Simplified universal dispersion curves for graded-index planar waveguides based on the WKB method

A new way of normalizing the WKB equation for graded-index optical planar waveguides is presented. It is found that the normalized propagation constant for the guided mode of a waveguide depends only on a single parameter, called the normalized mode order. For each profile shape, the new normalized WKB equation allows a single universal dispersion curve to be obtained that applies to all guided modes under all operating conditions. Examples are given for a number of practical profile shapes. The present approach provides a particularly simple description of the dispersion characteristics of graded-index optical waveguides.<
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