RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. Currently, numerous ideas and different methods have been in growth for generating vortex beams — areas of the circular motion of the electromagnetic wave energy flow around the so-called phase singularity points caused by a violation of the wave front topological structure. The purpose of this work is to obtain analytical expressions describing the nonparaxial diffraction of wave modes of the waveguide resonator of a terahertz laser during the wave mode interaction with a spiral phase plate. The resulting vortex beams are examined for their physical features in free space propagation.

Methods and Methodology. The Rayleigh-Sommerfeld vector theory is adopted to consider the propagation of vortex laser beams generated by wave modes of the quasi-optical waveguide cavity when interacting with a spiral phase plate in different diffraction zones.

Results. For the first time, analytical expressions have been obtained to describe the nonparaxial diffraction of wave modes of the waveguide resonator of a terahertz laser, when resonator modes interact with a spiral phase plate at different topological charges, n. The physical features of the resulting vortex beams were studied in their free space propagation. It has been shown that a spiral phase plate modifies the structure of the linearly polarized EH₁₁ mode so that the original (n=0) intensity profile with the maximum energy at the center turns at n=1 and 2 into a ring-like donut shape with an energy hole in the center. The azimuthally polarized TE₀₁ mode has originally (n=0) a ring-shaped intensity. At n=1, this configuration changes to have the maximum intensity in the center. At n=2, it becomes annular again. In the process, the spherical phase front of the beam of the linearly polarized EH₁₁ mode becomes spiral and have one singularity point on the axis, whereas the phase structure of the azimuthally polarized TE₀₁ mode gains a region with two phase singularity points off the axis.

Conclusions. The results of the study can effectively facilitate information transfer in high-speed THz communication systems. They can provide a real platform to perform tasks related to tomography, exploring properties of materials, detecting astrophysical sources, which makes them very promising in modern technologies.

Keywords: terahertz laser; waveguide resonator; spiral phase plate; vortex beams; polarization; radiation propagation

Manuscript submitted 11.12.2023

Radio phys. radio astron. 2024, 29(2): 127-136

REFERENCES

1. Headland, D., Monnai, Y., Abbott, D., Christophe, F., and Withawat, W., 2018. Tutorial: Terahertz beamforming, from concepts to realizations. APL. Photonics, 3(5), pp. 051101. DOI: https://doi.org/10.1063/1.5011063

2. Forbes, A., 2023. Advances in orbital angular momentum lasers. J. Light. Technol., 41(7), pp. 2079—2086. DOI: https://doi.org/10.1109/JLT.2022.3220509

3. Wang, H., Song, Q., Cai, Y., Lin, Q., Lu, X., Shangguan, H., Ai, Y., and Xu, Y., 2020. Recent advances in generation of terahertz vortex beams and their applications. Chin. Phys. B., 29(9), pp. 097404. DOI: https://doi.org/10.1088/1674-1056/aba2df

4. Petrov, N.V., Sokolenko, B., Kulya, M.S., Gorodetsky, A., and Chernykh, A.V., 2022. Design of broadband terahertz vector and vortex beams: I. Review of materials and components. Light: Adv. Manuf., 3(4), pp. 640—652. DOI: https://doi.org/10.37188/lam.2022.043

5. Nagatsuma, T., Ducournau, G., and Renaud, C.C., 2016. Advances in terahertz communications accelerated by photonics. Nat. Photonics., 10(6), pp. 371—379. DOI: https://doi.org/10.1038/nphoton.2016.65

6. Chen, S., C., Feng, Z., Li, J., Tan, W., Du, L., H., Cai, J., and Zhu, L.G., 2020. Ghost spintronic THz-emitter-array microscope. Light Sci. Appl., 9(1), 99. DOI: https://doi.org/10.1038/s41377-020-0338-4

7. Nobahar, D., Khorram, S., 2022. Terahertz vortex beam propagation through a magnetized plasma-ferrite structure. Opt. Laser Technol., 146, 107522. DOI: https://doi.org/10.1016/j.optlastec.2021.107522

8. Hibberd, M.T., Healy, A.L., Lake, D.S., Georgiadis, V., Smith, E.J., Finlay, O.J., and Jamison, S.P, 2019. Acceleration of relativistic beams using laser generated terahertz pulses. Nat. Photonics, 14(12), pp. 755—759. DOI: https://doi.org/10.1038/s41566-020-0674-1

9. Klug, A., Nape, I., and Forbes, A., 2021. The orbital angular momentum of a turbulent atmosphere and its impact on propagating structured light fields. New J. Phys., 23(9), 093012. DOI: https://doi.org/10.1088/1367-2630/ac1fca

10. Pinnock, S.W., Roh, S., Biesner, T., Pronin, A.V., and Dressel, M., 2022. Generation of THz vortex beams and interferometric determination of their topological charge. IEEETrans. Terahertz Sci. Technol., 13(1), pp. 44—49. DOI: https://doi.org/10.1109/TTHZ.2022.3221369

11. Rubano, A., Cardano, F., Piccirillo, B., and Marrucci, L., 2019. Q-plate technology: a progress review [Invited]. J. Opt. Soc. Am. B., 36(5), pp. D70—D87. DOI: https://doi.org/10.1364/JOSAB.36.000D70

12. Imai, R., Kanda, N., Higuchi, T., Konishi, K., and Kuwata-Gonokami, M., 2014. Generation of broadband terahertz vortex beams. Opt. Lett., 39(13), pp. 3714—3717. DOI: https://doi.org/10.1364/OL.39.003714

13. Yang, Y., Ye, X., Niu, L., Wang, K., Yang, Z., and Liu, J., 2020. Generating terahertz perfect optical vortex beams by diffractive elements. Opt. Express, 28(2), pp. 1417—1425. DOI: https://doi.org/10.1364/OE.380076

14. Zhang, K., Wang, Y., Burokur, S.N., and Wu, Q., 2022. Generating dual-polarized vortex beam by detour phase: from phase gradient metasurfaces to metagratings. IEEE Trans. Microw. Theory Techn., 70(1), pp. 200—209. DOI: https://doi.org/10.1109/TMTT.2021.3075251

15. Zhang, X.D., Su, Y.H., Ni, J.C., Wang, Z.Y., Wang, Y.L., Wang, C.W., and Chu, J.R., 2017. Optical superimposed vortex beams generated by integrated holographic plates with blazed grating. Appl. Phys. Lett., 111(6), 061901. DOI: https://doi.org/10.1063/1.4997590

16. Ge, S.J., Shen, Z.X., Chen, P., Liang, X., Wang, X.K., Hu, W., and Lu, Y.Q., 2017. Generating, separating and polarizing terahertz vortex beams via liquid crystals with gradient-rotation directors. Crystals, 7(10), 314. DOI: https://doi.org/10.3390/cryst7100314

17. Guan, S., Cheng, J., and Chang, S., 2022. Recent progress of terahertz spatial light modulators: materials, principles and applications. Micromachines, 13(10), 1637. DOI: https://doi.org/10.3390/mi13101637

18. Al Dhaybi, A., Degert, J., Brasselet, E., Abraham, E., and Freysz, E.A., 2019. Terahertz vortex beam generation by infrared vector beam rectification. J. Opt. Soc. Am. B., 36(1), pp. 12—18. DOI: https://doi.org/10.1364/JOSAB.36.000012

19. Miyamoto, K., Sano, K., Miyakawa, T., Niinomi, H., Toyoda, K., Vallés, A., and Omatsu, T., 2019. Generation of high-quality terahertz OAM mode based on soft-aperture difference frequency generation. Opt. Express, 27(22), pp. 31840—31849. DOI: https://doi.org/10.1364/OE.27.031840

20. Sobhani, H., and Dadar, E., 2019. Terahertz vortex generation methods in rippled and vortex plasmas. J. Opt. Soc. Am. A., 36(7), pp. 1187—1196. DOI: https://doi.org/10.1364/JOSAA.36.001187

21. Chevalier, P., Amirzhan, A., Wang, F., Piccardo, M., Johnson, S.G., Capasso, F., and Everitt, H.O., 2019. Widely tunable compact terahertz gas laser. Science, 366(6467), pp. 856—860. DOI: https://doi.org/10.1126/science.aay8683

22. Farhoomand, J., and Pickett, H.M., 1987. Stable 1.25 watts CW far infrared laser radiation at the 119 μm methanol line. Int. J. Infrared Millim. Waves, 8(5), pp 41—447. DOI: https://doi.org/10.1007/BF01013257

23. Marcatilі, E.A.J., and Schmeltzer, R.A., 1964, Hollow metallic and dielectric waveguides for long distance optical transmission and lasers. Bell Syst. Tech. J., 43(4), pp. 1783—1809. DOI: https://doi.org/10.1002/j.1538-7305.1964.tb04108.x

24. Beijersbergen, M.W., Coerwinkel, R.P.C., Kristensen, M., and Woerdman, J.P., 1994. Helical-wavefront laser beams produced with a spiral phase plate. Opt. Commun., 112(5—6), pp. 321—327. DOI: https://doi.org/10.1016/0030-4018(94)90638-6

25. Kotlyar, V.V., and Kovalev, A.A., 2010. Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization. J. Opt. Soc. Am. A., 27(3), pp. 372—380. DOI: https://doi.org/10.1364/JOSAA.27.000372

26. Gu, B., and Cui, Y., 2012. Nonparaxial and paraxial focusing of azimuthal-variant vector beams. Opt. Express, 20(16), pp. 17684— 17694. DOI: https://doi.org/10.1364/OE.20.017684

27. Zhang, Y., Wang, L., and Zheng, C., 2005. Vector propagation of radially polarized Gaussian beams diffracted by an axicon. J. Opt. Soc. Am. A., 22(11), pp. 2542—2546. DOI: https://doi.org/10.1364/JOSAA.22.002542

28. Lu, B., and Duan, K., 2003. Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture. Opt. Lett., 28(24), pp. 2440—2442. DOI: https://doi.org/10.1364/OL.28.002440

29. Jia, X., Wang, Y., and Li, B., 2010. Nonparaxial analyses of radially polarized beams diffracted at a circular aperture. Opt. Express, 18(7), pp. 7064—7075. DOI: https://doi.org/10.1364/OE.18.007064

30. Cui, X., Wang, C., and Jia, X., 2019. Nonparaxial propagation of vector vortex beams diffracted by a circular aperture. J. Opt. Soc. Am. A, 36(1), pp. 115—123. DOI: https://doi.org/10.1364/JOSAA.36.000115

31. Nye, J.F., and Berry, M.V., 1974. Dislocations in wave trains. Proc. R. Soc. London. Ser. A., 336(1605), pp. 165—190. DOI: https://doi.org/10.1098/rspa.1974.0012

32. Gurin, O.V., Degtyarev, A.V., Dubinin, N.N., Legenkiy, M.N., Maslov, V.A., Muntean, K.I., Ryabykh, V.N., and Senyuta, V.S., 2021. Formation of beams with nonuniform polarisation of radiation in a cw waveguide terahertz laser. Quantum Electron., 51(4), pp. 338—342. DOI: https://doi.org/10.1070/QEL17511

33. Gurin, O.V., Degtyarev, А.V., Dubinin, M.M., Maslov, V.A., Muntean, K.I., Ryabykh, V.N., and Senyuta, V.S., 2020. Focusing of modes with an inhomogeneous spatial polarization of the dielectric resonator of a terahertz laser. Telecommunications and Radio Engineering, 79(2), pp. 105—116. DOI: https://doi.org/10.1615/TelecomRadEng.v79.i2.30

34. Guo, J., Zheng, S., Zhou, K., and Feng, G., 2021. Measurement of real phase distribution of a vortex beam propagating in free space based on an improved heterodyne interferometer. Appl. Phys. Lett., 119(2), 023504. DOI: https://doi.org/10.1063/5.0054755