A. V. Degtyarеv, M. M. Dubinin, O. V. Gurin, V. O. Maslov, K. I. Muntean, V. M. Ryabykh, V. S. Senyuta, O. O. Svystunov


Subject and Purpose. The problems under consideration concern selection and focusing of higher-order modes in a waveguide-based dielectric laser. The purpose is to clarify the physics underlying the behavior of, and permitting control over, continuous terahertz-frequency laser beams of various spatial polarizations.

Methods and Methodology. The mode parameters of the waveguide-based laser resonator involving an inhomogeneous phase-stepped mirror were calculated in a matrix technique. To analyze the propagation and focusing of the laser beams that can be excited in a variety of diffraction zones by the wave modes of a waveguide-based quasi-optical resonator, a vectorial Rayleigh–Sommerfeld theory was used. The pertinent experimental studies were performed with the use of known measurement methods suitable for the terahertz frequency range.

Results. A method for selecting the higher-order EH12q-mode of a terahertz-range laser resonator has been suggested, substantiated theoretically and approbated in experiment. It envisages placing an additional element to perform control over the system’s modal structure, namely a (2.3…2.8) λ-wide groove on the surface of one of the resonator mirrors. This measure can significantly increase losses for all undesirable modes. At the same time, the losses for the higher EH12q-mode remain practically unchanged, which creates conditions for its predominant excitation. Theoretical and experimental studies of moderate and ‘sharp’ focusing in free space of higher-order modes with different spatial polarizations of a dielectric waveguide-based resonator have been carried out.

Conclusion. As has been shown, the proposed phase-stepped mirror with a groove can effectively select the higher-order transverse modes that may be required. The linearly polarized EH12q-mode has maximum field intensity in the focal region of the lens employed. For azimuthally polarized TE02q- and TE03q-modes the central lobes, noticeably shifted from the focus of the lens, have a field maximum. An increase in the axial intensity is observed upon ‘sharp’ focusing in the field distribution of the radially polarized TM02q- and TM03q-modes. In this case their central lobes, like those of the higher TE0nq-modes, are noticeably shifted from the lens focus.

Manuscript submitted 20.04.2022

Radio phys. radio astron. 2022, 27(2): 129-139


  1. Valusis, G. and Lisauskas, A., 2021. Roadmap of terahertz imaging 2021. Sensors, 21(12), Art. 4092. DOI:
  2. Fu, J., Yu, X., Wang, Y. and Chen, P., 2018. Generation of pure longitudinal magnetization needle with tunable longitudinal depth by focusing azimuthally polarized beams. Appl. Phys. B, 124(1), Art. 11. DOI:
  3. Kozawa, Y. and Sato, S., 2007. Sharper focal spot formed by higher-order radially polarized laser beams. JOSA-A, 24(6), pp. 1793–1798. DOI:
  4. Stafeev, S.S., Kozlova, E.S., Nalimov, A.G. and Kotlyar, V.V., 2020. Tight focusing of a cylindrical vector beam by a hyperbolic secant gradient index lens. Opt. Lett., 45(7), pp. 1687–1690. DOI:
  5. Kallioniem, L., Turquet, L., Lipsanen, H., Kauranen, M. and Bautista, G., 2020. Tailoring the longitudinal electric fields of high-order laser beams and their direct verifi cation in three dimensions. Opt. Commun., 459, Art. 124894. DOI:
  6. Stafeev, S.S., Kozlova, E.S. and Nalimov, A.G., 2020. Focusing a second-order cylindrical vector beam with a gradient index Mikaelian lens. Comput. Opt., 44(1), pp. 29–33. DOI:
  7. Jin, X., Zhang, H., Xu, Y., Zhang, X. and Zhu, H., 2015. Representation and focusing properties of higher-order radially polarized Laguerre–Gaussian beams. J. Mod. Opt., 62(8), pp. 626–632. DOI:
  8. Khonina, S.N., Alferov, S.V. and Karpeev, S.V., 2013. Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams. Opt. Lett., 38(17), pp. 3223–3226. DOI:
  9. Kulipanov, G.N., Lisenko, A.A., Matvienko, G.G., Oshlakov, V.K., Kubarev, V.V., Chesnokov, E.N. and Babchenko, S.V., 2014. Experimental study of the interaction between terahertz radiation from the Novosibirsk free electron laser and water aerosol. Atmos. Ocean. Opt., 28(2), pp. 165–168. DOI:
  10. Volodenko, A.V., Gurin, O.V., Degtyarev, A.V., Maslov, V.A., Svich, V.A. and Topkov, A.N., 2010. Selection of the higher transverse modes of a waveguide quasi-optical resonator. Quantum Electron., 40(1), pp. 68–72. DOI:
  11. Li, G., Wang, D., Fang, L., Ran, Z. and Yan, Q., 2019. Improvement to beam quality of optically pumped terahertz gas lasers with hole-coupling resonators. Opt. Eng., 58(2), pp. 026104 (1–6 p.). DOI:
  12. Gurin, O.V., Degtyarev, А.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 polarization of radiation in a cw waveguide terahertz laser. Quantum Electron., 51(4), pp. 338–342. DOI:
  13. Gurin, O.V., Degtyarev, А.V., Dubinin, N.N., 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:
  14. Degtyarev, A., Maslov, V. and Topkov, A., 2020. Continuous-wave terahertz waveguide lasers. LAP LAMBERT Academic Publishing.
  15. Epi shin, V.A., Maslov, V.A., Pokormyakho, N.G. and Svich, V.A., 1989. Investigation of the oscillation modes and optimization of the output power of optically pumped submillimeter waveguide lasers. Sov. J. Quantum Electron., 19(8), pp. 1007–1010. DOI:
  16. Marcatily, 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:
  17. Hen ningsen, J., Hammerich, M. and Olafsson, A., 1990. Mode structure of hollow dielectric waveguide lasers. Appl. Phys. B., 51(4), pp. 272–284. DOI:
  18. Lűneburg, R.K., 1966. Mathematical theory of optics. California: University of California Press.
  19. Goodman, J.W., 1996. Introduction to Fourier optics. McGraw-Hill.
  20. Greivenkamp, J.E., 2003. Geometrical optics. Arizona: University of Arizona.
  21. Ivanov, V.S., Zolotarevsky, Yu.M., Kotyuk, A.F. (ed.), Lieberman, A.A., 2003. Fundamentals of optical radiometry. Moscow, Russia: Fizmatlit Publ. (in Russian).


terahertz laser, dielectric resonator, inhomogeneous mirror, polarization, selection, focusing, high-order modes

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