The refractor problem in reshaping light beams

DOI10.1007/s00205-008-0165-xzbMath1173.78005OpenAlexW1987245369MaRDI QIDQ834764

Qingbo Huang, Cristian E. Gutiérrez

Publication date: 27 August 2009

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-008-0165-x

zbMATH Keywords

existence of solutionuniqueness of solutionrefractor problem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Transport processes in time-dependent statistical mechanics (82C70) Variational methods applied to problems in optics and electromagnetic theory (78M30)

Related Items (26)

Existence of weak solutions to refraction problems in negative refractive index materials ⋮ On the numerical solution of the far field refractor problem ⋮ Radial solutions for fully nonlinear elliptic equations of Monge-Ampère type ⋮ On the numerical solution of the near field refractor problem ⋮ \(C^{1, \alpha}\) estimates for the parallel refractor ⋮ On the \(L_q\)-reflector problem in \(\mathbb{R}^n\) with non-Euclidean norm ⋮ \(L^\infty\)-estimates in optimal transport for non quadratic costs ⋮ On the generalized \(L_q\)-reflector inverse problem with variational methods ⋮ On singular sets of \(c\)-concave functions ⋮ Monotone discretization of the Monge–Ampère equation of optimal transport ⋮ An iterative method for generated Jacobian equations ⋮ Entire subsolutions of a kind of \(k\)-Hessian type equations with gradient terms ⋮ The near field refractor ⋮ Chromatic aberration in metalenses ⋮ On the existence of dichromatic single element lenses ⋮ InteriorC^2,αRegularity for Potential Functions in Optimal Transportation ⋮ Regularity for the near field parallel refractor and reflector problems ⋮ Freeform lens design for scattering data with general radiant fields ⋮ Refractor surfaces determined by near-field data ⋮ Local near field refractors and reflectors ⋮ Aspherical Lens Design and Imaging ⋮ An overview of mathematical modeling of geometric optics problems involving refraction ⋮ Refractors in anisotropic media associated with norms ⋮ An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design ⋮ Metasurfaces and optimal transport ⋮ Boundary \(C^{2, \alpha}\) estimates for Monge-Ampère type equations

Cites Work

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• Weak solutions of one inverse problem in geometric optics
• On the regularity of solutions of optimal transportation problems
• Reflector problem in \({\mathbb R^n}\) endowed with non-Euclidean norm
• On a Monge-Ampère equation arising in geometric optics
• On the design of a reflector antenna. II
• Regularity of potential functions of the optimal transportation problem
• On the regularity of reflector antennas
• Existence of optimal maps in the reflector-type problems
• On the design of a reflector antenna
• Optimal Transport

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