An iterative method for optical reconstruction of graded index profiles inplanar dielectric waveguides

A nondestructive technique for the reconstruction of refractive index profi les in planar waveguides is presented and analyzed, The approach is based o n the integral scattering equations, which permit to relate the refractive index of an inhomogeneous layer to the reflected field intensity at differe nt incidence angles, From this formulation, an iterative algorithm is devel oped, such as at each iteration step the problem is formulated as the minim ization of a functional representing the error between the measurements and the model data. The recovered profile is then used to improve the validity of the approximation in performing the next step. In this approach, the un known index profile is represented as the sum of a finite series of basis f unctions avoiding to select a priori the particular functional form (e.g., Gaussian function, complementary error function, etc). The practical effect iveness of this approach is demonstrated by numerically simulating the meas urements for different planar waveguides. The influence of measurement unce rtainty and noise on the stability of the technique is also evaluated.