Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Reconstruction of the refractive index profile of planar waveguides using ray tracing analysis

We propose a method for refractive index profiling based on measuring coordinates and angles of laser beams passing across the waveguide layer. Calculations are performed by solving an integral equation using new global optimization methods.

Planar waveguide refractive index profile reconstruction using global optimization

The approach taken here of reconstruction of the refractive index profile of planar waveguides involves solving a non-linear integral equation with Tikhonov regularization. Using global optimization with the new cutting angle and discrete gradient methods has yielded an acceptable reconstruction, even in the presence of significant noise in the data.