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

摘要

Light reflection plays a crucial role in a number of modern technologies. Inthis paper, analytical expressions for maximal reflected power in any directionand for any polarization are given for generic planar structures made of asingle material represented by a complex scalar susceptibility. The problem ofoptimal light-matter interactions to maximize reflection is formulated as thesolution of an optimization problem in terms of the induced currents, subjectto energy conservation and passivity, which admits a global upper bound byusing Lagrangian duality. The derived upper bounds apply to a broad rangeof planar structures, including metasurfaces, gratings, homogenized films,photonic crystal slabs, and more generally, any inhomogeneous planar structureirrespective of its geometrical details. These bounds also set the limiton the minimum possible thickness, for a given lossy material, to achieve adesired reflectance. Moreover, the results allow the discovery of parameterregions where large improvements in the efficiency of a reflective structureare possible compared to existing designs. Examples are given of the implicationsof these findings for the design of superior and compact reflectivecomponents made of real, imperfect (i.e., lossy) materials, such as ultra-thinand efficient gratings, polarization converters, and light-weight mirrors forsolar/laser sails.