Coherent terahertz beams with radial polarization of the 1st, 2nd, and 3rd orders have been generated with the use of silicon subwavelength diffractive optical elements (DOEs). Silicon elements were fabricated by a technology similar to the technology used before for the fabrication of DOEs forming laser terahertz beams with pre-given mode content. The beam of the terahertz Novosibirsk Free Electron Laser was used as the illuminating beam. The experimental results are in good agreement with the results of the computer simulation.

A technique of high-frequency laser ablation using a 2D beam scanner has been designed and applied to creation of a silicon diffractive optical element (DOE) with a continuous profile to focus a terahertz Gaussian beam into a square region. The microrelief of the resulting silicon DOE has been analyzed with a white-light interferometer and a scanning electron microscope. The distribution of radiation behind the DOE illuminated by a high-power beam of the Novosibirsk free-electron laser at a wavelength of 130 µm, recorded with a pyroelectric camera, has been demonstrated. The measured diffraction efficiency of the DOE is equal to 97 ± 2 % .

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In this paper, we experimentally demonstrated excitation of terahertz vortex surface plasmon polaritons by end-fire coupling of radially-polarized annular beams with orbital angular momentum (the wavelength was 141 µm, and the topological charges were ±3 and ±9) to a 70 mm long, simply connected axis-symmetric transmission line and their propagation to the end of the line and diffraction into a free wave possessing the same topological charge as the input beam. The diameter of the line exceeded greatly the radiation wavelength, and, in contrast to experiments with nanowires, no azimuthal electromagnetic modes existed. We observed that 18 plasmons, locally excited on the input face perimeter by a wave with topological charge of ±9, traveled rotating over the tapering cylindrical line and transformed into 18 lobes of the decoupled free wave. The evidence of the possibility of the transformation of a vortex beam into vortex plasmons and back into vortex beam with the conservation of the topological charge opens a way for the development of plasmonic communication lines with coding and decoding of information at the free-wave stage. Application of this technique to complex beams consisting of a combination of different vortex modes can be a technological base for the development of multiplex plasmonic communication lines in the terahertz range. Since wave characteristics are easier to record than plasmon characteristics, sorting of free waves by the topological charges can be used for demultiplexing combined plasmons in multiplex systems.

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The paper is devoted to investigation of forming multimode coherent beams of terahertz radiation with pre-given transverse mode content and terahertz vector beams by use of silicon diffractive optical elements forming single modes from terahertz free-electron laser illuminating beam.

The fact that light beams are able to carry a mechanical angular momentum is well-known. In paraxial beams, angular momentum can be represented as a sum of the spin (SAM) and orbital (OAM) angular momentum. After paper Allen et al.[1], a lot of articles devoted to the generation, study and the use of beams with orbital angular momentum, or "vortex beams", have been published. To date, vortex beams were obtained in the range from radio frequencies [2] to the soft X-ray radiation [3]. Nevertheless, there are only five studies [4][5][6][7][8], in which vortex beams in the terahertz range have been generated.Recently, using radiation of the Novosibirsk free electron laser [9] and silicon binary spiral phase axicons, terahertz Bessel beams with OAM with topological charges 1 l r and 2 l r have been generated for the first time [7]. The intensity distributions of the beams formed by the axicons are in good agreement with the distributions calculated for Bessel beams, but they are identical for both left-handed and right-handed helicities. To determine the characteristics of the beams associated with their rotation, we applied classical experiments on diffraction and interference, adapting them to the terahertz range.A direct method of detecting the rotation of a beam was its diffraction on a half-plane (Fig. 1, a). Similar experiments with Laguerre-Gaussian and Bessel vortex beams were performed in the visible region in [11], where for the Bessel beams only qualitative results were obtained because of the short laser wavelength and the tiny interference pattern.In Fig. 1, b the diffraction patterns calculated numerically at several distances are shown. In the experiments, a 16.32 12.24 u mm 2 microbolometer array (MBA) with pixel size of 0.051 mm was used as a detector for imaging of diffraction pattern. Because of geometrical restrictions, only planes located at a distance z of more than 35 mm could be recorded. The recorded patterns were identical with the calculated ones.The diffraction patterns shown in Fig. 1 clearly demonstrate the rotation of the beam. According to the theory [12], the rate of change of azimuthal angle of the trajectory of the Poynting vector with z is given by 2