Light propagation in a birefringent plates with topological charge

TL;DR

This paper derives the Fresnel propagator for a birefringent q-plate, analyzing how it transforms beam profiles and efficiently converts photon spin into orbital angular momentum under ideal conditions.

Contribution

It provides an analytical solution for beam propagation in a birefringent q-plate and demonstrates near-perfect spin-to-orbital angular momentum conversion.

Findings

Analytical beam profile propagation in q-plates.

High-efficiency spin to orbital angular momentum conversion.

Effect of plate thickness on conversion efficiency.

Abstract

We calculated the Fresnel paraxial propagator in a birefringent plate having topological charge $q$ at its center, named "$q$-plate". We studied the change of the beam transverse profile when it traverses the plate. An analytical closed form of the beam profile propagating in the "$q$-plate" can be found for many important specific input beam profiles. We paid particular attention to the plate having a topological unit charge and we found that if small losses due to reflection, absorption and scattering are neglected, the plate can convert the photon spin into orbital angular momentum with up to 100% efficiency, provided the thickness of the plate is less than the Rayleigh range of the incident beam.