Efficient solution of eigenvalue equations of optical waveguiding structures

A general numerical method is presented that is capable of extracting all the zeros of a complex equation. This method allows accurate determination of the complex propagation constants of general multilayer optical and microwave planar waveguides, the computation of energy states and their lifetimes of semiconductor heterostructures, and the roots of complex transcendental equations from other scientific disciplines. The method differs from previous approaches in that the time-consuming differentiation of the complex function is not required. Furthermore, the present method is not affected by the presence of complex poles and so can be used for the solution of meromorphic transcendental equations. In practice, the method is found to be much faster than other rigorous approaches