# Constructing the Near field and Far field with Reactive Metagratings: Study on the Degrees of Freedom

## TL;DR

This paper demonstrates that passive, lossless metagratings with engineered near fields can precisely control all diffraction orders, enabling advanced wavefront manipulation across the electromagnetic spectrum.

## Contribution

It introduces a method to achieve perfect control of diffraction orders using 2 degrees of freedom per propagating order in passive, lossless metagratings.

## Key findings

- Theoretical framework for near and far field control with metagratings
- Verification through numerical simulations and experiments
- Applicable to wavefront manipulation across the electromagnetic spectrum

## Abstract

We report that metamaterial-inspired one-dimensional gratings (or metagratings) can be used to control nonpropagating diffraction orders as well as propagating ones. By accurate engineering of the near field, it becomes possible to satisfy power-conservation conditions and achieve perfect control over all propagating diffraction orders with passive and lossless metagratings. We show that each propagating diffraction order requires 2 degrees of freedom represented by passive and lossless loaded thin "wires." This provides a solution to the old problem of power management between diffraction orders created by a grating. The theory developed is verified by both three-dimensional full-wave numerical simulations and experimental measurements, and can be readily applied to the design of wavefront-manipulation devices over the entire electromagnetic spectrum as well as in different fields of physics.