Excellent convergence properties of the cylindrical vector wave functions in these application examples are numerically verified, whichestablishes the reliability and applicability of the present cylindrical vector wave functions

Vector Wave Functions in Gyromagnetic Uniaxial Chiral Medium and Applications