Spatial Dynamics of a Radially Polarized Terahertz Laser Beam with a Phase Singularity
Abstract
Analytical expressions are obtained that describe the nonparaxial diffraction in free space of the TM01 mode with radial polarization of the field of the dielectric waveguide resonator of a terahertz laser during its interaction with a spiral phase plate with different topological charge (n). The physical features of the obtained vortex beams during their propagation and tight focusing are studied by numerical simulation. The integral diffraction Rayleigh-Sommerfeld transforms are used to simulate the propagation and focusing of the obtained beams. In free space the use of the spiral phase plate at the waveguide output with a topological charge of n = 1 leads to a change in the transverse beam profile from annular to a beam that has a field maximum on the axis, and then for n = 2 again to annular. During focusing the transverse distribution of the total field intensity in the absence of a spiral phase plate has a ring structure. In this case there is a slight intensity on the axis due to the contribution of the longitudinal component of the field. The transverse profile of the beam changes in the same way as during its propagation when using a phase plate. In this case the phase front changes from spherical to spiral with the presence of two (n = 1) and four (n = 2) branching vortices.
Downloads
References
G.S. Park, M. Tani, J.S. Rieh, and S.Y. Park, Advances in Terahertz Source Technologies, (CRC Press, 2024).
A. Saha, A. Biswas, K. Ghosh, and N. Mukhopadhyay, Optical to Terahertz Engineering, (Springer, 2023).
B. Gu, Y. Hu, X. Zhang, M. Li, Z. Zhu, G. Rui, and Y. Cui, “Angular momentum separation in focused fractional vector beams for optical manipulation”, Optics Express, 29(10), 14705 (2021). https://doi.org/10.1364/OE.423357
B. Gao, J. Wen, G. Zhu, L. Ye, and L.G. Wang, “Precise measurement of trapping and manipulation properties of focused fractional vortex beams”, Nanoscale, 14(8), 3123 (2022). https://doi.org/10.1039/D1NR06163A
B. Pant, B.K. Mishra, S. Singh, and B.K. Singh, “Mode transformation and dark spot formation of cylindrical vector beams by thin dielectric film”, Optics & Laser Technology, 180, 111539 (2025). https://doi.org/10.1016/j.optlastec.2024.111539
J. Ma, Z. Xie, and X. Yuan, “Tailoring arrays of optical stokes skyrmions in tightly focused beams”, Laser & Photonics Reviews, 19(3), 2401113 (2025). https://doi.org/10.1002/lpor.202401113
M. Liu, Y. Lei, L. Yu, X. Fang, Y. Ma, L. Liu, and P. Gao, “Super-resolution optical microscopy using cylindrical vector beams”, Nanophotonics, 11(15), 3395 (2022). https://doi.org/10.1515/nanoph-2022-0241
X. Yuan, H. Guo, S. Zhuang, and J. Hu, “Generation and high-resolution focusing of higher-order vector beam via metasurface”, IEEE Photonics Journal, 16, 2201206 (2024). https://doi.org/10.1109/JPHOT.2024.3406534
S. Boichenko, “Fast-speed algorithm to compute tight focusing of laser beams: Effectiveness of circularly polarized vortex beam series as a mathematical basis”, Physical Review A, 109(4), 043501 (2024). https://doi.org/10.1103/PhysRevA.109.043501
V.V. Kotlyar, S.S. Stafeev, V.D. Zaitsev, A.M. Telegin, and E.S. Kozlova, “Spin–orbital transformation in a tight focus of an optical vortex with circular polarization”, Applied Sciences, 13(14), 8361 (2023). https://doi.org/10.3390/app13148361
Y. Miao, L. Wang, Q. Zhang, X. Sun, X. Gao, J. Wan, and S. Zhuang, “Tight-focusing properties of propagable fractional-order vector vortex beams”, Journal of the Optical Society of America B, 40(5), 1113 (2023). https://doi.org/10.1364/JOSAB.485509
D. Maluenda, M. Aviñoá, K. Ahmadi, R. Martínez-Herrero, and A. Carnicer, “Experimental estimation of the longitudinal component of a highly focused electromagnetic field”, Scientific Reports, 11(1), 17992 (2021). https://doi.org/10.1038/s41598-021-97164-z
Z. Qing, W. Yan, X. Long, Z. Yuan, Z.C. Ren, X.L. Wang, and H.T. Wang, “Longitudinal manipulation of local nonseparability in vector beams”, Optics Letters, 49(10), 2557 (2024). https://doi.org/10.1364/OL.524647
D.A. Ikonnikov, S.A. Vyunisheva, D.V. Prokopova, N.N. Losevsky, S.A. Samagin, S.P. Kotova, and A.M. Vyunishev, “Configurable vortex laser beams for optical manipulations of microparticle ensembles”, Laser Physics Letters, 20(8), 086002 (2023). https://doi.org/10.1088/1612-202X/ace0af
J. Zeng, Y. Dong, Y. Wang, J. Zhang, and J. Wang, “Optical imaging using orbital angular momentum: interferometry, holography and microscopy”, Journal of Lightwave Technology, 41(7), 2025 (2022). https://doi.org/10.1109/JLT.2022.3225214
M. Cheng, W. Jiang, L. Guo, J. Li, and A. Forbes, “Metrology with a twist: probing and sensing with vortex light”, Light: Science & Applications, 14(1), 4 (2025). https://doi.org/10.1038/s41377-024-01665-1
F. Pang, L. Xiang, H. Liu, L. Zhang, J. Wen, X. Zeng, and T. Wang, “Review on fiber-optic vortices and their sensing applications”, Journal of Lightwave Technology, 39(12), 3740 (2021). https://opg.optica.org/jlt/abstract.cfm?URI=jlt-39-12-3740
S.K. Noor, M.N.M. Yasin, A.M. Ismail, M.N. Osman, P.J. Soh, N.Ramli, and A.H. Rambe, “A review of orbital angular momentum vortex waves for the next generation wireless communications”, Ieee Access, 10, 89465 (2022). https://doi.org/10.1109/ACCESS.2022.3197653
D. Bongiovanni, D. Li, M. Goutsoulas, H. Wu, Y. Hu, D. Song, and Z. Chen, “Free-space realization of tunable pin-like optical vortex beams”, Photonics Research, 9(7), 1204 (2021). https://doi.org/10.1364/PRJ.420872
G. Wang, X. Weng, X. Kang, Z. Li, K. Chen, X. Gao, and S. Zhuang, “Free-space creation of a perfect vortex beam with fractional topological charge”, Optics Express, 31(4), 5757 (2023). https://doi.org/10.1364/OE.483304
Z. Shen, and S. Huang, “Generation of subdiffraction optical needles by simultaneously generating and focusing azimuthally polarized vortex beams through Pancharatnam–Berry metalenses”, Nanomaterials, 12(22), 4074 (2022). https://doi.org/10.3390/nano12224074
J. Chen, and Q. Xu, “Superlong uniform light tunnel created by focusing radially polarized vortex beam”, Journal of Applied Physics, 124, 4 (2018). https://doi.org/10.1063/1.5033926
P.B. Singh, and B. Kumar, “Formation of subwavelength tunable flat-top focus with double foci characteristic by tightly focused cylindrical vector beams”, Optics Communications, 572, 130972 (2024). https://doi.org/10.1016/j.optcom.2024.130972
X. Zhang, Y. Xu, B. Hong, F. Zhang, A. Wang, and W. Zhao, “Generation of a focused THz vortex beam from a spintronic THz emitter with a helical Fresnel zone plate”, Nanomaterials. 13(14), 2037 (2023). https://doi.org/10.3390/nano1314203
X. Feng, X. Chen, Y. Lu, Q. Wang, L. Niu, Q. Xu, and W. Zhang, “Direct emission of focused terahertz vortex beams using Indium‐Tin‐Oxide‐based Fresnel zone plates”, Advanced Optical Materials, 11(1), 2201628 (2023). https://doi.org/10.1002/adom.202201628
M. Zhong, and J.S. Li, “Terahertz vortex beam and focusing manipulation utilizing a notched concave metasurface”, Optics Communications, 511, 127997 (2022). https://doi.org/10.1016/j.optcom.2022.127997
H. Li, C. Zheng, H. Xu, J. Li, C. Song, F. Yang, and J. Yao, “All-graphene geometric terahertz metasurfaces for generating multi-dimensional focused vortex beams”, Opt. Laser Technol, 159, 108986 (2023). https://doi.org/10.1016/j.optlastec.2022.108986
J. Farhoomand, and H.M. Pickett, “Stable 1.25 watts CW far infrared laser radiation at the 119 μm methanol line”, Int. J. Infrared Millim. Waves, 8, 441 (1987). https://doi.org/10.1007/BF01013257
M.W. Beijersbergen, R.P.C. Coerwinkel, M. Kristensen, and J.P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate”, Opt. Commun., 112(5-6), 321 (1994). https://doi.org/10.1016/0030-4018(94)90638-6
A.V. Ustinov, S.N. Khonina, P.A. Khorin, and A.P. Porfirev, “Control of the intensity distribution along the light spiral generated by a generalized spiral phase plate”, Journal of the Optical Society of America B, 38(2), 420 (2021). https://doi.org/10.1364/JOSAB.408884
V.V. Kotlyar, and A.A. Kovalev, “Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization”, J. Opt. Soc. Am. A, 27(3), 372 (2010). https://doi.org/10.1364/JOSAA.27.000372
B. Gu, and Y. Cui, “Nonparaxial and paraxial focusing of azimuthal-variant vector beams”, Opt. Express, 20(16), 17684 (2012). https://doi.org/10.1364/OE.20.017684
Y. Zhang, L. Wang, and C. Zheng, “Vector propagation of radially polarized Gaussian beams diffracted by an axicon”, J. Opt. Soc. Am. A, 22(11), 2542 (2005). https://doi.org/10.1364/JOSAA.22.002542
E.A.J. Marcatilі, and R.A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers”, Bell Syst. Tech. J., 43(4), 1783 (1964). https://doi.org/10.1002/j.1538-7305.1964.tb04108.x
J.F. Nye, and M.V. Berry, “Dislocations in wave trains”, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 336(1605), 165 (1974). https://doi.org/10.1098/rspa.1974.0012
H. Wang, Q. Song, Y. Cai, Q. Lin, X. Lu, H. Shangguan, Y. Ai, and S. Xu, “Recent advances in generation of terahertz vortex beams and their applications”, Chin. Phys. B, 29(9), 097404 (2020). https://doi.org/10.1088/1674-1056/aba2df
J.W. Goodman, Introduction to Fourier optics, (Roberts and Company Publishers, 2005).
O.V. Gurin, A.V. Degtyarev, N.N. Dubinin, M.N. Legenkiy, V.A. Maslov, K.I. Muntean, V.N. Ryabykh and V.S. Senyuta, “Formation of beams with nonuniform polarisation of radiation in a cw waveguide terahertz laser”, Quantum Electron., 51(4), 338 (2021). https://doi.org/10.1070/QEL17511
A.V. Degtyarev, M.M. Dubinin, O.V. Gurin, V.A. Maslov, K.I. Muntean, V.N. Ryabykh, V.S. Senyuta, “Control of tightly focused laser beams in the THz range”, Microwave and Optical Technology Letters, 63(11), 2888 (2021). https://doi.org/10.1002/mop.32946
A.V. Degtyarev, M.M. Dubinin, O.V. Gurin, V.A. Maslov, K.I. Muntean, V.M. Ryabykh, V.S. Senyuta, and O.O. Svystunov, “Control over higher-order transverse modes in a waveguide-based quasi-optical resonator”, Radio Physics and Radio Astronomy, 27(2), 129 (2022). https://doi.org/10.15407/rpra27.02.129
Copyright (c) 2025 Andrey V. Degtyarev, Mykola M. Dubinin, Vyacheslav A. Maslov, Konstantin I. Muntean, Oleh O. Svystunov

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).



