JournalsaihpcVol. 31, No. 4pp. 655–684

The near field refractor

  • Cristian E. Gutiérrez

    Department of Mathematics, Temple University, Philadelphia, PA 19122, United States
  • Qingbo Huang

    Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, United States
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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 n1n−1 dimensional hypersurface. The input and output energy are prescribed. This implies the existence of lenses focusing radiation in a prescribed manner.

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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