[Paper Review] Symmetry-compatible angular momentum conservation relation in plasmonic vortex lenses with rotational symmetries

Jie Yang, Pengyi Feng+13 more|Lirias (KU Leuven)|Sep 28, 2022

Orbital Angular Momentum in Optics4 citations

TL;DR

This paper introduces a symmetry-compatible angular momentum conservation relation in plasmonic vortex lenses (PVLs) with rotational symmetries, using finite group representation theory to reveal the origin of multiple plasmonic vortices (PVs). It derives a topological charge upper bound at the PVL center and establishes a two-step symmetry-based procedure linking incident and generated PV angular momentum, validated numerically and enabling precise control for nanophotonic applications.

ABSTRACT

Plasmonic vortex lenses (PVLs), producing vortex modes, known as plasmonic vortices (PVs), in the process of plasmonic spin-orbit coupling, provide a promising platform for the realization of many optical vortex-based applications. Very recently, it has been reported that a single PVL can generate multiple PVs. This work exploits the representation theory of finite groups, reveals the symmetry origin of the generated PVs, and derives a new conservation relation based on symmetry principles. Specifically, the symmetry principles divide the near field of the PVL into regions, designate integers, which are the topological charges, to the regions, and, particularly, give an upper bound to the topological charge of the PV at the center of the PVL. Further application of the symmetry principles to the spin-orbit coupling process leads to a new conservation relation. Based on this relation, a two-step procedure is suggested to link the angular momentum of the incident field with the one of the generated PVs through the symmetries of the PVL. This theory is well demonstrated by numerical calculations. This work provides an alternative but essential symmetry perspective on the dynamics of spin-orbit coupling in PVLs, forms a strong complement for the physical investigations performed before, and therefore lays down a solid foundation for flexibly manipulating the PVs for emerging vortex-based nanophotonic applications.

Motivation & Objective

• To uncover the symmetry-driven origin of multiple plasmonic vortices (PVs) in plasmonic vortex lenses (PVLs) with rotational symmetries.
• To derive a new conservation relation for angular momentum in PVLs based on group representation theory.
• To establish a two-step procedure linking the angular momentum of the incident field to that of the generated PVs using PVL symmetry.
• To provide a theoretical framework that complements existing physical models and enables flexible PV manipulation in nanophotonic devices.

Proposed method

• Applying finite group representation theory to analyze the rotational symmetries of PVLs and classify their near-field modes.
• Partitioning the PVL near field into symmetry-defined regions and assigning topological charges as integers to each region.
• Deriving a symmetry-compatible angular momentum conservation relation by analyzing spin-orbit coupling processes under group symmetry constraints.
• Proposing a two-step method: first, using symmetry to assign topological charges to PVs; second, linking incident and generated angular momentum via symmetry selection rules.
• Validating the theoretical framework through numerical simulations of PVLs with various rotational symmetries.
• Establishing an upper bound on the topological charge of the central PV based on the symmetry group's irreducible representations.

Experimental results

Research questions

• RQ1 What is the symmetry origin of multiple plasmonic vortices generated by a single PVL with rotational symmetry?
• RQ2 How can the angular momentum of incident light be conserved and transferred to generated plasmonic vortices in symmetric PVLs?
• RQ3 What is the maximum possible topological charge of the central plasmonic vortex in a PVL with a given rotational symmetry?
• RQ4 How can the symmetry of a PVL be used to predict and control the topological charges of its generated PVs?
• RQ5 Can a systematic two-step procedure be established to link incident field angular momentum to the resulting PVs using symmetry principles?

Key findings

• The symmetry of the PVL divides the near field into regions, each assigned an integer topological charge, which determines the vortex structure.
• A strict upper bound on the topological charge of the central plasmonic vortex is derived from the irreducible representations of the PVL's rotational symmetry group.
• A new symmetry-compatible angular momentum conservation relation is established, linking the angular momentum of the incident field to that of the generated PVs.
• The two-step procedure—symmetry-based charge assignment followed by angular momentum matching—enables predictable and flexible PV engineering.
• Numerical simulations confirm the theoretical predictions, demonstrating consistent agreement between symmetry-derived charge assignments and simulated vortex patterns.
• The framework provides a robust, symmetry-driven alternative to prior phenomenological models, enhancing control over PVs in nanophotonic systems.