Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths

It is well known that, under the WKB approximation, the refractive-index profile of a graded-index planar waveguide can be calculated from the corresponding effective-index function, which can be found approximately by least-squares fitting of a set of measured effective indexes. In the previous work, effective indexes measured for a particular type of modes (the TE or TM modes) at a single wavelength are used. This requires that the waveguide supports at least three modes of the same type. In this paper, techniques of combining the effective indexes measured for both mode types and at different wavelengths are proposed and demonstrated with examples. With these techniques, single-mode and two-mode waveguides can be profiled