Negative Refraction Requires Strong Inhomogeneity

TL;DR

This paper derives explicit lower bounds on the size of periodic structures needed for negative refraction, showing that at optical frequencies, strong inhomogeneity is essential for backward wave support.

Contribution

It provides the first explicit bounds linking lattice cell size to negative refraction capabilities in metamaterials and photonic crystals.

Findings

Lattice cell size must be a significant fraction of the wavelength for negative refraction.

Strong inhomogeneity is necessary at optical frequencies.

Supports the design of metamaterials with negative refraction properties.

Abstract

The paper establishes explicit lower bounds for the lattice cell size of periodic structures (metamaterials and photonic crystals) capable of supporting backward waves and producing negative refraction. At optical frequencies, this result implies strong inhomogeneity, in the sense that the cell size cannot be negligible relative to the vacuum wavelength and the Bloch wavelength.