Optical Tornado Waves: Vortex Photonics

• Optical tornado waves are structured optical fields featuring vortex-like phase singularities and rotating intensity patterns across diverse regimes.
• They rely on quantized phase circulation and tailored energy-flow dynamics to control angular momentum and achieve unique autofocusing behaviors.
• These phenomena open pathways for advanced applications in ultrafast optics, plasmonic routing, and nanoscale energy manipulation.

Optical tornado waves are structured optical fields in which vortex-like circulation is manifested through the phase, the Poynting-vector field, or the propagation of rotating intensity maxima. In current usage, the term covers several distinct but related constructions: spatiotemporal optical vortices (STOVs), described as a “dynamic torus” of phase singularity and field null that loops around a short pulse and moves with it (Jhajj et al., 2016); spatiotemporal vortices with controllable purely transverse orbital angular momentum (OAM), presented as a “photonic cyclone” (Chong et al., 2019); ring-Airy- or circular-vortex-Airy-beam superpositions whose bright lobes rotate, shrink, and angularly accelerate after autofocusing (Brimis et al., 2021, Chen et al., 2022, Mansour et al., 15 Sep 2025); and plasmonic near-field optical vortices, or “optical tornadoes,” formed by circulating power flow around nanostructures (Boriskina, 2014). The common elements are phase winding, singular or near-singular flow topology, and the conversion of longitudinal propagation into structured azimuthal dynamics.

1. Terminological scope and major realizations

The phrase “optical tornado wave” does not denote a single universally fixed beam class in the cited literature. Rather, it is used for several optical vortex constructions that share tornado-like circulation or twisting propagation.

Usage	Defining structure	Representative paper
STOV	Ring-shaped null and spiral phase in space–time	(Jhajj et al., 2016)
Photonic cyclone	ST vortex in the $x$-$t$ plane with purely transverse OAM	(Chong et al., 2019)
Ring-Airy / CVAB ToW	Rotating, shrinking lobes from overlapping autofocusing vortex beams	(Brimis et al., 2021, Chen et al., 2022, Mansour et al., 15 Sep 2025)
Plasmonic optical tornado	Nanoscale circulating Poynting flow around plasmonic obstacles	(Boriskina, 2014)

In beam optics, the term usually emphasizes a propagating spiral or funnel-like intensity structure, especially when abrupt autofocusing and angular acceleration coexist. In ultrafast optics, the emphasis shifts to phase singularities embedded in the combined space–time structure of a pulse. In plasmonics, the tornado analogy refers to near-field energy circulation rather than a free-space rotating beam. This plurality of meanings is central to the topic: the literature uses a common metaphor for different regimes of vortex-mediated optical transport.

2. Topological basis and energy-flow geometry

The common topological foundation is the optical-vortex condition for a complex field written as $\psi = u e^{i\phi}$. The phase circulation around a closed contour is quantized,

$$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$

with $m \in \mathbb{Z}$ the topological charge. Because the circulation is quantized, the phase becomes undefined at the vortex core and the field magnitude must vanish there. In ordinary spatial vortices this is encoded by a factor such as $\exp(i l\theta)$; in STOVs the same logic is extended into the $(r,\xi)$ or $(x,\xi)$ space–time plane (Jhajj et al., 2016).

The corresponding flow observables depend on regime. In plasmonics, the central quantity is the time-averaged Poynting vector,

$$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$

which is interpreted in a “photon fluid” picture as the electromagnetic analogue of a fluid flux. The hydrodynamic analogy is summarized by $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$, with field intensity as density and phase gradient as velocity (Boriskina, 2014). For linearly polarized free-space ToWs generated from circular vortex Airy beams, the transverse energy flow is written as

$t$0

and the total angular momentum per photon follows from the energy-weighted topological charges of the constituent beams (Chen et al., 2022).

In the pulse-frame description of STOVs, the energy current density is

$t$1

which makes the local flow explicitly dispersion-dependent. The cited work distinguishes saddle-like flow for $t$2, spiral-like flow for $t$3, and a degenerate limit when longitudinal and transverse contributions are extremely unbalanced (Jhajj et al., 2016). Across these formulations, “tornado-like” is therefore not merely visual language: it denotes organized circulation of optical energy around a singularity or rotating interference structure.

3. Spatiotemporal optical vortices and transverse-OAM cyclones

STOVs are the spatiotemporal analogue of ordinary optical vortices. A STOV consists of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus concentric with and tracking the propagating pulse. In the local pulse frame, a representative field can be written as

$t$4

with $t$5. The null is at $t$6, and the phase winds by $t$7 around it in the $t$8 plane. The cited analysis identifies STOVs as a fundamental element of nonlinear collapse and subsequent propagation of short optical pulses in material media. In self-focusing media, collapse sharpens the phase shear between a high-intensity core and lower-intensity periphery; when the phase difference approaches $t$9, the field passes through a null and a vortex ring appears. STOVs are created either in pairs with opposite windings or from a point null, and their later propagation, collision, and annihilation preserve the total topological charge. In air-filament experiments, nonlinear propagation was interrupted by sending the beam from air into helium, thereby freezing the beam for interferometric reconstruction; the direct signatures were abrupt phase flips of approximately $\psi = u e^{i\phi}$0 at collapse threshold and ring-shaped intensity nulls accompanied by phase jumps of $\psi = u e^{i\phi}$1 across the ring in the spatio-spectral representation (Jhajj et al., 2016).

The “photonic cyclone” is a different spatiotemporal realization, designed so that the OAM is purely transverse rather than longitudinal. The construction begins in the $\psi = u e^{i\phi}$2 plane with a spectral spiral phase $\psi = u e^{i\phi}$3. After a two-dimensional Fourier transform, the spatiotemporal field becomes

$\psi = u e^{i\phi}$4

so the topological charge survives the transformation, but the vortex now lives in the $\psi = u e^{i\phi}$5-$\psi = u e^{i\phi}$6 plane. Because the circulation is in a meridional space–time plane, the corresponding OAM is transverse to the propagation direction. Experimentally, the ST vortex was generated with a pulse shaper using a 2D spatial light modulator, starting from a chirped mode-locked pulse of about 3 ps duration; phase reconstruction used interference with a short reference pulse of about 90 fs. For $\psi = u e^{i\phi}$7, the measurements showed the phase singularity through the disappearance of the center fringe and a $\psi = u e^{i\phi}$8 phase jump across the singularity; for $\psi = u e^{i\phi}$9, the phase difference across the center became $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$0, and the higher-order ST vortex quickly split into two $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$1 vortices under propagation while preserving total topological charge. The magnitude of the transverse OAM is controlled directly by the programmed charge $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$2, and reversing the sign of $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$3 reverses the handedness (Chong et al., 2019).

These two spatiotemporal lines of work describe different objects. STOVs arise naturally during nonlinear collapse arrest, whereas the photonic cyclone is deliberately synthesized. Both, however, make the tornado analogy precise by embedding vortex circulation in space–time rather than only in the transverse spatial plane.

4. Autofocusing ring-Airy tornado waves and controlled angular acceleration

A second major usage of “optical tornado wave” concerns superpositions of abruptly autofocusing ring-Airy beams carrying OAM of opposite handedness. In this construction,

$$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$4

with $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$5. Each constituent follows an abrupt autofocusing trajectory, with focus

$$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$6

When beams of opposite helicity are tailored to autofocus at overlapping focal regions, the interference lobes rotate around the axis while their radius decreases, producing a funnel-like pattern. The cited work reports angular acceleration of about $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$7 for partial focal overlap and about $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$8 for complete overlap, corresponding to roughly $$\Gamma = \left| \oint \nabla \phi \cdot d\mathbf{l} \right| = 2\pi m,$$9. It also identifies a scaling law in which tighter focusing boosts angular velocity and angular acceleration according to $m \in \mathbb{Z}$0 and $m \in \mathbb{Z}$1, or equivalently $m \in \mathbb{Z}$2 and $m \in \mathbb{Z}$3 when expressed through the focus shift parameter $m \in \mathbb{Z}$4. The number of primary bright lobes is approximately $m \in \mathbb{Z}$5, and tornado-like structures persist even when the total OAM is zero, as in $m \in \mathbb{Z}$6, $m \in \mathbb{Z}$7 (Brimis et al., 2021).

A closely related experimental program defines ToWs as superpositions of two circular vortex Airy beams,

$m \in \mathbb{Z}$8

with self-focusing lengths

$m \in \mathbb{Z}$9

The total angular momentum per photon is

$\exp(i l\theta)$0

which, under $\exp(i l\theta)$1 and $\exp(i l\theta)$2, reduces to the energy-weighted expression given in the cited paper. An important consequence is that the total angular momentum need not vanish even if the sum of topological charges is zero. Experimentally, generation used a He-Ne laser at $\exp(i l\theta)$3 nm, a half-wave plate, a polarized beam splitter, a phase-only spatial light modulator (Holoeye PLUTO-2-VIS-056), a 4-f optical system with an iris, and a movable CCD camera. The accumulated rotation angle $\exp(i l\theta)$4 and angular velocity $\exp(i l\theta)$5 were measured. One reported case showed about $\exp(i l\theta)$6 of rotation within the first $\exp(i l\theta)$7 mm after the focus, later decreasing to about $\exp(i l\theta)$8 per $\exp(i l\theta)$9 mm, with a small systematic longitudinal offset of about $(r,\xi)$0 mm between experiment and simulation. Control is achieved through three parameters: self-focusing length, total angular momentum $(r,\xi)$1, and deviation between the two self-focusing foci. Shorter self-focusing length gives faster rotation; representative values are $(r,\xi)$2 mm $(r,\xi)$3, $(r,\xi)$4 mm $(r,\xi)$5, and $(r,\xi)$6 mm $(r,\xi)$7. When $(r,\xi)$8, the lobes do not rotate; increasing $(r,\xi)$9 generally increases both $(x,\xi)$0 and $(x,\xi)$1, but nonlinearly, and sufficiently large $(x,\xi)$2 can induce a short-distance reversal. The paper demonstrates control of the accumulated rotation angle from $(x,\xi)$3 to $(x,\xi)$4 and shows that the highest angular velocity occurs when the two foci coincide (Chen et al., 2022).

A later experimental implementation generates ToWs by spatial multiplexing on a single phase modulation device. The system uses a CW Gaussian laser beam at $(x,\xi)$5 nm, expanded by a factor of 2, reflected from a phase SLM with $(x,\xi)$6 pixels and $(x,\xi)$7 pixel size, with only the zero diffraction order imaged on a camera translated along $(x,\xi)$8. The interference of two OAM-carrying fields is written as

$(x,\xi)$9

yielding an intensity modulation governed by $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$0, $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$1, and $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$2. The number of bright lobes is

$$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$3

which becomes $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$4 for opposite-helicity beams. Their angular positions satisfy

$$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$5

and the longitudinally induced angular velocity and acceleration are

$$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$6

In the funnel region the radial position of the lobes shrinks by about $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$7. Experimental examples are given for $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$8, $$\mathbf{S}=\frac{1}{2}\Re[\mathbf{E}\times \mathbf{H}^*],$$9, and $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$0. The same work also proposes a two-color ToW, for which the beat period is

$\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$1

and the full rotation period of the $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$2-lobe structure is

$\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$3

For $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$4 nm and $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$5 nm, the reference beat period is about $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$6 fs; the full rotation period is then about $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$7 fs for $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$8 and about $\mathbf S \propto p(\mathbf r)\mathbf v(\mathbf r)$9 fs for $t$00, which the paper identifies with THz-rate twisting (Mansour et al., 15 Sep 2025).

5. Plasmonic optical tornadoes and vortex nanogear transmissions

In plasmonics, optical tornadoes are not propagating spiral beams but engineered circulations of electromagnetic energy in the near field. The central idea is to steer optical power flow around nano-obstacles by sculpting the Poynting-vector field, rather than to treat the system mainly as a set of dipolar scatterers. In the “photon fluid” picture, nanostructures redirect and compress the energy stream, producing optical vortices—tornado-like areas of circular motion of power flux—connected into transmission-like sequences. The hydrodynamic analogy is expressed through relations such as

$t$01

where $t$02 is photon-fluid density, $t$03 is velocity, $t$04 is a quantum-pressure term, and $t$05 represents sources or sinks due to gain or loss (Boriskina, 2014).

The associated nanofocusing mechanism is described as convective acceleration followed by conversion of kinetic energy into pressure-like energy, producing a sharp local increase in field density or intensity. This is the basis of the vortex nanogear transmission (VNT): multiple nanoscale vortices are coupled so that the flow is threaded through a sequence of circulating cells and narrow gaps. Electromagnetically, the effect arises from radiationless electromagnetic interference of evanescent fields rather than from interference of propagating waves radiated by nanoparticle dipoles. The chapter reinterprets standard plasmonic motifs in these terms, including energy-flow reversal near resonant nanoparticles, the formation of optical vortices near plasmon resonances, coupled vortex nanogears, and nanolens focusing as channeling by counter-rotating vortices rather than simple lens action (Boriskina, 2014).

The claimed advantages are likewise phrased in energy-flow terms. By routing power away from metal and into nanoscale dielectric gaps, VNTs can reduce dissipative losses, increase energy accumulation within a nanoscale volume, and activate magnetic response in non-magnetic nanostructures through circulating displacement currents. The cited applications include SERS and fluorescence enhancement, refractive-index sensing, stress/strain sensing, optical trapping and conveyor-like transport of particles, photovoltaics and photocatalysis, reconfigurable plasmonic nanocircuits, metamaterial building blocks, and wavelength-controlled nanoscale switching in which power flow can be turned on, off, or reversed (Boriskina, 2014). In this regime, “optical tornado” refers to subwavelength circulation of power flux rather than to rotating beam lobes in free space.

6. Conceptual distinctions, analogs, and open directions

Several recurring misconceptions are resolved by distinguishing the principal optical usages. Ring-Airy ToWs are rotating interference structures whose bright lobes twist and shrink after abrupt autofocusing. STOVs are toroidal phase singularities and field nulls embedded in a propagating ultrafast pulse. The photonic cyclone is a space–time vortex with purely transverse OAM. Plasmonic optical tornadoes are near-field Poynting-vector circulations around nanostructures. These constructions are related by vortex topology and structured energy transport, but they are not interchangeable definitions of a single beam (Jhajj et al., 2016, Chong et al., 2019, Brimis et al., 2021, Boriskina, 2014).

The tornado terminology also appears in non-optical analogs. “Alfvénic tornadoes” are modified-kinetic Alfvén-wave Laguerre–Gaussian vortex beams in a magnetoplasma, characterized by plasma density whirls or magnetic flux ropes carrying OAM (Shukla, 2012). Solar “small-scale tornado” studies describe persistent rotating magnetic-plasma vortex flows in which wave analyses suggest upwardly propagating fast kink waves with phase speeds of about $t$06–$t$07 km/s, evidence for standing-wave behavior, and localized torsional Alfvénic signatures associated with chromospheric swirls (Tziotziou et al., 2020, Tziotziou et al., 2019). These works are analogical rather than optical, but they clarify why tornado language remains attractive: it emphasizes coherent rotating transport, substructure, and wave-guided circulation.

Within optics itself, several open directions are explicit in the cited papers. STOV dynamics should depend much more strongly on the sign and magnitude of $t$08 in solids than in air, and STOV solitons could exist in anomalously dispersive, self-defocusing media (Jhajj et al., 2016). Ring-Airy ToWs show that focal overlap, self-focusing length, and total angular momentum provide separate control knobs for angular velocity and accumulated rotation (Chen et al., 2022). The spatial-multiplexing approach shows that angular acceleration is governed by the longitudinal variation of the relative phase and that frequency detuning can convert a longitudinally twisting tornado into a temporally rotating optical “drill” (Mansour et al., 15 Sep 2025). In plasmonics, wavelength-tuned optical tornadoes provide a route to active nanoscale routing and switching (Boriskina, 2014). This suggests a unifying research direction in which optical tornado waves are treated less as a single canonical mode and more as a family of vortex-mediated energy-flow architectures spanning ultrafast pulse physics, free-space structured beams, and nanophotonic transport.