Equivalent Circuits in Fourier Space for the Calculation of Guided Modes in Cylindrical Dielectric Configurations Based on Measured Index Profile

Mode analysis and dispersion relations are the basic characteristics for cylindrical dielectric waveguides. The waveguide configuration is based on geometry and on the index profile. The nominal index profile is the basis for the calculation of the field profile and the dispersion relations. However, a strong motivation exists for the evaluation of a real index profile. The modern index profile measurement techniques provide with accuracy the index profile in many geometric configurations. Since analytical solutions are non-existent for arbitrary index inhomogeneity, the easily applicable numerical method of equivalent circuits in Fourier space is applied for the evaluation of index profile measurement data. As an example of the application of the method, an arbitrary index profile based on the step index is examined, consisting of a random sequence of index values around the nominal, versus the distance from the center. Very useful results are obtained for dispersion relations and field distribution.