How Thin and Efficient Can a Metasurface Reflector Be? Universal Bounds on Reflection for Any Direction and Polarization

• Published in: Advanced optical materials Vol. 11; no. 4
• Main Authors: Abdelrahman, Mohamed Ismail, Monticone, Francesco
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.02.2023
• Subjects: fundamental limits; gratings; Light reflection; light sails; Materials science; Mathematical analysis; Metasurfaces; Optics; Optimization; Photonic crystals; Planar structures; Polarization; reflection; Sails; Upper bounds; Weight reduction
• DOI: 10.1002/adom.202201782
• ISSN: 2195-1071

Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single material represented by a complex scalar susceptibility. The problem of optimal light‐matter interactions to maximize reflection is formulated as the solution of an optimization problem in terms of the induced currents, subject to energy conservation and passivity, which admits a global upper bound by using Lagrangian duality. The derived upper bounds apply to a broad range of planar structures, including metasurfaces, gratings, homogenized films, photonic crystal slabs, and more generally, any inhomogeneous planar structure irrespective of its geometrical details. These bounds also set the limit on the minimum possible thickness, for a given lossy material, to achieve a desired reflectance. Moreover, the results allow the discovery of parameter regions where large improvements in the efficiency of a reflective structure are possible compared to existing designs. Examples are given of the implications of these findings for the design of superior and compact reflective components made of real, imperfect (i.e., lossy) materials, such as ultra‐thin and efficient gratings, polarization converters, and light‐weight mirrors for solar/laser sails. Light reflection plays a crucial role in a number of modern technologies. In this paper, universal bounds for maximal reflected power in any direction and for any polarization are derived for generic planar structures. Examples are given of the implications of these findings for the design of ultra‐thin and efficient reflective gratings, polarization converters, and light‐weight mirrors for solar/laser sails.