Alexey P. Porfirev

Polarization conversion when focusing cylindrically polarized vortex beams

Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro- and nano-particles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. The creation of these laser beams is carried out using segmented polarizing plates, subwavelength gratings, interference, or light modulators. Here, we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher-order vortex phase singularity. To simultaneously generate several vortex phase singularities of different orders, we utilized a multi-order diffractive optical element. Both the theoretical and the experimental results regarding the radiation transmitted through the diffractive optical element show that increasing the order of the phase singularity leads to more efficient conversation of the polarization from radial to azimuthal. This demonstrates a close connection between the polarization and phase states of electromagnetic beams, which has important implications in many optical experiments.

Vortex Hermite–Gaussian laser beams

We study elliptical vortex Hermite-Gaussian (vHG) beams, which are described by the complex amplitude proportional to the nth-order Hermite polynomial whose argument is a function of a real parameter a. At |a|<1, on the vertical axis of the beam cross section, there are n isolated optical nulls that produce optical vortices with topological charge +1(a<0) or -1(a>0). At |a|>1, similar isolated optical nulls of the vHG beams are found on the horizontal axis. At a=0, the vHG beam becomes identical to the HG mode of the order (0,n). We derive the orbital angular momentum (OAM) of the vHG beams, which depends on the parameter a and an ellipticity parameter of the Gaussian beam. The derived equation allows the transverse intensity of the vHG-beam to be changed without changing its OAM. The experimental and theoretical results are in good agreement.

Generation of an array of optical bottle beams using a superposition of Bessel beams

A procedure for computing the phase transmission function of diffractive optical elements intended to form an array of optical bottle beams is proposed and studied. The procedure is based on a superposition of Bessel beams. We show that the hollow circular beams (optical bottle beams) are suited for trapping transparent spherical micro-objects matched in radius with the beam radius. A series of experiments on trapping transparent micro-objects in the optical bottle arrays is described. Results of an experiment on trapping opaque spherical microparticles in a double optical bottle are reported.

Half Pearcey laser beams

We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Ring et al (2012) Opt. Express 20 18955, since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectra of plane waves, which are non-zero at a half parabola. For functions of HP-beam complex amplitudes, the orthogonality properties have been revealed. Using a spatial phase modulator, we generated superposition of HP-beams. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.

Optical trapping and moving of microparticles by using asymmetrical Laguerre–Gaussian beams

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.

Experimental investigation of multi-order diffractive optical elements matched with two types of Zernike functions

The paper presents an experimental investigation of diffractive optical elements matched with two types of Zernike functions. For elements of the first type the invariance to rotation is observed. For elements of the second type there is the agreement with standard aberrations. These elements can be used for wavefront analyzing and allow us to determine the presence of aberrations.

Optimal phase element for generating a perfect optical vortex

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.

Study of propagation of vortex beams in aerosol optical medium

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.

Diffractive axicon with tunable fill factor for focal ring splitting

We have considered effect of fill factor of circular binary phase grating on intensity distribution in the focal plane. A theoretical analysis is performed in two approaches. One of them allows us to describe the general distribution structure in the focal plane, but it is not suitable for solving the inverse problem. The second approach allows us to explain the fine structure in the intensity maxima corresponding diffraction orders. In particular, this approach explains the possibility of focal ring splitting and allows us to calculate the ratio of the intensities of the two rings. The theoretical calculations and numerical simulation are confirmed by experimental studies. As a result, we have shown the ability to dynamically change the focal structure due to regulation of the grating’s fill factor by means of a spatial light modulator.

Local foci of a parabolic binary diffraction lens.

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.