A technique is presented for computing the spatial variation of dielectric permittivity in waveguides, directly from the distribution with mode number of the mode indices. The method applies to two-dimensional as well as to three-dimensional axially symmetric media in which the permittivity varies only in a direction transverse to the axis of guidance. It provides a means for inverting the well-known WKB formula for mode guidance, and by design contains only the limitations that are inherent in the WKB asymptotic method.
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