Surface Field Analytical Solution of the Impedance Boundary Condition Circular Cylinder Canonical Problem

A surface field analytical solution of the impedance boundary condition circular cylinder canonical problem is contributed in the work at hand. The accurate representation of the primary ray contribution of the tangential surface magnetic field, of a tangential magnetic current excited relative electromagnetic structure, is given via series expansion in powers of the normalized surface impedance. Furthermore, each term in the series is represented as series of the inverse of the cylinder radius. This is achieved by approximating the Hankel functions by a uniform asymptotic expansion within the spectral integral representation of the relevant Green's function. All the resulted integrals are evaluated analytically in an exact fashion, and thus, the final process entails only summations and differentiations. The attained formulas are valid both within and outside the paraxial region. Validity of the contributed analytical solution is provided by successful comparison with published results.