Features of search for complex solutions of non-self-adjoint boundary value problems of electrodynamics

Abstract

The features of finding of complex solutions of the dispersion equations of guiding electrodynamic structures waves described by non-self-adjoint operators have been considered. These solutions are found using the combined numerical method for complex roots finding combining the Muller method and the phase variation method. A brief explanation of the combined search method essence has been given, and its advantages have been described. As examples, structures with simple geometry are selected in order to avoid difficult mathematical expressions and focus on the process of complex solutions finding. The guiding electrodynamic structures both without losses and with absorbing metal films have been considered in the approximation of the surface current method and based on its real thickness. A new approach to evaluate the physical correctness and accuracy of the results of solving dispersion problems set in an open form for guiding structures described by non-self-adjoint operators has been shown – by the tendency to zero of the power flow of proper complex waves on average over a period through the cross section of a non-dissipative guide structure. The formulation and the solution features of the adjoint boundary value problem for a round open dielectric waveguide have been considered. The existence possibility of the adjoint waves in this waveguide has been shown.