The near field refractor
Cristian E. Gutiérrez
Department of Mathematics, Temple University, Philadelphia, PA 19122, United StatesQingbo Huang
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, United States
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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 homogeneous media with different refractive indices that refract radiation emanating from the origin into a target domain contained in an dimensional hypersurface. The input and output energy are prescribed. This implies the existence of lenses focusing radiation in a prescribed manner.
Cite this article
Cristian E. Gutiérrez, Qingbo Huang, The near field refractor. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 4, pp. 655–684
DOI 10.1016/J.ANIHPC.2013.07.001