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Creation and characterization of vector vortex modes for classical and quantum communication
Bienvenu Ndagano, Isaac Nape, Mitchell A. Cox, Carmelo Rosales-Guzman, Andrew Forbes
TL;DR
The paper addresses how vector vortex modes can serve as structured information carriers while being created, characterized, detected, and propagated through imperfect media. It reviews these tools, compares probabilistic and deterministic detection, and reports modal degradation from perturbations alongside a deterministic scheme that overcomes detection losses.
Problem
Vector vortex communication requires understanding how to create, characterize, detect, and preserve non-separable spatial-polarization modes in classical and quantum links.
Method
The paper reviews generation, propagation, and detection methods, uses entanglement-inspired measures and modal decomposition, and compares filter-based with deterministic detection.
Results
Modal crosstalk degrades vector vortex modes in turbulence and imperfect fibre, while deterministic detection avoids the dimension-dependent loss of probabilistic filtering.
Takeaways & Limitations
Deterministic detection preserves the benefits of increased dimensionality for quantum communication and signal for classical communication links.
Abstract
from arXiv · showhide
Vector vortex beams are structured states of light that are non-separable in their polarisation and spatial mode, they are eigenmodes of free-space and many fibre systems, and have the capacity to be used as a modal basis for both classical and quantum communication. Here we outline recent progress in our understanding of these modes, from their creation to their characterization and detection. We then use these tools to study the propagation behaviour of such modes in free-space and optical fibre and show that modal cross-talk results in a decay of vector states into separable scalar modes, with a concomitant loss of information. We present a comparison between probabilistic and deterministic detection schemes showing that the former, while ubiquitous, negates the very benefit of increased dimensionality in quantum communication while reducing signal in classical communication links. This work provides a useful introduction to the field as well as presenting new findings and perspectives to advance it further.
I. INTRODUCTION
Structured light adds spatial degrees of freedom to optical communication, while vector vortex modes couple spatial mode and polarization non-separably. The paper reviews their creation, propagation, and detection for classical and quantum communication.
- Structured light is being explored to provide new optical communication degrees of freedom for increased bandwidth and security.
- Mode division multiplexing uses orthonormal spatial modes as independent classical communication channels.
- Higher-dimensional QKD can improve security and secure key rates, with each photon carrying up to log2(d) bits.
- Vector modes combine spatial mode and polarization non-separably, and vector vortex modes support rotationally symmetric, alignment-free QKD.
- The paper reviews generation, propagation, and detection, then examines atmospheric turbulence and optical-fibre modal crosstalk.
II. BASIC DEFINITIONS
Vector vortex modes combine oppositely charged OAM components with polarization, forming non-separable states that can be represented on higher-order Poincaré spheres. Their amplitudes and spatial envelopes determine whether the resulting field is vectorial or scalar and how it propagates.
- Scalar OAM modes form a subset of vector vortex modes, which combine spatial and polarization degrees of freedom.
- The field E combines exp(iℓφ) right-circular and exp(−iℓφ + iγ) left-circular components, with θ controlling their relative amplitudes.
- At θ = π/4 the field produces vector vortex modes, whereas θ = 0 or π produces right- or left-circularly polarized scalar OAM beams.
- A rotating linear polarizer produces a two-lobe intensity pattern that rotates with the transmission axis, linking polarization measurements to spatial structure.
- On the higher-order Poincaré sphere, scalar OAM basis modes occupy the poles while vector modes occupy the equator.
- Amplitude envelopes can tailor vector beams for Bessel, fibre, or free-space propagation, but propagation can excite undesired radial modes with substantial energy.
III. GENERATION OF VECTOR VORTEX MODES
The paper reviews accessible methods for generating vector vortex modes, contrasting interferometric SLM schemes with geometric-phase approaches such as q-plates.
- Dynamic-phase generation: Standard vector-mode generation uses an SLM to independently modulate orthogonal polarization components before recombination.An interferometric arrangement splits the beam into orthogonal polarizations, aligns them to the SLM, modulates them separately, and recombines them.
- Dynamic-phase generation: A Sagnac-interferometer implementation uses a PBS, separate SLM holograms, and a dove prism to produce opposite OAM charges.The beam is divided into horizontal and vertical polarization paths, each modulated by an SLM hologram; the dove prism ensures opposite charges ℓ.
- Practical constraints: SLMs are versatile but lossy because only the first diffracted order contains the desired modulation.Spiral phase plates avoid this loss mechanism but are difficult to manufacture and lack versatility in operating wavelength and spatial mode.
- Geometric-phase generation: Geometric phase can be generated through birefringence, including q-plates that provide locally varying birefringence and spin-orbit coupling.The q-plate transformation depends on its charge q, and this approach can produce the states represented on the high-order Poincaré sphere.
- Geometric-phase generation: Geometric-phase transformations have also been implemented experimentally using sub-wavelength gratings and metamaterials.These implementations are followed by the need to determine which mode was produced and its purity.
IV. DETECTION OF VECTOR VORTEX BEAMS
Qualitative rotating-polarizer patterns indicate vectorial structure, but they do not quantitatively determine the quality of a vector vortex beam.
- Qualitative detection: Rotating-polarizer measurements produce changing intensity patterns that are routinely used as qualitative evidence of vectorial structure.Because vector vortex beams have spatially varying polarization, their intensity patterns change as the polarizer transmission axis rotates.
A. The vector quality factor
The vector quality factor quantifies polarization–spatial-mode non-separability, using Pauli-matrix projections to track the transition from scalar to maximally vectorial modes.
- Definition: The vector quality factor measures whether a beam’s spatial and polarization degrees of freedom are separable or non-separable.For θ = π/4, the electric field cannot be written as a product of space and polarization, motivating the quantum-inspired measure.
- Measurement: The projection layout measures left- and right-circular polarization components against OAM eigenstates for vector and scalar modes.The phase holograms encoded on the SLM realize the spatial projections used in the measurement.
- Measurement: The VQF is obtained from the Bloch-vector length calculated from expectation values of the Pauli matrices.These expectation values come from optical projections onto the matrices’ eigenvectors, with OAM and polarization serving as alternative projection degrees of freedom.
- Results: The VQF varies from 0 to 1 as θ increases from 0 to π/4.This parameter change corresponds to movement on the high-order Poincaré sphere from a pole to the equator, where vector vortex modes have maximum non-separability.
B. Deterministic and filter-based detections
The paper contrasts probabilistic filtering with deterministic sorting for vector vortex modes, showing that deterministic detection can sort all modes without dimension-dependent loss, whereas filtering incurs substantial loss.
- Modal decomposition: Vector modal decomposition expresses an arbitrary optical field as a weighted superposition of basis vector modes.
- Modal decomposition: The four-dimensional ℓ=1 modal decomposition measures cross-talk by quantifying power detected in mode i for input mode j.The experiment decomposes each vector mode with respect to itself and the other basis modes.
- Filter-based measurement: Filtering uses geometric-phase optics and two paths, but its beamsplitter introduces an inherent 50% intensity loss and each arm detects at most two vector modes.The two arms use slightly different filters, with a half-wave plate changing the q-plate charge sign.
- Deterministic measurement: Deterministic sorting combines geometric-phase polarization splitting, 50:50 beam-splitter interference, and refractive OAM mode sorters.The interferometer sets the optical phase difference between paths to π/2 before the outputs enter the mode sorters.
- Deterministic measurement: All vector modes in the defined basis can be mapped to independent spatial positions with unit efficiency at both classical and quantum levels.The OAM sorters map ±ℓ_OAM states to distinct positions in each output arm.
- Communication performance: Filtering detects a d-dimensional state with average probability ≤1/d, while the deterministic system avoids dimension-dependent loss.Photon efficiency and effective key rate are compared experimentally and theoretically as functions of dimension.
V. PROPAGATION THROUGH PERTURBING MEDIA
Perturbations couple vector vortex modes across spatial modes, reducing their vector quality and degrading the information encoded in the initial state. Experiments show this effect in step-index fibre and increasingly strong atmospheric turbulence.
- Atmospheric turbulence scatters the spatial degree of freedom among OAM states while leaving polarisation largely unaffected.
- In infinitely strong turbulence, equal-probability OAM scattering erases information about the initial state.
- VQF decreases from 1 for an unperturbed pure vector mode to 0 when infinitely strong turbulence produces a separable scalar mode.
- A 5 cm step-index fibre with a 30 µm core supports 76 modes at 633 nm and exhibits strong anti-diagonal cross-talk, so different vector modes are often detected.
- Under medium and strong turbulence, detection probabilities diminish and VQF decreases with increasing turbulence strength.
VI. CONCLUSION
The paper reviews creation, characterization, and detection tools for vector vortex beams and examines their use in classical and quantum communication. It reports degradation in perturbing media and contrasts probabilistic detection with a deterministic scheme that overcomes its stated communication limitations.
- The work reviews tools for creating, characterizing, and detecting vector vortex beams, including their use as information carriers in classical and quantum communication.
- Modal degradation is demonstrated in free-space turbulence and imperfect optical fibre.
- Probabilistic detection negates the benefit of increased dimensionality in quantum communication while reducing signal in classical communication links.
- The proposed deterministic scheme overcomes this limitation.