Contributor: Stas Fainer

This is a simulation of a rectangular dielectric material with a refractive index \(n(\rho) = n_0 \sqrt{1-(\alpha \rho)^2}\), where \(n_0=2\) is the refractive index on its central axis and \(\rho \) is the radial distance from its central axis, such that \(\alpha=\frac{\sqrt{3}}{2R} \) where \(R=100 \) is its radius.

The top dielectric in this simulation is made of thin dielectric rectangles of constant refractive index, according to \(n(\rho)\) (the script for creating this dielectric is available here), while the bottom dielectric is a gradient-index material with the refractive index \(n(\rho)\).