# Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic

TL;DR: In this paper, a 3D focus shaping technique using the combination of partially coherent circularly polarized vortex beams with a binary diffractive optical element (DOE) is reported, where the intensity distribution near the focus can be tailored in three dimensions by appropriately adjusting the parameters of the incident beams, numerical aperture of the objective lens, and the design of the DOE.

Abstract: The three-dimensional (3D) focus shaping technique using the combination of partially coherent circularly polarized vortex beams with a binary diffractive optical element (DOE) is reported. It is found that the intensity distribution near the focus can be tailored in three dimensions by appropriately adjusting the parameters of the incident beams, numerical aperture of the objective lens, and the design of the DOE. Numerical results show that partially coherent circularly polarized vortex beams can be used to generate several special beam patterns, such as optical chain, optical needle, optical dark channel, flat-topped field, and 3D optical cage. Furthermore, compared with the ordinary 3D optical cage, this kind of 3D optical cage generated by our method has a controllable switch; that is, it can be easy to ?open? and ?close? by controlling the coherence length of the incident beams. Our work may find valuable applications in optical tweezers, microscopes, laser processing, and so on.

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TL;DR: In this article, the generation of cylindrical vector beams in birefringent crystals is studied analytically and experimentally in paraxial and non-paraxial regimes.

Abstract: The generation of cylindrical vector beams in birefringent crystals is studied analytically and experimentally in paraxial and non-paraxial regimes. At sharp focusing (in the non-paraxial case), two foci corresponding ordinary and extraordinary beams are formed along the crystal’s axis. There is the radially polarized distribution in one focus and the azimuthally polarized distribution in the other focus when the incident beam has the vortex phase of the first order and circular polarization of the opposite direction. The results are extended to the generation of higher-order radially and azimuthally polarized laser beams. The physical experiments with an Iceland spar crystal have been conducted.

59 citations

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TL;DR: The proposed strategy creates an orthogonal direction in the STED parametric space that uniquely allows independent tuning of resolution and contrast using a single depletion beam in a conventional (circular polarization-based) STED setup.

Abstract: Stimulated emission depletion (STED) fluorescence microscopy squeezes an excited spot well below the wavelength scale using a doughnut-shaped depletion beam. To generate a doughnut, a scale-free vortex phase modulation (2D-STED) is often used because it provides maximal transverse confinement and radial-aberration immunity (RAI) to the central dip. However, RAI also means blindness to a defocus term, making the axial origin of fluorescence photons uncertain within the wavelength scale provided by the confocal detection pinhole. Here, to reduce the uncertainty, we perturb the 2D-STED phase mask so as to change the sign of the axial concavity near focus, creating a dilated dip. By providing laser depletion power, the dip can be compressed back in three dimensions to retrieve lateral resolution, now at a significantly higher contrast. We test this coherent-hybrid STED (CH-STED) mode in x-y imaging of complex biological structures, such as the dividing cell. The proposed strategy creates an orthogonal direction in the STED parametric space that uniquely allows independent tuning of resolution and contrast using a single depletion beam in a conventional (circular polarization-based) STED setup.

29 citations

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TL;DR: Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase, and some focal fields with novel structure can be formed by choosing suitable fractional values of topological charges and spatial coherence length.

Abstract: In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

28 citations

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TL;DR: Modified Richards-Wolf vector diffraction integration equations are applied to successfully simulate experimental phenomena and the application potential of circularly polarized terahertz vortex beams in microscopy is experimentally demonstrated.

Abstract: Linearly and circularly polarized terahertz (THz) vortex beams are generated by adopting a THz quarter wave plate and spiral phase plates with topological charges 1 and 2. Taking advantage of a THz digital holographic imaging system, longitudinal components of THz vortices with different polarizations and topological charges are coherently measured and systemically analyzed in a focusing condition. The application potential of circularly polarized THz vortex beams in microscopy is experimentally demonstrated and the transformation between the spin angular momentums and orbital angular momentums of THz waves is also checked. Modified Richards-Wolf vector diffraction integration equations are applied to successfully simulate experimental phenomena.

26 citations

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TL;DR: In this paper, a review summarizes basic concepts, theoretical models, generation and propagation of partially coherent vortex beams with non-Gaussian correlated Schell-model functions is presented, based on the sufficient condition for devising a genuine correlation function of a partially coherent beam.

Abstract: Ever since vortex beams were proposed, they are known for owning phase singularity and carrying orbital angular momentum (OAM). In the past decades, coherent optics developed rapidly. Vortex beams have been extended from fully coherent light to partially coherent light, from scalar light to vector light, from integral topological charge (TC) to fractional TC. Partially coherent vortex beams have attracted tremendous interest due to their hidden correlation singularity and unique propagation properties (e.g., beam shaping, beam rotation and self-reconstruction). Based on the sufficient condition for devising a genuine correlation function of partially coherent beam, partially coherent vortex beams with nonconventional correlation functions (i.e., non-Gaussian correlated Schell-model functions) were introduced recently. This timely review summarizes basic concepts, theoretical models, generation and propagation of partially coherent vortex beams.

24 citations

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TL;DR: In this article, an investigation of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source is made, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor.

Abstract: An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.

2,636 citations

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TL;DR: An overview of the recent developments in the field of cylindrical vector beams is provided in this paper, where the authors also discuss the potential of using these beams in other fields.

Abstract: An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

2,361 citations

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TL;DR: In this article, a high-numerical-aperture lens is used to achieve light with longitudinal polarization, which has some intriguing possibilities for particle acceleration. But it is difficult to obtain longitudinal polarization.

Abstract: Light is often thought of in terms of radial polarization, but longitudinal polarization is also possible, and it has some intriguing possibilities for particle acceleration. Binary optics, combined with a high-numerical-aperture lens, is a potential route to achieving light with this unusual property.

799 citations

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TL;DR: A focus shaping technique using generalized cylindrical vector beams that can be tailored by appropriately adjusting the rotation angle to obtain peak-centered, donut and flattop focal shapes is reported.

Abstract: We report a focus shaping technique using generalized cylindrical vector beams. A generalized cylindrical vector beam can be decomposed into radially polarized and azimuthally polarized components. Such a generalized cylindrical beam can be generated from a radially polarized or an azimuthally polarized light using a two-half-wave-plate polarization rotator. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. Peak-centered, donut and flattop focal shapes can be obtained using this technique.

572 citations

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TL;DR: It is demonstrated that optical spin-to-orbital angular momentum conversion can occur in a homogeneous and isotropic medium and that the orbital rotation speeds of trapped particles are altered because of this conversion as predicted by theory.

Abstract: As a fundamental property of light, the angular momentum of photons has been of great interest. Here, we demonstrate that optical spin-to-orbital angular momentum conversion can occur in a homogeneous and isotropic medium. This Letter presents both theoretical and experimental studies of this conversion in a tightly focused beam and shows that the orbital rotation speeds of trapped particles are altered because of this conversion as predicted by theory.

524 citations