Geometrical optical activity induced by a continuous distribution of screw dislocations

TL;DR

This paper demonstrates that uniform torsion in a medium induces optical activity and circular birefringence, enabling geometric control of polarization rotation and phase gates, with potential applications in metamaterials and topological insulators.

Contribution

It introduces a geometric theory linking torsion with optical activity, providing design rules for torsion-induced polarization rotation and connecting it to topological electronic responses.

Findings

Torsion causes intrinsic chirality and birefringence in light propagation.

Polarization rotation is linearly proportional to dislocation density and path length.

Millidegree polarization rotations are achievable with current technology.

Abstract

We study light propagation in a medium with uniform torsion, modeled as a continuum of screw dislocations within the geometric theory of defects. By solving Maxwell's equations in covariant form, we show that torsion induces intrinsic chirality and circular birefringence: right- and left-circular polarizations acquire different wavenumbers, leading to a purely geometric optical activity. The polarization plane of a linearly polarized beam rotates according to the simple law $\Delta\theta = \Omega\rho L$, linear in the dislocation density $\Omega$, propagation length $L$, and transverse coordinate $\rho$. This can be recast as an effective birefringence $\Delta n = 2c\Omega\rho/\omega$, providing geometric design rules for torsion-induced rotatory power. Using parameters from dislocated semiconductors, we obtain millidegree rotations over millimetre-scale paths, within reach of modern polarimetric techniques and amenable to enhancement in metamaterial platforms. We also show that the same spiral geometry implements a broadband geometric phase gate for polarization qubits and has an electronic analogue on the surface of cylindrical topological insulators, where torsion shears the Dirac cone, establishing a unified geometric link between torsion, optical activity, and topological electronic responses.