Reconstruction of refractive index profile of planar waveguide using inverse WKB method

Abstract

A characterization method of planar waveguides, namely m- line measurement has been utilized to reconstruct refractive index profile in planar waveguide. This method gives some values of incident angle that can be coupled in to waveguide, which after some mathematical calculations can provide its mode indices. To reconstruct the refractive index profile from mode indices as a function of normalized film thickness we use Inverse Wentzel-Kramers-Brillouin method. Furthermore, we select the value of n<SUB>0</SUB> that give the smoothest refractive index profile by finding the minimum sum of the squares of second differences of the profile. For this purpose, we implement reiterative, trial and error method on some values above the measured fundamental effective index value as a guess of the surface index. The result has been smoothed using curve fitting algorithm to exponential and Gaussian profile. The result confirm that index profile of planar waveguide can be reconstructed mathematically and the profile can be obtained more accurate by the proposed curve fitting technique than the basic IWKB method.