A Fast Iterative Procedure To Solve Wkb Equation In Optical Planar Waveguides With Graded-Index Profiles

Abstract

We propose a numerical method to determine effective indices and other related parameters of a planar graded-index waveguide. The secant method uses initial guess to iterate solutions of the WKB equation which is applied to waveguides characterization. The initial guess we choose is the normalized propagation constant of the waveguide. Effective indices, turning points, dispersion curves and cutoff frequencies of a guide with known index profile are obtained by simple iterations for a mode order m. The method is easy to implement and it gives results with good accuracy and may be compared to those existing in literature.