English

The Near Field Refractor

Analysis of PDEs 2015-06-16 v1 Optics

Abstract

We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces separating two homogenous media with different refractive indices that refract radiation emanating from the origin into a target domain contained in an n-1 dimensional hypersurface. The input and output energy are prescribed. This implies the existence of lenses focusing radiation in a prescribed manner.

Keywords

Cite

@article{arxiv.1307.5709,
  title  = {The Near Field Refractor},
  author = {Cristian E. Gutierrez and Qingbo Huang},
  journal= {arXiv preprint arXiv:1307.5709},
  year   = {2015}
}

Comments

39 pages, 4 figures, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (to appear). Geometric optics, lens design, measure equations, Descartes ovals, Monge-Ampere type equations

R2 v1 2026-06-22T00:55:25.716Z