%0 Journal Article %T Detailed derivation of the generalized Snell–Descartes laws from Fermat’s principle %+ Laboratoire Charles Coulomb (L2C) %A Rousseau, Emmanuel %A Felbacq, Didier %< avec comité de lecture %@ 1084-7529 %J Journal of the Optical Society of America. A Optics, Image Science, and Vision %I Optical Society of America %V 40 %N 4 %P 676 %8 2023 %D 2023 %R 10.1364/JOSAA.478123 %K metasurfaces %K Fermat's principle %K generalized Snell-Descartes laws %Z Physics [physics]/Physics [physics]/Optics [physics.optics]Journal articles %X 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. %G English %2 https://hal.science/hal-04073052/document %2 https://hal.science/hal-04073052/file/2023_04_18_HAL%2FOptica-template.pdf %L hal-04073052 %U https://hal.science/hal-04073052 %~ CNRS %~ L2C %~ UNIV-MONTPELLIER %~ UM-2015-2021 %~ UM-EPE