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

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.

Automated summary

This paper explores the importance of light reflection in modern technologies and provides analytical expressions for the maximal reflected power in any direction and polarization for generic planar structures. By solving an optimization problem, the authors obtain global upper bounds and discover parameter regions for improving existing designs. The findings have implications for the design of efficient reflective components such as gratings, polarization converters, and lightweight mirrors.