Orientation-dependent handedness and chiral design

TL;DR

This paper introduces an orientation-dependent framework for quantifying chirality, allowing objects to be simultaneously right and left handed, and demonstrates its application across biological, mechanical, and optical systems.

Contribution

It proposes a novel chirality quantification scheme based on viewing direction, resolving paradoxes and aiding the design of chiral metamaterials from symmetry principles.

Findings

Orientation dependence of handedness demonstrated in three systems

Quantitative agreement with computed chirality pseudotensors

Framework resolves longstanding paradoxes in chirality definition

Abstract

Chirality occupies a central role in fields ranging from biological self-assembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the right-hand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systems - a biomimetic elastic bilayer, a chiral propeller, and optical metamaterial - and find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.