Analytical Design of Printed-Circuit-Board (PCB) Metagratings for Perfect Anomalous Reflection

TL;DR

This paper introduces an analytical method for designing PCB-based metagratings that achieve highly efficient, wide-angle anomalous reflection, simplifying the design process and eliminating the need for extensive simulations.

Contribution

It provides a closed-form formalism for designing PCB metagratings with perfect reflection efficiency, avoiding complex numerical optimizations and enabling practical implementation.

Findings

Design method verified with commercial solvers

Achieves near-unity reflection efficiency

Simplifies the transition from theory to physical structure

Abstract

We present an analytical scheme for the design of realistic metagratings for wide-angle engineered reflection. These recently proposed planar structures can reflect an incident plane wave into a prescribed (generally non-specular) angle with very high efficiencies, using only a single meta-atom per period. Such devices offer a means to overcome the implementation difficulties associated with standard metasurfaces (consisting of closely-packed subwavelength meta-atoms) and the relatively low efficiencies of gradient metasurfaces. In contrast to previous work, in which accurate systematic design was limited to metagratings unrealistically suspended in free space, we derive herein a closed-form formalism allowing realization of printed-circuit-board (PCB) metagrating perfect reflectors, comprised of loaded conducting strips defined on standard metal-backed dielectric substrate. The derivation yields a detailed procedure for the determination of the substrate thickness and conductor geometry required to achieve unitary coupling efficiencies, without requiring even a single full-wave simulation. Our methodology, verified via commercial solvers, ultimately allows one to proceed from a theoretical design to synthesis of a full physical structure, avoiding the time-consuming numerical optimizations typically involved in standard metasurface design.