RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. The paper concerns the effect of tight focusing of the terahertz-range vortex laser beams, formed byradially polarized TM0m modes of a dielectric waveguide-based resonator, that results from beam’s passage through a spiral phase changing plate. The work is aimed at obtaining analytical expressions to describe the field structure and determine the effect exerted by the topological charge of the plate, as well as order of the participating mode, upon the spatial-energy characteristics of the radiation within the lense’s focal region.

Methods and Methodology. The propagation and focusing of the radiation are described within the framework of the Rayleigh-Sommerfeld vector theory, making use of a nonparaxial approximation. The mode structure of the resonant cavity is determined by the TM01, TM02 and TM03 modes of a hollow circular dielectric waveguide. The action of the spiral phase changing plate is taken into account in terms of a complex-valued transfer function using topological charge numbers n=0, 1, 2.

Results. Analytical expressions have been obtained for components of the electric field of the laser beams as excited by the radially polarized TM0m modes passing through the spiral phase changing plate during their tight focusing. As has been found, in the absence of a phase-changing plate in the focal region of the lens, an annular field structure with a non-zero axial field’s intensity is preserved for all the modes involved. When using a phase plate with a topological charge n= 1 the field intensity maxima are localized near the axis, while in the case of n= 2 an annular field distribution with a zero intensity at the axis is restored. The highest magnitudes of the maximum field intensity for the modes TM01, TM02 and TM03 correspond to the to- pological charge n= 1. In the case of a phase-changing plate with n= 1, the phase fronts of all the three field components of the modes under study acquire a single-lobe vortex structure, while with n= 2 — a two-lobe structure.

Conclusions. Making use of a TM0m mode of a certain established order, along with a spiral phase-changing plate with a selected topological charge makes it possible to control the field structure of the terahertz vortex beams involved, as well as their phase fronts, axial intensities, effective diameters and field component composition during their tight focusing in the focal region of the lens.

Keywords: terahertz laser, vortex beam, spiral phase plate, topological charge, radial polarization, TM0m modes, dielectric waveguide-based resonator, tight focusing

Manuscript submitted 06.05.2026

Radio phys. radio astron. 2026, 31(2): 126-137

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