https://doi.org/10.1051/epjconf/202023802005
An energy conservative hp-scheme for light propagation using Liouville’s equation for geometrical optics
1 Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, the Netherlands
2 Signify - High Tech Campus 7, 5656 AE, Eindhoven, the Netherlands
* e-mail: r.a.m.v.gestel@tue.nl
Published online: 20 August 2020
In this contribution an alternative method to standard forward ray-tracing is briefly outlined. The method is based on a phase-space description of light propagating through an optical system. The propagation of light rays are governed by Hamilton’s equations. Conservation of energy and étendue for a beam of light, allow us to derive a Liouville’s equation for the energy propagation through an optical system. Liouville’s equation is solved numerically using an hp-adaptive scheme, which for a smooth refractive index field is energy conservative. A proper treatment of optical interfaces ensures that the scheme is energy conservative over the full domain.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
