Abstract
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.
Mathematics Subject Classification (2010): 78A05, 35Q60
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Notes
- 1.
This inclusion follows from condition (A).
References
C. E. Gutiérrez and Qingbo Huang, The refractor problem in reshaping light beams, Arch. Rational Mech. Anal. 193 (2009), no. 2, 423–443.
C. E. Gutiérrez, The Monge–Ampère equation, Birkhäuser, Boston, MA, 2001.
Acknowledgements
The first author was partially supported by NSF grant DMS–0901430. The second author was supported by CONICET, Argentina.
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Dedicated to the memory of Leon Ehrenpreis
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Gutiérrez, C.E., Tournier, F. (2013). The Parallel Refractor. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_14
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DOI: https://doi.org/10.1007/978-1-4614-4075-8_14
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