Andrey V. Ustinov

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.

Near-field propagation of vortex beams: Models and computation algorithms

We have analyzed the diffraction of a plane wave and a vortex beam on a circular micro-aperture in the near field (a few wavelengths away from the source) using different models and computation algorithms: the Reyleigh-Sommerfeld integral, plane wave expansion method, and finite-difference time-domain (FDTD) method.Comparison of the models showed that the plane wave expansion method modified by the Mansuripur matrix allows us to avoid the singularity in the region of high spectral frequencies and take into account all components of the vector field when the incident beam is bounded with an aperture. Comparison of the computation algorithms in respect to accuracy and computation time showed that it is possible to use integral methods even if the distance from the optical element is less than a wavelength.The simulation of the near-field diffraction of a vortex beam on a circular micro-aperture allowed us to discover oscillations of the vortex beam in the central shade area: the size of the light vortex oscillates as the beam propagates and can be much smaller than it is predicted by the paraxial theory. In addition, the expressions obtained for vortex beams show that near the axis the total intensity will not be zero when the order of the vortex is |m| ≤ 2.

Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams

Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams.

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.

Layered lens with a linear dependence of the refractive index change

The paper considers the action of radial-layered lenses with a linear dependence of refractive index. The effect of such lenses depending on their thickness investigated. Numerical simulation based on the finite-difference time-domain method showed the possibility of sub-wavelength focusing singular Gaussian beams through such lenses.

Singular laser beams nanofocusing with dielectric nanostructures: theoretical investigation

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.

Focused, evanescent, hollow, and collimated beams formed by microaxicons with different conical angles

Diffraction patterns formed by axicons with different tip (vertex) angles are analytically and numerically investigated. Results show that the axicon (or tapered dielectric probe) can form an extended axial light beam, a compact evanescent field, a hollow beam, and a collimated beam, depending on the vertex angle. Two-dimensional and three-dimensional models of a tapered dielectric probe show that, with small changes to the vertex angle, light transmitted by the probe is scattered rather than focused, and vice versa. Angle meanings corresponded to boundary transitions have a quantum character and densify as the angle approaches zero. These features should be taken into consideration when manufacturing microaxicons intended for various applications.

Diffraction patterns with mth order symmetry generated by sectional spiral phase plates

The possibility of generating diffraction patterns with mth order symmetry when laser beams of different wavelengths illuminate sectional spiral phase plates (SPPs) is investigated analytically, numerically and experimentally. Such distributions are generated by a SPP with m sections in which the phase increases from 0 to 2π for the base wavelength. If the wavelength of laser light is changed, we get a decomposition of the mth order vortex beam into m off-axis vortices of the first order. We show that generating array of first-order optical vortices by the sectional SPPs can be dynamically controlled by the laser wavelength. Numerical simulation and experimental results are in a good agreement with the analytical calculations.

Analyzing the Symmetry Properties of a Distribution in the Focal Plane for a Focusing Element with Periodic Angle Dependence of Phase

We analyze the symmetry properties of the focal plane distribution when light is focused with an element characterized by a periodic angular dependent phase, sin () or cos (). The majority of wave aberrations can be described using the said phase function. The focal distribution is analytically shown to be a real function at odd values of m, which provides a simple technique for generating designed wave aberrations by means of binary diffractive optical elements. Such a possibility may prove useful in tight focusing, as the presence of definite wave aberrations allows the focal spot size to be decreased. The analytical computations are illustrated by the numerical simulation, which shows that by varying the radial parameters the focal spot configuration can be varied, whereas the central part symmetry is mainly determined by the parity of m: for even the symmetry order is 2m and for odd is m.

Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates

Nowadays, the well-known cylindrical vector beams (CVBs) – the axially symmetric beam solution to the full-vector electromagnetic wave equation – are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.