The Parallel Refractor

Part of the Developments in Mathematics book series (DEVM, volume 28)


Given two homogenous and isotropic media I and II with different refractive indices n I and n II , respectively, we have a source Ω surrounded by media I and a target screen Σ surrounded by media II. We prove existence of interface surfaces between the media that refract collimated radiation emanating from Ω into Σ with prescribed input and output intensities.

Key words

Geometric optics Optimization Refraction 



The first author was partially supported by NSF grant DMS–0901430. The second author was supported by CONICET, Argentina.


  1. GH09.
    C. E. Gutiérrez and Qingbo Huang, The refractor problem in reshaping light beams, Arch. Rational Mech. Anal. 193 (2009), no. 2, 423–443.Google Scholar
  2. Gut01.
    C. E. Gutiérrez, The Monge–Ampère equation, Birkhäuser, Boston, MA, 2001.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA
  2. 2.Instituto Argentino de Matemática, CONICETBuenos AiresArgentina

Personalised recommendations