Topologically protected four-dimensional optical singularities

TL;DR

This paper introduces a topologically protected four-dimensional polarization singularity in optical fields, created using a metasurface-lens system, with potential applications in topological photonics and sensing.

Contribution

It is the first demonstration of a complete, topologically protected polarization singularity in 4D space, expanding the understanding of optical singularities.

Findings

First complete 4D polarization singularity demonstrated

Field Jacobian used for designing higher-dimensional singularities

Potential applications in topological photonics and sensing

Abstract

Optical singularities play a major role in modern optics and are frequently deployed in structured light, super-resolution microscopy, and holography. While phase singularities are uniquely defined as locations of undefined phase, polarization singularities studied thus far are either partial, i.e., bright points of well-defined polarization, or unstable for small field perturbations. We demonstrate for the first time a complete, topologically protected polarization singularity; it is located in the 4D space spanned by the three spatial dimensions and the wavelength and is created in the focus of a cascaded metasurface-lens system. The field Jacobian plays a key role in the design of such higher-dimensional singularities, which can be extended to multidimensional wave phenomena, and pave the way to novel applications in topological photonics and precision sensing.