Semi-Analytical Method for Electromagnetic Propagation in Biaxially Anisotropic Cylindrical Waveguides

This paper introduces a semi-analytical method for decoupling and solving Maxwell's equations in biaxially anisotropic media expressed in cylindrical coordinates. The problem is reduced to a pair of coupled differential equations for the axial electric and magnetic fields, and conditions for their decoupling are examined. As a preliminary case study, we verify that the field solutions for a homogeneous anisotropic coaxial waveguide can be expressed as a linear combination of Bessel and Hankel functions of the first kind, generally with complex-valued, non-integer orders. This approach enables a reduction in the modal cutoff frequency, which is advantageous for minimizing waveguide dimensions in right-handed media and enables unconventional propagation characteristics in metamaterial devices.