Fast calculation of combinations of arbitrary-order cylindrical functions arising in analyses of slotted structures

A fast method is suggested to approximately calculate the combinations of cylindrical functions of noninteger-order (CCFN), which are met in eigenvalue and scattering problems, for various structures treated in cylindrical coordinates. The method is based on low-order interpolation using known values of the combinations of integer- and semi-integer-order cylindrical functions, which are mostly obtained from recurrent formulas. The presented numerical results demonstrate the potentials of the suggested method to calculate a separate CCFN and the cutoff wavenumbers of a slotted structure, whose characteristic matrix contains such CCFNs.