# Optical Raytracing by using Adiabatic Hamiltonian Method

I'm looking into raytracing a Lüneburg Lens which is a gradient index (GRIN) optical element with a radially varying refractive index: $$n(\rho)=n_0\sqrt{2-\left(\frac{\rho}{R}\right)^2}, 0<\rho<R$$ The good paper by Hanhong Gao et.al, "Design of thin-film photonic metamaterial Lüneburg lens using analytical approach" describes the theoretical background and applies it to the Lüneburg lens, but does not indicate any code which can be used to carry out the raytracing. I'm considering to try out an implementation in Mathematica, however if there is any comparable example of the application of Hamiltonian optics raytracing this would give me a head start.

In the book "Geometric Optics" by Antonio Romano has provided an online site of Mathematica notebooks which were offering some implementation of the Hamiltonian formulations but the Link to these notebooks seems to be broken.

Any info about already existing implementations on Optical Raytracing with Hamiltonian Method would thus be most welcome!

-
Check out anything written on this topic by Greg Forbes. He revolutionized modern raytracing software with Hamiltonian optics. Most of his important works are published through the Journal of the Optical Society of America, stream A (JOSA-A). Go to the OSA website to get to their search engine. Most of his papers will be paywalled, but he did quite a bit of work for Focus software (who sells Zemax) so his stuff published with them may be free access. Otherwise you'll need to go to a uni library. –  WetSavannaAnimal aka Rod Vance Oct 16 '13 at 11:38
@WetSavannaAnimal: I found the Paper series "Using Rays better" by Greg Forbes and Miguel Alonso (who seems to have worked closely together with Greg). I need to check the contents of the papers. Fortunately I'm an OSA member and have access to papers. Thx for the tip! –  Rainer Oct 18 '13 at 5:43