Hermite-Laguerre-Gaussian Vector Modes

TL;DR

This paper introduces a new class of vector modes, called Hybrid Hermite-Laguerre-Gaussian (HHLG) modes, combining modes from Hermite- and Laguerre-Gaussian families, with potential applications in communications and optical technologies.

Contribution

The paper presents the first demonstration of vector modes formed from scalar modes of different families, expanding the design space for vector beam applications.

Findings

HHLG vector modes exhibit polarization dependence on propagation.

First demonstration of cross-family scalar mode superposition in vector modes.

Potential for diverse applications in optical communications and metrology.

Abstract

Vector modes are well-defined field distributions with spatially varying polarisation states, rendering them irreducible to the product of a single spatial mode and a single polarisation state. Traditionally, the spatial degree of freedom of vector modes is constructed using two orthogonal modes from the same family. In this letter, we introduce a novel class of vector modes whose spatial degree of freedom is encoded by combining modes from both the Hermite- and Laguerre-Gaussian families. This particular superposition is not arbitrary, and we provide a detailed explanation of the methodology employed to achieve it. Notably, this new class of vector modes, which we term Hybrid Hermite-Laguerre-Gaussian (HHLG) vector modes, gives rise to subsets of modes exhibiting polarisation dependence on propagation due to the difference in mode orders between the constituent Hermite- and Laguerre-Gaussian modes. To the best of our knowledge, this is the first demonstration of vector modes composed of two scalar modes originating from different families. We anticipate diverse applications for HHLG vector modes in fields such as free-space communications, information encryption, optical metrology, and beyond.