Computation of electromagnetic fields guided by a cylindrical inhomogeneity in a homogeneous medium of infinite extent

A rigorous numerical method is presented for computing time-harmonic electromagnetic fields that are guided by a transparent, lossless inhomogeneity in a homogeneous medium of infinite extent. Geometrically, the inhomogeneity is a cylinder of arbitrary cross-section. The structure is typical for a uniform open waveguide. On using the wave functions of the circular cylinder outside a cylinder that surrounds the inhomogeneity, and on transforming the electromagnetic-field equations inside this cylinder into a system of first-order ordinary differential equations, a two-point differential eigenproblem is obtained that is solved using standard techniques. Results are presented for waveguides with an equilaterally triangular and a rectangular cross-section, respectively. The latter is studied in detail.