Vortex Bessel Beams: Structure & Applications

• Vortex Bessel beams are propagation-invariant field solutions defined by a radial Bessel function and quantized orbital angular momentum, enabling precise wavefront control.
• They offer robust non-diffracting propagation with tunable phase and intensity profiles that benefit applications in particle manipulation, quantum information, and integrated optics.
• Experimental and computational techniques such as holographic encoding and nonlocal metasurfaces enable detailed characterization and practical implementation of these beams.

Vortex Bessel beams are propagation-invariant field configurations exhibiting phase singularities—optical, acoustic, or matter-wave vortices—characterized by a quantized orbital angular momentum (OAM) and a radial structure given by Bessel functions. These beams, and their nonlinear and engineered counterparts, underpin a wide range of advances in structured light, quantum information, particle manipulation, and materials science across optics and acoustics. They provide an analytically tractable and experimentally robust platform for generating, studying, and controlling fields with complex spatial and topological properties.

1. Field Structure, OAM, and Bessel Basis

Vortex Bessel beams are exact solutions of the scalar or vector wave equations under cylindrical symmetry, possessing a spatial envelope given by $J_{\ell}(k_{\perp} r) e^{i\ell\phi}$, where $J_{\ell}$ is a Bessel function of order $\ell$ (the topological charge or OAM quantum number). The longitudinally and transversely invariant form ensures non-diffracting propagation over an extended range, within experimental limits set by finite aperture or energy.

A general vortex beam can be decomposed as

$$\psi(r, \phi) = \sum_{\ell} c_{\ell} J_{\ell}(k_{\perp} r) \exp(i\ell\phi)$$

where $c_{\ell}$ are the OAM amplitudes. The phase singularity's quantization ($\ell \in \mathbb{Z}$) results in a $2\pi\ell$ phase change around the origin and an intensity null (vortex core) for $|\ell|>0$. The OAM per photon (or phonon) is $\ell\hbar$, and the beams serve as OAM eigenmodes for electromagnetic, acoustic, and matter waves (Rehacek et al., 2010, Glukhova et al., 2022).

These modes can be generalized, including:

• Superpositions for hard-wall (cylindrical) traps, producing stationary vortex arrays (Lusk et al., 2023, Voitiv et al., 18 Jan 2024).
• Fractional OAM and Hankel–Bessel hybrids with arbitrary phase dislocations (Reis et al., 2023).
• Extension to vectorial (TE/TM, LE/LM, CS, CS′) Bessel-type beams via Hertz potential formalism (Glukhova et al., 2022).

2. Propagation-Invariant, Spatio-Temporal, and Nonlocal Aspects

Unlike paraxial Laguerre–Gaussian (LG) beams, ideal Bessel vortex beams maintain their core features (ring structure, phase, and OAM) regardless of propagation distance until truncated by aperture or damping. Their extension to spatio-temporal and nonparaxial domains brings additional physical richness:

• Spatio-temporal Bessel beams are constructed by either spectral (k-space) translation or Lorentz boosts, yielding beams with OAM at an angle relative to the propagation axis, non-collinear momentum and OAM, and time-evolving dislocation geometry. These are exact solutions to the Klein–Gordon equation for both relativistic and nonrelativistic quantum fields, accommodating massive and massless excitations (Bliokh et al., 2012).
• In acoustic or electronic settings, the presence of synthetic vector potentials (e.g., flows mimicking Aharonov–Bohm flux) modifies the effective Bessel index, leading to pressure and velocity profiles in which energy redistribution and beam radii are sensitive to OAM-field alignment. These show phenomena beyond scalar field analogs, notably for nonparaxial beams or in synthetic magnetic fields (Rondon et al., 2019).
• The use of engineered momentum-space distributions (via nonlocal metasurfaces) enables direct creation of non-diffracting vortex beams with tunable spatial properties, controlled real-space emergence, and order-of-magnitude enhancements in propagation length for fixed diameter compared to LG modes. The band curvature determines effective space compression or expansion, and the internal phase engineering supports topological robustness (Kim et al., 30 Sep 2025).

3. Generation, Characterization, and Tomography

Vortex Bessel beams are generated and characterized via a suite of experimental and computational techniques:

• Holographic encoding (spatial light modulators; PB-FSGs for open vortex beams (Zeng et al., 2020); CGHs for fractional or Hankel–Bessel beams (Reis et al., 2023)).
• Passive elements such as Archimedes' spiral gratings for acoustic Bessel vortices (Jiménez et al., 2016).
• Nonlocal metasurfaces, leveraging high-Q guided resonances for on-chip, ultracompact beam synthesis (Kim et al., 30 Sep 2025).
• Bessel–Gaussian beams via axicons or holographically controlled SLMs for robust propagation and braiding experiments (Voitiv et al., 2021).

Full tomographic characterization—including OAM amplitude, phase, and even Wigner function reconstruction—can be achieved by encoding the state in Bessel-like beams, implementing quadratic OAM transformations through free-space propagation, and measuring angular projections at various propagation distances. Fourier inversion recovers the density matrix and Wigner distribution, furnishing a complete phase-space description on the discrete cylinder (angle $\phi$, OAM $\ell$) (Rehacek et al., 2010).

4. Nonlinear, Dissipative, and Engineered Vortex Bessel Beams

The interplay of nonlinearity and dissipation in optical media substantially broadens the phenomenology:

• Nonlinear Bessel vortex beams (BVBs) are stationary, localized solutions of the nonlinear Schrödinger equation with embedded vorticity and a dissipative (multiphoton absorption) term (Porras et al., 2016, Porras et al., 2017).
• Dissipation, far from being wholly deleterious, stabilizes BVBs against modulation instability and collapse. An inward conical (Hankel) flux of energy and OAM replenishes core losses, with the stationarity condition set by a nonzero net inward component (Porras et al., 2017).
• The BVB becomes an attractor for axicon-generated beams in high-intensity regimes, explaining observed transitions between tubular, rotating, and speckle-like filamentation as respective consequences of stability, weak instability, and strong instability (Porras et al., 2016, Porras et al., 2017).
• Vortex annihilation and attraction: In nonlinear absorbing media, embedded “foreign” vortices are driven toward the beam center, where they merge—modifying the beam’s topological charge but preserving the inward current. This leads to efficient cleaning (removal of unwanted vortices), robust multiply charged vortex formation without alignment sensitivity, and fast annihilation of vortex dipoles (Riquelme et al., 2018).
• Tunable self-similar Bessel-like vortex beams are engineered via amplitude and phase design at the input plane, allowing independent control of core radius and intensity during propagation. Self-similar propagation is achieved by tailoring the input profile for desired scaling, extending the flexibility of beam dynamics for applications (Goutsoulas et al., 2020, Yan et al., 2022).

5. Scattering, Manipulation, and Matter/Wave Interactions

Vortex Bessel beams, due to their propagation invariance and OAM structure, serve as highly efficient tools for particle manipulation, microscale fluid control, and advanced scattering studies:

• The radiation force and torque on various geometries (spheres, oblate/prolate spheroids) are calculated via partial-wave series expansion methods, with the beam’s OAM order, half-cone angle, and amplitude ratio controlling whether trapping (acoustic tweezers) or pulling (tractor beam) dominates (Mitri, 2014, Mitri, 2016).
• Passive acoustic devices—such as spiral gratings—enable generation of high-order beams with controllable vortex core size and vorticity, suitable for reconfigurable tweezers and force fields (Jiménez et al., 2016).
• Vector Bessel beams, described by matrix-parametrized Hertz potentials, encapsulate a broad taxonomy including linearly and circularly polarized beams as special cases, and offer foundations for generalized scattering calculations (Mueller matrix generalization to OAM modes) in the ADDA DDA code (Glukhova et al., 2022).
• In nonlinear media, stable background nonlinear Bessel beams enable vortex solitons to be nested and interact with quasi-ideal steering (i.e. no spiraling or decay over tenfold-increased distance vs. Gaussian backgrounds), providing a natural environment for multivortex waveguiding and manipulation (Porras, 2017).

6. Topological, Quantum, and Emerging Applications

The diverse topological and dynamical features of vortex Bessel beams have far-reaching implications:

• Quantum vortex tomography enables full state reconstruction for high-dimensional OAM-based quantum information channels, with phase and magnitude information encoded and retrieved via spatial interference and quadratic OAM transformations (Rehacek et al., 2010).
• Braiding of optical vortices is achieved via linear superposition of Bessel and plane (or Gaussian) waves; the rotation of braid patterns is determined by beam parameters and can be controlled experimentally, offering robust mechanisms for chiral microstructure fabrication and quantum entanglement studies (Voitiv et al., 2021).
• Stationary vortex arrays in rotating frames and Bessel hard-trap environments enable classical analogs of few-body vortex physics and geometric phase accumulation previously confined to Bose–Einstein condensates or quantum fluids. The quantization of rotation rates, vortex nucleation/annihilation, and nontrivial precession emerge from the interplay of boundary symmetry and mode structure (Lusk et al., 2023, Voitiv et al., 18 Jan 2024).
• “Perfect” non-diffracting vortex beams remove OAM–radius coupling via precise radial wavevector engineering, supporting OAM-multiplexed communications and trapping with constant ring size over multiple OAM channels (Yan et al., 2022).
• Open vortex beams and fractional charge Bessel–Hankel beams (via CGH/SLM methods) demonstrate tunable phase discontinuities, offering unique trapping, metrological, and encoding strategies for classical and quantum optical systems (Zeng et al., 2020, Reis et al., 2023).

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A plausible implication, given the programmatic generalization and simulations across increasingly complex beam classes, is that vortex Bessel beams and their nonlinear/dissipative extensions will continue to serve as a canonical framework not only for wave field engineering in optics and acoustics but also for onward translation to emerging fields such as topological photonics, quantum communications, and light–matter angular momentum transfer at the nanoscale. The continued synthesis of analytic, numerical, and experimental advances (including metasurface-enabled platforms and machine-optimized input designs) is likely to further expand both the versatility and the foundational theoretical understanding of vortex Bessel beams.