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We demonstrate an easy two-step maskless method for the fabrication of so-called compound fork-shaped gratings in nanomultilayer structures (NMLSs) based on chalcogenide glasses. Such elements allow one to generate different configurations of optical vortex (OV) beams with given topological charges (TCs). The used NMLS is particularly interesting because it enables one to realize the direct one-step writing of the surface relief without selective etching. We show that it is possible to control TCs of the generated OV beam arrays, their locations, and intensity. The proposed approach can easily be adapted to the fabrication of compound diffractive gratings performing the desired one- and two-dimensional generation and splitting of other structured laser beams.

We report on a theoretical and numerical study of a Gaussian beam modulated by several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. The TC of such a multi-vortex beam equals the sum of the TCs of all OVs. If the OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such a beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the OVs to appear at the infinity of such a combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such a quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time to our knowledge, and we obtained the TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) the TC is unchanged, while the OAM changes by less than 10% if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

The rotation of optically trapped particles is used in many applications for the realization of different micromechanical devices, such as micropumps, microrotors, and microgyroscopes, as well as for the investigation of particle interactions. Although for transparent micro-objects in both liquid media and vacuum, the rotation can easily be realized by transfer of the spin angular or orbital angular momentum from the light to the object. In the case of light-absorbing micro-objects in gaseous media, such transfers are insignificant in comparison with the thermal effects arising from the photo- and thermo-phoresis phenomena initiating the movement of trapped particles in a laser beam. Currently, proposed methods using a single focused laser beam, tapered-ring optical traps, or single and multiple bottle beams (BBs) have various limitations—for example, the inability to control the direction of the revolution of trapped particles or the low revolution frequency and small revolution angles. Here we propose a simple method for the realization of the revolution of airborne light-absorbing particles. The method is based on a combination of a circular diaphragm and a rotating cylindrical lens, enabling the generation of linear optical BBs. Our results show the flexibility and reliability of the proposed technique, allowing such laser traps to be used in various optical systems for the manipulation of micro-objects with different dimensions and shapes.

We investigate the astigmatic transformation of vortex and nonvortex cylindrical vector beams (CVBs) of different orders performed by a cylindrical lens. The total intensity does not change when the cylindrical lens rotates; however, the individual components can be significantly transformed. We show that the modulus of the polarization order |p| of the investigated CVBs can be defined by the astigmatic intensity distribution. In addition, in the case of vortex CVBs, it is only possible to determine a change in the sign of the order of the optical vortex. The experimentally obtained results are in agreement with the modeling results. The results obtained can be useful in optical communications for the detection of vortex beams with different polarization states and in polarization-dependent laser nanopatterning of various materials.

Here we obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude, passed through an off-axis spiral phase plate (SPP). The formula shows that the OAM is zero if the incident light is bounded by a diaphragm, and the SPP center is outside it. Another consequence of the obtained formula is that if the incident light is limited by an annular diaphragm then the full angular momentum is the same, regardless of the position of the SPP center inside the shaded circle of the annular diaphragm. This means that it is more appropriate to illuminate the SPP by beams with an annular intensity distribution because, in this case, the inaccurate alignment of the SPP center and the center of the annular intensity distribution do not affect the total OAM of the beam. In addition, we obtain a formula for the OAM density of such a light beam in the initial plane. The experimentally measured OAM is in good agreement with that calculated by the obtained formula.

We investigate several methods of focus shift and focus extension in detail. These methods are divided into two groups: (1) changing the radius of the illuminating beam and/or limiting diaphragm; and (2) adding an optical system with an adjustable element (lens or axicon). In the cases of a planar and Gaussian illuminating beam, values of the focus position and depth of focus (DOF) are calculated theoretically and numerically, depending on the beam radius. In addition, theoretical and numerical evaluations of displacement and DOF increase for the focusing system with the adjustable lens or axicon obtained. We show that these methods for changing the parameters of the focal area provide flexibility and efficiency in the control of its characteristics. Recommendations about possible applications in which such control is important are formulated on the basis of the results obtained.

Halide-perovskite microlasers have demonstrated fascinating performance owing to their low-threshold lasing at room temperature and low-cost fabrication. However, being synthesized chemically, controllable fabrication of such microlasers remains challenging, and it requires template-assisted growth or complicated nanolithography. Here, we suggest and implement an approach for the fabrication of microlasers by direct laser ablation of a thin film on glass with donut-shaped femtosecond laser beams. The fabricated microlasers represent MAPbBrxIymicrodisks with 760 nm thickness and diameters ranging from 2 to 9 μm that are controlled by a topological charge of the vortex beam. As a result, this method allows one to fabricate single-mode perovskite microlasers operating at room temperature in a broad spectral range (550–800 nm) with Q-factors up to 5500. High-speed fabrication and reproducibility of microdisk parameters, as well as a precise control of their location on a surface, make it possible to fabricate centimeter-sized arrays of such microlasers. Our finding is important for direct writing of fully integrated coherent light sources for advanced photonic and optoelectronic circuitry.

We investigate theoretically, numerically, and experimentally a novel type of laser beam—an aberration laser beam (ALB). To generate the ALB, a diffractive optical element with a phase transmission function having an arbitrary radial dependence of power q and a periodic angular dependence of sin(mϕ) or cos(mϕ) form can be used. Such a light distribution is more general than classic aberrations including Zernike polynomials. We demonstrate that such radial nonuniformity results in autofocusing properties of ALBs. The autofocusing feature of ALBs is analogous to that of circular Airy beams, but the ALBs’ autofocusing feature has more flexibility. The presence of the periodic angular dependence in the phase results in a diffraction pattern with mth-order symmetry. Transformation of ALBs during propagation in free space is analogous to transformation of the three-Airy beams; however, the generated light distributions have an arbitrary integer order of symmetry. The presence of an additional focusing lens leads to formation of an optical field in its focal plane with symmetry that depends on the parity of m: for even m, the generated light distribution has 2mth-order symmetry, and, for odd m, it has mth-order symmetry.

We demonstrate a new type of circular Airy beam, the azimuthally modulated circular superlinear Airy beam, generated by utilizing a diffraction element, whose transmission function is the sum of the transmission function of the element, generating a “petal” pattern and the transmission function of the element generating a circular Airy beam. We investigate the propagation dynamics of such beams and demonstrate that their autofocusing and self-healing properties are strongly dependent on the number of generated petals. In addition, we propose a simple way to control the shape of the caustic of the generated laser beams with a fixed number of generated petals. We believe that these results can be very useful for lensless laser fabrication and laser manipulation techniques, as well as for the development of new filament plasma multi-channel formation methods.

We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or through an inclined spherical lens. We also obtain similar analytical expressions describing propagation of an optical vortex generated when a Gaussian beam illuminates an inclined spiral phase plate (SPP) or when an elliptic Gaussian beam illuminates a SPP (not inclined). All these optical vortices with a topological charge (TC) n are described by the n-th order Hermite polynomial with a complex argument. It is shown that the argument is real only on a straight line in the transverse plane of the laser beam. There are n intensity nulls on this line. The treated here astigmatic transforms are used to determine the integer TC of optical vortices. We conduct a comparative experimental study of different astigmatic transforms and we show that the transform with a cylindrical lens is the best for determining the TC. Unlike other similar works, in this study we achieve transformation of n-degenerate intensity null of an optical vortex with the TC n=100 into n isolated first-order intensity nulls.

A theoretical and experimental study of the propagation of vortex laser beams in a random aerosol medium is presented. The theoretical study is based on the extended Huygens–Fresnel principle with the generation of a random field, using the fast Fourier transform. The simulation shows that the stability of vortex beams to fluctuations of an optical medium falls with rising order of optical vortices. Moreover, a coherence length (radius) of the random medium is of great importance. The coherence radius extension affects adversely the conservation of a beam structure in the random medium. During further free-space propagation, increasing coherence enables reduction of the negative effects of fluctuations for beams with high-value topological charges. Experimental studies in the random aerosol medium have shown that at small distances vortex beams mostly demonstrate lower stability than a Gaussian beam. However, at considerable distances, vortex beams start to demonstrate greater stability that may be explained by their capacity to be regenerated after they passed obstacles.

We theoretically study a Gaussian optical beam with an embedded off-axis optical vortex. We also experimentally generate such an asymmetric Gaussian optical vortex by using an off-axis spiral phase plate. It is shown that depending on the shift distance the laser beam has the form of a crescent, which is rotated upon propagation. An analytical expression is obtained for the orbital angular momentum of such a beam, which appears to be fractional. When the shift increases, the greater the number of spirality of the phase plate or the “fork” hologram, the slower the momentum decreases. The experimental results are in qualitative agreement with the theory.

We show that near-field nanoscale focusing is feasible using not only metallic but also dielectric sharp-edged structures. Based on vector Rayleigh–Sommerfeld integrals, we prove that the effect of an enhancement of the longitudinal electromagnetic field component occurs in the vicinity of the incident field phase discontinuities due to abrupt jumps in the optical element’s microrelief. Using a finite-element method, we simulate diffraction of the electromagnetic field on sharp edges of metallic and high-contrast dielectric structures. The resulting focal spot size is shown to be near directly proportional to the structure tip’s curvature radius. We propose a focusing arrangement that contains a radiation collector in the form of a conic axicon and a nanofocuser in the form of a nanosphere on the axicon’s apex. Using the finite-element method, we demonstrate that the focal spot size is approximately linearly proportional to the nanosphere radius. Thus, the proposed setup enables light to be confined to a thin focal spot with the size λ/373 when the silicon nanosphere radius is 2 nm.

We derived exact analytical relationships to describe the complex amplitude of a perfect optical vortex generated by means of three different optical elements, namely, (i) an amplitude-phase element with a transmission function proportional to a Bessel function, (ii) an optimal phase element with a transmission equal to the sign function of a Bessel function, and (iii) a spiral axicon. The doughnut intensity was shown to be highest when using an optimal phase element. The spiral-axicon-aided diffraction ring was found to be twice as wide as when generated using two other elements. Thus, the optimal filter was shown to be best suited for generating a perfect optical vortex. The simulation results were shown to corroborate theoretical predictions, with the experiment being in agreement with theory and simulation.

We considered a generalization of the Laguerre–Gaussian (LG) laser beam family by using a complex shift of the beam complex amplitude in Cartesian coordinates. In this case, LG-beams lose their axial symmetry. The normalized orbital angular momentum is the sum of the beam topological charge and the term which is in square dependence on the asymmetry parameter. By optical trapping and moving the polystyrene microspheres in the focus of the asymmetric LG-beam, it is proven that the velocity of the microspheres increases with increasing the asymmetry parameter and constant topological charge.

We demonstrate the possibility of generating a photonic nanojet with a helix shape (photonic nanohelix) at the diffraction of a Gaussian beam on a binary spiral axicon. We investigate the influence of the illuminating beam parameters on the shape and size of the generated photonic nanohelix by solving the Helmholtz equation using the finite element method. The simulated photonic nanohelix has depth of focus (DOF) of 2.21 μm (3.49λ) and FWHM of 304.5 nm (0.48λ), and the intensity maximum is 11.59 times higher than the incident beam maximum intensity. Using a near-field scanning optical microscope with a metal tip, it has been demonstrated that when we illuminate a binary spiral axicon with NA=0.5 and depth of etching of 500 nm by a linearly polarized plane wave (λ=633  nm), the output beam is in the form of a photonic nanohelix of DOF 2.00±0.25  μm (3.16±0.39λ) with FWHM 339±5  nm (0.54±0.01λ).

The intensity distribution on the optical axis of a parabolic binary diffraction lens is theoretically and experimentally studied. The binary diffraction lens is shown to form an array of focal spots of near-equal intensity on the optical axis. In each local focus, the focal-spot size decreases as the square of the focus number until the paraxiality condition is broken. Theory and experiment are shown to be in good agreement.