The near field refractor
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 4, p. 655-684
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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 homogeneous 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.

@article{AIHPC_2014__31_4_655_0,
author = {Guti\'errez, Cristian E. and Huang, Qingbo},
title = {The near field refractor},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {31},
number = {4},
year = {2014},
pages = {655-684},
doi = {10.1016/j.anihpc.2013.07.001},
zbl = {1301.78001},
mrnumber = {3249808},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2014__31_4_655_0}
}

Gutiérrez, Cristian E.; Huang, Qingbo. The near field refractor. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 4, pp. 655-684. doi : 10.1016/j.anihpc.2013.07.001. http://www.numdam.org/item/AIHPC_2014__31_4_655_0/

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