Solving Maxwell’s equations in cylindrical coordinates yields states in quantum theory with definite values of energy ℏω, longitudinal momentum ℏ k_z , and total angular momentum projection ℏ m on the z -axis (where ℏ is the Planck constant). Experimentally, values of up to ℏ m Ȉ 10⁴ ℏ have been obtained for the last quantity. The wave front of such states is like a meat grinder screw, with the lines of force of the Poynting vector representing the screw line. Such states differ from plane waves by the nonzero orbital angular momentum projection on the direction of motion, and from spherical waves, by the definite direction of motion. For brevity, these states are referred to as ‘twisted photons’. In this paper, recent experimental and theoretical results on twisted photons are reviewed, to which the present authors actively contributed. Detailed discussion is given to recent experiments on the production of high-intensity beams of terahertz (wavelength: 140 μm) twisted photons performed on the Novosibirsk free electron laser at the Budker Institute of Nuclear Physics, SB RAS. Recent theoretical work on the interaction of twisted photons with atoms is summarized. Due to their extra degree of freedom — the projection of the total angular momentum on the direction of motion — twisted photons represent a novel research tool of potentially wide application in physics.

The design and operational characteristics of the Novosibirsk free electron laser facility are described. Selected experiments in the terahertz range carried out recently at the user stations are surveyed in brief.

Bessel vortex beams with topological charges of $l=\pm 1$ and $l=\pm 2$ were produced in the terahertz spectral range from a free electron laser Gaussian beam ($\lambda =141\mu \mathrm{m}$) transformed using silicon binary diffractive optical elements. The spatial characteristics of the beams were obtained using a microbolometer array. A radius to path length ratio of $1:100$ was achieved for nondiffractive beams with the average power of 30 W. Surface plasmon polaritons (SPPs) on gold–zinc-sulphide–air interfaces were generated due to diffraction of vortex beams on a sample edge. A new effect, a dependence of the efficiency of SPP generation on the direction of the azimuthal component of incident-radiation Poynting vector, was revealed.

An uncooled microbolometer focal plane array (FPA) has been developed and used for imaging of objects illuminated by monochromatic coherent radiation of a free electron laser tunable in the range of $1.25–2.5\mathrm{THz}$ . A sensitivity threshold of $1.3\times {10}^{-3}\mathrm{W}∕{\mathrm{cm}}^2$ was obtained for the FPA with a homemade absolute interferometric power meter. Videos up to $90\text{frames}∕\mathrm{s}$ were recorded in both transmission and reflection/scattering modes. When objects were illuminated by laser radiation scattered by a rough metal surface, speckled images were observed. Good quality terahertz images were achieved through the fast rotation of the scatterer.

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\pm 1$ and $\pm 2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at $f=5.6$ MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about $L/r\approx 190$ and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, “diffraction-free” propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by $\pi$, the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 $\mu \mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.