Square Gradient-index Selfoc lenses (GRIN) were successfully prepared by Tl+ and K+ ion-exchange. The ion
concentration equation in square class fiber was calculated by variable separation method. The refractive-index profile of
Square GRIN lenses analytic solution is got based on the linear relation between refractive-index and ion concentration.
The computation results are in good agreement with the measured ones. MATLAB partial differential toolbox was used
to numerically solve ion diffusion equation on square boundary conditions, this works is easy to be handled and redound
to the research on Square GRIN Lenses. The refractive-index analytic solution can be predigested and modeled by a
square law function with introducing the concept of incidence directions angle. Based on the function, the ray's
trajectory equation and Numerical Aperture were got. This work shows that the optical properties of Square GRIN lenses
are related to the directions angle.