A curvilinear framework for vector light fields

TL;DR

This paper introduces a generalized framework for creating vector light fields where the polarization structure is entirely independent of spatial shape, using conformal maps and phase-only spatial light modulators.

Contribution

It presents a novel method to encode polarization structures solely in polarization degrees of freedom, decoupling them from spatial shape using conformal maps.

Findings

Experimental realization of polarization-encoded vector beams

Confirmation of theoretical predictions via Stokes polarimetry

Application to multiple conformal map systems

Abstract

Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce a generalized method to construct vector beams whose structure is entirely encoded in the polarization degree of freedom. Using conformal maps, we construct orthonormal polarization bases from the geometry of the coordinates and encode them experimentally via phase-only spatial light modulators. We apply our method to four systems, elliptical, parabolic, bipolar, and dipole, that represent algebraic and transcendental families of conformal maps. Stokes polarimetry measurements confirm agreement with theoretical predictions.