Draft:Photonic toroidal vortex

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A Photonic toroidal vortex (PTV) is a ring-shaped (toroidal) distribution of light.

Description

A light beam performs a dual rotation on the surface of a toroid: it runs around the poloidal axis as optical orbital angular momentum (OAM) while it passes around the toroidal axis. The torus can adopt translational motion along its axis.^{[citation needed]}

History

The scientific investigation of vortex rings dates to 1867 when Lord Kelvin proposed the vortex atom model. At that time, the rotational substance was held to be a hypothetical medium known as the luminiferous aether. In 2022, a photonic toroidal vortex was produced in the laboratory by converting a laser pulse into a spatiotemporal optical vortex (STOV) before using an afocal optical conformal mapping system to shape it into a toroid.^[1]

A related realization, the vector toroidal pulse or flying doughnut, was reported in the same year.^[2] This employed a field-based toroidal topology.^[3]

Generation

Longitudinally iterated photons are generated by a fiber laser and are separated into a reference pulse and a signal pulse. The reference is dechirped to a transform-limited pulse using a grating pair, while the latter is directed to a 2-D pulse shaper. The path length difference between the reference and signal is controlled by a moveable reflective mirror. Following a spatio-temporal Fourier transform, the signal pulse is converted to a wave packet with a spatio-temporal vortex (STOV). An afocal cylindrical beam expander stretches it along the vortex line before passing through spatial light modulators (SLM), which are programmed with phase profiles, to form an afocal mapping system. The stretched spatio-temporal vortex subsequently transforms into a toroidal vortex through the conformal mapping system. Its recombination with the reference pulse in a CCD camera allows an interference pattern to be observed. ^[1]

Dynamics

Photonic toroidal vortices constitute a family of three-dimensional, spacetime nonseparable structured light fields carrying transverse orbital angular momentum.^[4] Their dynamics are mediated by both transverse and longitudinal OAM. The swirling flow destabilizes the toroidal structure under dispersion and induces topological transformations of vortex lines, characterized by annihilation and subsequent reformation in vacuum.^[4]

Experimental application

Applications include optical manipulation, topological photonics, and quantum information.^[4]

Theoretical application

A photonic toroidal vortex model of the hydrogen atom fine structure has been proposed using a photon in the form of a string following a helical path (Sp-1 rotation). This runs around a guide tube as optical OAM (Sp-2 rotation) whose axis circulates as a toroid (Sp-3 rotation).^[5] Both the electron and proton are coaxial PTVs, the latter being a scaled-down version of the former. The two foundational principles of the model are as follows:^{[citation needed]}

Both the Sp-1 and Sp-2 action in a PTV tend to maintain action h.
An overloaded or underloaded PTV rotational mode can exchange action with its translational mode.

Quantized energy levels are generated by the introduction of an internal potential that consists of Sp-3 rotational energy. These levels are then transformed into the hydrogen fine structure by the intervention of the proton's external Coulomb field. The role of the oppositely-rotating external field is to displace the electron's Sp-3 energy (action underload) into translational energy which is radiated away when the converging proton and electron PTVs reach their bound-state distance. Calculated fine-structure intervals agreeing with the NIST reference data to better than one part in 10¹⁰ have been reported.^{[citation needed]}

Whereas the light beam in the STOV spans the whole toroid^[1], the hydrogen PTV model employs a discrete-wavelength photon structure.^[5]

References

^ ^a ^b ^c Wan, C., Cao, Q., Chen, J., Chong, A. and Zhan, Q., Toroidal vortices of light, Nature Photonics 16, 519–522 (2022). https://doi.org/10.1038/s41566-022-01013-y
^ Zdagkas, Apostolos; McDonnell, Cormac; Deng, Junhong; Shen, Yijie; Li, Guixin; Ellenbogen, Tal; Papasimakis, Nikitas; Zheludev, Nikolay I. (July 2022). "Observation of toroidal pulses of light". Nature Photonics. 16 (7): 523–528. doi:10.1038/s41566-022-01028-5. ISSN 1749-4885.
^ Chong, A., Wan, C., Chen, J. and Zhan, Q., Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum, Nature Photonics 14, 350–354 (2020). https://doi.org/10.1038/s41566-020-0587-z
^ ^a ^b ^c Liu, X., Zhang, N., Cao, Q., Liu, J., Liang, C., Zhan, Q. and Cai, Y., Dynamics of photonic toroidal vortices mediated by orbital angular momenta, Science Advances 11, eadz0843 (2025). https://doi.org/10.1126/sciadv.adz0843
^ ^a ^b Clarke, B. R., A photonic toroidal vortex model of the hydrogen atom, Quantum Studies: Mathematics and Foundations 12, 19 (2025). https://doi.org/10.1007/s40509-025-00364-9

Category:Optics Category:Topology

[wan2022-1] Wan, C., Cao, Q., Chen, J., Chong, A. and Zhan, Q., Toroidal vortices of light, Nature Photonics 16, 519–522 (2022). https://doi.org/10.1038/s41566-022-01013-y

[2] Zdagkas, Apostolos; McDonnell, Cormac; Deng, Junhong; Shen, Yijie; Li, Guixin; Ellenbogen, Tal; Papasimakis, Nikitas; Zheludev, Nikolay I. (July 2022). "Observation of toroidal pulses of light". Nature Photonics. 16 (7): 523–528. doi:10.1038/s41566-022-01028-5. ISSN 1749-4885.

[3] Chong, A., Wan, C., Chen, J. and Zhan, Q., Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum, Nature Photonics 14, 350–354 (2020). https://doi.org/10.1038/s41566-020-0587-z

[liu2025-4] Liu, X., Zhang, N., Cao, Q., Liu, J., Liang, C., Zhan, Q. and Cai, Y., Dynamics of photonic toroidal vortices mediated by orbital angular momenta, Science Advances 11, eadz0843 (2025). https://doi.org/10.1126/sciadv.adz0843

[clarke2025-5] Clarke, B. R., A photonic toroidal vortex model of the hydrogen atom, Quantum Studies: Mathematics and Foundations 12, 19 (2025). https://doi.org/10.1007/s40509-025-00364-9

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