Solution of dispersion relations for planar waveguides in the case of complex roots

A method for calculating the complex roots of a nonlinear equation is described whereby the solution of the problem is reduced to quadratures. Applications of the method to the investigation of dispersion relations for various open waveguide structures with a complex dielectric permittivity are discussed. The possibilities of the prismatic excitation of modes corresponding to the roots of the dispersion relations on different Riemann sheets are analyzed. Solutions are obtained for the inverse problems of reconstructing complex mode propagation constants and determining the parameters of films that guide waveguide and leaky modes. The solution is based on processing of the angular dependence of the reflection coefficient in a prismatic excitation scheme. Zh. Tekh. Fiz. 68, 88–95 (April 1998)