Knots of Darkness in Atmospheric Turbulence

TL;DR

This paper explores how optical knots, which are topologically stable light structures, behave under atmospheric turbulence, revealing their stability in weak turbulence and potential for turbulence probing.

Contribution

It provides the first experimental and theoretical analysis of optical knot stability in turbulent environments, demonstrating topological invariance in weak turbulence and its limits.

Findings

Number of crossings preserved in weak turbulence

Topological invariants may not be conserved in strong turbulence

Potential for 3D turbulence probing using optical knots

Abstract

Topology, which originated as a mathematical discipline, nowadays advances the understanding of many branches of science and technology from elementary particle physics and cosmology to condensed matter physics. In optics, the topology of light and darkness facilitates new degrees of freedom for sculpting optical beams beyond conventionally used amplitude, phase, and polarization. This fundamentally new, spatial dimension opens new opportunities for several optical applications, ranging from optical manipulation, trapping, data processing, optical sensing and metrology, enhanced imaging, and microscopy, to classical and quantum communications. While topological stability of mathematical knots implying robustness to perturbations suggests their potential as information carriers, the behavior of optical knots in perturbative environments such as atmospheric turbulence is largely unexplored. Here, we experimentally and theoretically investigate the effects of atmospheric turbulence of optical knot stability and demonstrate that the number of crossing (the topological invariant) is preserved in the weak-turbulence regime, but may not be conserved in the stronger turbulence conditions. The turbulent medium is simulated in the laboratory using phase screens, which carry the refractive index changes associated with the Kolmogorov power spectrum, encoded in a spatial light modulator. The optical knots are reconstructed by single-shot measurements of the complex field, and the resilience of the knot topology is analyzed for various realistic turbulence strengths. These studies may give rise to entirely new approaches to the three-dimensional (3D) spatially resolved probing of turbulence.