Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

NONHOMOGENEOUSLY POLARIZED AIRY BEAMS AND THEIR ACCELERATING LATTICES OF OPTICAL QUASIPARTICLES
Justas Berškys, Klemensas Laurinavičius, and Sergej Orlov
Coherent Optics Laboratory, State Research Institute Center for Physical Sciences and Technology, Saulėtekio 3, 10257 Vilnius, Lithuania
Email: justas.berskys@ftmc.lt; sergejus.orlovas@ftmc.lt

Received 24 June 2025; revised 21 August 2025; accepted 15 September 2025

Radially polarized Airy vector beams are numerically investigated in terms of their spatial spectra, electromagnetic field distribution, and topological structure. Airy-type beams, which belong to the class of non-diffracting optical beams, are notable for their ability to propagate in a bent accelerating trajectory while reconstructing their intensity profiles even after encountering obstructions. This work analytically investigates vector beams with non-uniform, radial and azimuthal polarization distributions, which exhibit phase singularities and intensity zeros (dark spots). Additional topological features are observed, and the skyrmionic density of the electric field and the linear momentum are analyzed numerically, revealing the existence of an accelerating lattice of optical quasiparticles in the beams.
Keywords: Airy beams, polarization, topological quasiparticles

NEVIENALYTIŠKAI POLIARIZUOTI AIRY PLUOŠTAI IR JŲ GREITĖJANČIOS OPTINIŲ KVAZIDALELIŲ GARDELĖS
Justas Berškys, Klemensas Laurinavičius, Sergej Orlov

Valstybinio mokslinių tyrimų instituto Fizinių ir technologijos mokslų centro Koherentinės optikos laboratorija, Vilnius, Lietuva

Darbe tiriama sferiškai poliarizuotų Airy tipo pluoštų topologinėms dalelėms būdinga lauko struktūra. Šie pluoštai pasižymi taškinio tipo singuliarumu židinio plokštumoje ir išlaiko skaliariniams Airy pluoštams būdingą parabolinę, greitėjančią sklidimo trajektoriją. Pirmiausia apžvelgiama metodika, leidžianti iš skaliarinių laukų sprendinių gauti elektromagnetinių ortogonalių vektorinių modų bazę. Tokie vektoriniai pluoštai yra Maksvelo lygčių sprendiniai. Taikant šią metodiką, parenkamas vektorinių modų simetriją nusakantis vektorius, nukreiptas radiališkai sferinėje koordinačių bazėje. Tokio vektoriaus pasirinkimas lemia taškinio tipo singuliarumą pluošto židinyje. Taip pat pateikiami šių laukų erdviniai intensyvumo profiliai dviem ortogonaliems vektorinių laukų sprendiniams – M ir N – bei analizuojama jų poliarizacija. Matyti, kad atvaizdavus amplitudės modulį ir poliarizacijos kryptį, šie laukai įgauna skersinei elektrinei (TE) ir magnetinei (TM) modoms būdingą struktūrą ir yra radiališkai bei azimutiškai poliarizuoti. Nagrinėjant šių laukų topologiją, apskaičiuojamas atitinkamo lauko skirmioninis tankis. Analizuojant TM modos elektrinio lauko domeną, aptinkamos su pagreičiu judančios topologinių lauko struktūrų gardelės, kurių mazgai atitinka Bloch ir Néel tipo bimeronines topologines kvazidaleles. Taip pat Poyntingo vektoriaus domene aptiktos Néel ir priešingo (anti) tipo skirmioninės lauko struktūros, judančios pluošte su pagreičiu ir sudarančios gardelę.

References / Nuorodos

[1] A.H. Dorrah and F. Capasso, Tunable structured light with flat optics, Science 376, eabi6860 (2022),
https://doi.org/10.1126/science.abi6860
[2] Y. Shimotsuma, P.G. Kazansky, J. Qiu, and K. Hirao, Self-organized nanogratings in glass irradiated by ultra-short light pulses, Phys. Rev. Lett. 91, 247405 (2003),
https://doi.org/10.1103/PhysRevLett.91.247405
[3] Y. Yang, Y.-X. Ren, M. Chen, Y. Arita, and C. Rosales-Guzmán, Optical trapping with structured light: a review, Adv. Photonics 3, 034001 (2021),
https://doi.org/10.1117/1.AP.3.3.034001
[4] T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R.W. Boyd, and G. Leuchs, Observation of optical polarization Möbius strips, Science 347, 964 (2015),
https://doi.org/10.1126/science.1260635
[5] J. Durnin, J. Miceli Jr, and J.H. Eberly, Diffraction-free beams, Phys. Rev. Lett. 58, 1499 (1987),
https://doi.org/10.1103/PhysRevLett.58.1499
[6] D. McGloin and K. Dholakia, Bessel beams: Diffraction in a new light, Contemp. Phys. 46, 15 (2005),
https://doi.org/10.1080/0010751042000275259
[7] D. Sugic, R. Droop, E. Otte, D. Ehrmanntraut, F. Nori, J. Ruostekoski, C. Denz, and M.R. Dennis, Particle-like topologies in light, Nat. Commun. 12, 1 (2021),
https://doi.org/10.1038/s41467-021-26171-5
[8] Y. Shen, Q. Zhang, P. Shi, L. Du, X. Yuan, and A.V. Zayats, Optical skyrmions and other topological quasiparticles of light, Nat. Photonics 18, 15 (2024),
https://doi.org/10.1038/s41566-023-01325-7
[9] J. Broky, G.A. Siviloglou, A. Dogariu, and D.N. Christodoulides, Self-healing properties of optical Airy beams, Opt. Express 16, 12880 (2008),
https://doi.org/10.1364/OE.16.012880
[10] R. Dorn, S. Quabis, and G. Leuchs, Sharper focus for a radially polarized light beam, Phys. Rev. Lett. 91, 233901 (2003),
https://doi.org/10.1103/PhysRevLett.91.233901
[11] F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, Generation and dynamics of optical beams with polarization singularities, Opt. Express 21, 8815 (2013),
https://doi.org/10.1364/OE.21.008815
[12] K.Y. Bliokh, F.J. Rodríguez-Fortuño, F. Nori, and V. Zayats, Spin–orbit interactions of light, Nat. Photonics 9, 796 (2015),
https://doi.org/10.1038/nphoton.2015.201
[13] T.H.R. Skyrme, A non-linear field theory, Proc. R. Soc. Lond. A 260, 127 (1961),
https://doi.org/10.1098/rspa.1961.0018
[14] C.D. Parmee, M.R. Dennis, and J. Ruostekoski, Optical excitations of skyrmions, knotted solitons, and defects in atoms, Commun. Phys. 5, 1 (2022),
https://doi.org/10.1038/s42005-022-00829-y
[15] Y. Shen, E.C. Martínez, and C. Rosales-Guzmán, Generation of tunable optical skyrmions on Skyrme-Poincaré sphere, arXiv:2107.04394 (2021),
https://doi.org/10.1021/acsphotonics.1c01703
[16] R. Gutiérrez-Cuevas and E. Pisanty, Optical polarization skyrmionic fields in free space, J. Opt. 23, 024004 (2021),
https://doi.org/10.1088/2040-8986/abe8b2
[17] L. Du, A. Yang, A.V. Zayats, and X. Yuan, Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum, Nat. Phys. 15, 650 (2019),
https://doi.org/10.1038/s41567-019-0487-7
[18] D. Marco, I. Herrera, S. Brasselet, and M.A. Alonso, Propagation-invariant optical meron lattices, ACS Photonics 11, 2397 (2024),
https://doi.org/10.1021/acsphotonics.4c00292
[19] Y. Shen, Y. Hou, N. Papasimakis, and N.I. Zheludev, Supertoroidal light pulses as elec tromagnetic skyrmions propagating in free space, Nat. Commun. 12, 5891 (2021),
https://doi.org/10.1038/s41467-021-26037-w
[20] R. Droop, D. Ehrmanntraut, and C. Denz, Transverse energy flow in an optical Skyrmionic Hopfion, Opt. Express 31, 11185 (2023),
https://doi.org/10.1364/OE.480471
[21] H. Guo, T. Das, H. Wu, V. Dev, Z. Zhu, and Y. Shen, Self-healing of optical skyrmionic beams, J. Opt. 27, 025604 (2025),
https://doi.org/10.1088/2040-8986/adab84
[22] L. Chen, Y. Shen, X.Y. Li, Z. Gu, J.L. Su, Q. Xiao, Q. Huang, S.L. Qin, Q. Ma, J.W. You, et al., Programmable skyrmions for robust communication and intelligent sensing, arXiv:2507.05944 (2025),
https://doi.org/10.48550/arXiv.2507.05944
[23] S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, Propagation of Bessel beams carrying optical vortices, Opt. Commun. 209, 155 (2002),
https://doi.org/10.1016/S0030-4018(02)01667-X
[24] J. Berškys and S. Orlov, Accelerating Airy beams with particle-like polarization topologies and free-space bimeronic lattices, Opt. Lett. 48, 1168 (2023),
https://doi.org/10.1364/OL.483339
[25] D. Marco, I. Herrera, S. Brasselet, and M.A. Alonso, Periodic skyrmionic textures via confor mal cartographic projections, APL Photonics 9 (2024),
https://doi.org/10.1063/5.0230959
[26] X. Lei, A. Yang, P. Shi, Z. Xie, L. Du, A.V. Zayats, and X.Yuan, Photonic spin lattices: Symmetry constraints for skyrmion and meron topologies, Phys. Rev. Lett. 127, 237403 (2021),
https://doi.org/10.1103/PhysRevLett.127.237403
[27] H. Wu, W. Zhou, Z. Zhu, and Y. Shen, Optical skyrmion lattices accelerating in a free-space mode, APL Photonics 10 (2025),
https://doi.org/10.1063/5.0255824
[28] A. Hansen, J.T. Schultz, and N.P. Bigelow, Singular atom optics with spinor Bose–Einstein conden sates, Optica 3, 355 (2016),
https://doi.org/10.1364/OPTICA.3.000355
[29] L. Han, C. Addiego, S. Prokhorenko, M. Wang, H. Fu, Y. Nahas, X. Yan, S. Cai, T. Wei, Y. Fang, et al., High-density switchable skyrmion-like polar nanodomains integrated on silicon, Nature 603, 63 (2022),
https://doi.org/10.1038/s41586-021-04338-w
[30] Z. Wan, H. Wang, Q. Liu, X. Fu, and Y. Shen, Ultra-degree-of-freedom structured light for ultracapacity information carriers, ACS Photonics 10, 2149 (2023),
https://doi.org/10.1021/acsphotonics.2c01640
[31] R. Tamura, P. Kumar, A.S. Rao, K. Tsuda, F. Getzlaff, K. Miyamoto, N.M. Litchinitser, and T. Omatsu, Direct imprint of optical skyrmions in azopolymers as photoinduced relief structures, APL Photonics 9 (2024),
https://doi.org/10.1063/5.0192239
[32] J.A. Stratton, Electromagnetic Theory, IEEE Press Series on Electromagnetic Wave Theory, Vol. 33 (John Wiley & Sons, 2007),
[PDF]
[33] P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Technology Press, 1946),
[Part I PDF], [Part II PDF]
[34] T.H.R. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31, 556 (1962).
https://doi.org/10.1016/0029-5582(62)90775-7