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Article Dans Une Revue (Article De Synthèse) Journal of the Optical Society of America. A Optics, Image Science, and Vision Année : 2023

Detailed derivation of the generalized Snell–Descartes laws from Fermat’s principle

Résumé

Beginning with Fermat’s principle, we provide a detailed derivation of the generalized laws of refraction and reflection for a geometry realizing a metasurface. We first solve the Euler–Lagrange equations for a light ray propagating across the metasurface. The ray-path equation is found analytically, and the results are supported by numerical calculations. We get generalized laws of refraction and reflection that have three main features: (i) They are relevant in gradient-index optics and in geometrical optics; (ii) A collection of rays emerges from the metasurface as a result of multiple reflections inside the metasurface; and (iii) The laws, although derived from Fermat’s principle, differ from previously published results.
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Dates et versions

hal-04073052 , version 1 (11-05-2023)

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Emmanuel Rousseau, Didier Felbacq. Detailed derivation of the generalized Snell–Descartes laws from Fermat’s principle. Journal of the Optical Society of America. A Optics, Image Science, and Vision, 2023, 40 (4), pp.676. ⟨10.1364/JOSAA.478123⟩. ⟨hal-04073052⟩
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