Hypergeometric-Gaussian Modes

TL;DR

This paper introduces a new family of laser beam modes called hypergeometric-Gaussian (HyGG) modes, characterized by a singular phase profile, finite power, and specific intensity patterns, with potential applications in optics.

Contribution

The paper presents the first experimental generation and analysis of HyGG modes, a novel set of laser beam modes with unique phase and intensity characteristics.

Findings

HyGG modes have a singular phase profile and a single bright ring intensity pattern.

HyGG modes are eigenfunctions of photon orbital angular momentum.

HyGG modes can be generated using liquid-crystal spatial light modulators.

Abstract

We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes (Opt. Lett. {\textbf 32}, 742 (2007)), the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some sub-families of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes and the modified Laguerre-Gaussian modes.