The variable separation method and coordinate transformation is presented for solving the
refractive index distribution of the regular hexagon GRIN lens. Through the software
programming, the exact solution of the refractive index distribution is proved by the correctness.
The result is obtained for the manufacture of imaging systems and characteristics. The model can
be extended to solve the even-numbered polygon edges in the positive refractive index distribution
of GRIN lens.
A buried 3-D optical waveguide have been fabricated by Tl<sup>+</sup>-Na<sup>+</sup> ion-exchange technology on BK7 glass substrates, the
refractive-index profile of the waveguides in cross-sectional were determined with the interference method technique;
The refractive-index distribution function n(x,y) for optical waveguides in cross-sectional was improved, and the
refractive index profile was reconstructed by MATLAB, and the shapes of the index profile in the cross-sectional are in
good agreement with experimental results; The shapes of the refractive-index distribution of 3-D optical waveguide in
cross-sectional can be reconstructed by the improved function n(x,y) easily.