Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes

From a set of effective indexes, a continuous effective-index function is defined, which is then used to construct a refractive-index profile by numerically solving a WKB equation. The method applies to synthesis of profiles from prescribed propagation constants. Profiles for spatial image transmission are presented as an example. The method can also be applied to recovery of Smooth profiles from measured effective indexes. Effects on the recovery of profiles due to errors in measured effective indexes are demonstrated and procedures are given to alleviate those effects.