Abstract
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.
© 2023 Optica Publishing Group
Full Article | PDF ArticleMore Like This
M. A. Dupertuis, M. Proctor, and B. Acklin
J. Opt. Soc. Am. A 11(3) 1159-1166 (1994)
W. B. Joyce and Alice Joyce
J. Opt. Soc. Am. 66(1) 1-8 (1976)
Hassan A. Elagha
J. Opt. Soc. Am. A 29(12) 2679-2687 (2012)