Study on refractive index distribution of the square self-focusing lens

In order to acquire the refractive index distribution of the square self-focusing lens, a semi-empirical method is reported. The diffusion equation's solution under the square boundary conditions is approximated by the solution under the circular boundary conditions. The four unknown coefficients of the approximate solution are acquired by the known refractive index of the square self-focusing lens, and the refractive index is obtained by Jamin interference method. The calculation result agrees well with the experimental data, the average value of the relative error is less than 0.3%.