Finding Propagation Constants of Leaky and Degenerate Modes Using Simultaneous Transcendental Equations of Holey Optical Fibers

This paper presents a simple solution to simultaneous transcendental equations of propagation constants for leaky and degenerate modes. Using a block version of the Sakurai-Sugiura method (SSM) and a criterion for distinguishing physical solutions from spurious ones, we solved a nonlinear matrix equation formulated by the multipole method in a two-dimensional cylindrical coordinate system. Numerical examples showed that we can obtain accurate propagation constants and extract field distributions of leaky and degenerate modes of holey fibers without imposing symmetry. In addition, the condition numbers of the eigenvalues are efficient criteria for distinguishing solutions computed by the block version of the SSM.