On solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers

The problem of solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers is considered. A method combining the positive features of the Muller method and the phase variation method based on the argument principle is proposed. The implementation of the method is described. For estimating the correctness of the solutions obtained, a new approach employing the convergence to zero of the period-averaged power flux of complex waves is suggested.