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Journal ArticleDOI

Generation of an elliptic Bessel beam

01 Jan 2006-Optics Letters (Optical Society of America)-Vol. 31, Iss: 1, pp 38-40

TL;DR: A technique is reported for the generation of elliptic hollow beams, which are actually scaled versions of higher-order Bessel beams, based on the fact that stretching coordinates in the space domain results in a contraction in the frequency domain, along with a change in the overall amplitude of the spectrum.

AbstractIn an elliptic coordinate system the solution for a diffraction-free beam is given by a Mathieu beam, which is mathematically complicated and therefore takes considerable computational time and a large memory space. A technique is reported for the generation of elliptic hollow beams, which are actually scaled versions of higher-order Bessel beams. The analysis is based on the fact that stretching coordinates in the space domain results in a contraction of the coordinates in the frequency domain, along with a change in the overall amplitude of the spectrum. The beam, produced holographically, is structurally stable and retains its shape up to approximately 1 m.

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Citations
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Journal ArticleDOI
Abstract: We show that among the multitude of rotating light beams whose complex amplitude can be represented as a linear superposition of the Laguerre–Gaussian (LG) modes with definite numbers there are light beams with zero orbital angular momentum (OAM) and vice versa, multi-mode LG beams that show no rotation and are lacking the radially symmetric intensity distribution can possess the non-zero OAM. Also, we give examples of the rotating light beams with zero OAM, represented as a superposition of the Bessel and new hypergeometric modes. Using an SLM, we generate a rotating Bessel beam with zero OAM for the first time.

63 citations

Journal ArticleDOI
TL;DR: This work has fabricated by photolithography a binary diffractive optical element able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 microm.
Abstract: We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 μm.

62 citations

Journal ArticleDOI
Abstract: We generalize the concept of perfect optical vortices, studying the elliptic perfect optical vortices (EPOVs), which also have diameters independent of the topological charge. A phase-only diffractive optical element is proposed for the efficient generation of such EPOV. The intensity of the EPOV generated by this element is higher than that of the EPOV generated approximately by an elliptical axicon. We obtain exact analytical expressions for the orbital angular momentum (OAM) density and for the total OAM of the EPOV. These expressions show that the normalized OAM of the EPOV is fractional and it exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. It allows continuous controlling of the OAM by changing the ellipticity. We show analytically that the OAM density is maximal on the smaller side of the EPOV. The ratio of the maximal to the minimal OAM density equals the squared ratio of the ellipse dimensions. Using the proposed element, EPOVs that carry ...

37 citations

Journal ArticleDOI
TL;DR: It is shown that hollow beams are generated by light rays that propagate along a spiral path through the light guide, and the properties of the hollow beam depend on the tilt angle and location of the input beam on the front surface of the light guides.
Abstract: The generation of hollow beams by a multimode light guiding device is analyzed. The light propagation through the light guide is simulated by ray tracing. It is shown that hollow beams are generated by light rays that propagate along a spiral path through the light guide. The properties of the hollow beam depend on the tilt angle and location of the input beam on the front surface of the light guide. The properties of the output beam are investigated experimentally.

21 citations

Journal ArticleDOI
Abstract: We present a highly efficient method of generating and shaping ellipse perfect vector beams (EPVBs) with a prescribed ellipse intensity profile and continuously variant linear polarization state. The scheme is based on the coaxial superposition of two orthogonally polarized ellipse laser beams of controllable phase vortex serving as the base vector components. The phase-only computer-generated hologram is specifically designed by means of a modified iteration algorithm involving a complex amplitude constraint, which is able to generate an EPVB with high diffraction efficiency in the vector optical field generator. We experimentally demonstrate that the efficiency of generating the EPVB has a notable improvement from 1.83% in the conventional complex amplitude modulation based technique to 11.1% in our method. We also discuss and demonstrate the simultaneous shaping of multiple EPVBs with independent tunable ellipticity and polarization vortex in both transversal (2D) and axial (3D) focusing structures, proving potentials in a variety of polarization-mediated applications such as trapping and transportation of particles in more complex geometric circumstances.

14 citations


References
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Journal ArticleDOI
Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

2,074 citations

Journal ArticleDOI
TL;DR: The characteristics of a singularity in a nondiffracting Bessel beam is explored experimentally by use of a programmable spatial light modulator with 64-level phase holograms and the diffraction efficiency is greatly improved.
Abstract: A laser beam with phase singularities is an interesting object to study in optics and may have important applications in guiding atoms and molecules. We explore the characteristics of a singularity in a nondiffracting Bessel beam experimentally by use of a programmable spatial light modulator with 64-level phase holograms. The diffraction efficiency with 64-level phase holograms is greatly improved in comparison with that obtained with a binary grating. The experiments show that the size and deflection angle of the beam can be controlled in real time. The observations are in agreement with scalar diffraction theory.

199 citations

Journal ArticleDOI
TL;DR: A 1-mm-diameter all-light atom guide capable of transporting ultracold atoms tens of centimeters with high efficiency is described and it is shown that it is possible for one to control the direction and speed of the atoms in the tunnel by varying the detuning of the tunnel beam.
Abstract: A 1-mm-diameter all-light atom guide capable of transporting ultracold atoms tens of centimeters with high efficiency is described. We made the atom tunnel, a dark hollow beam that is blue detuned from resonance, by passing a few tens of milliwatts of power from a TEM00 diode laser beam through an optical sequence composed of three axicons and a simple lens. We demonstrate transport of 108 Cs atoms approximately 20 cm with minimal heating. We show that it is possible for one to control the direction and speed of the atoms in the tunnel by varying the detuning of the tunnel beam.

184 citations

Journal ArticleDOI
Abstract: We report the first experimental observation of zero-order Mathieu beams which are fundamental non-diffracting solutions of the wave equation in elliptic cylindrical coordinates.

165 citations