# Generation of nondiffracting Bessel beams by use of a spatial light modulator

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.

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TL;DR: In this paper, the authors discuss the motivation and requirements for these recent experiments, including the underpinning mathematics, and discuss exciting new directions for single-molecule biophysics.

Abstract: Single-molecule biophysics has transformed our understanding of biology, but also of the physics of life. More exotic than simple soft matter, biomatter lives far from thermal equilibrium, covering multiple lengths from the nanoscale of single molecules to up to several orders of magnitude higher in cells, tissues and organisms. Biomolecules are often characterized by underlying instability: multiple metastable free energy states exist, separated by levels of just a few multiples of the thermal energy scale k B T, where k B is the Boltzmann constant and T absolute temperature, implying complex inter-conversion kinetics in the relatively hot, wet environment of active biological matter. A key benefit of single-molecule biophysics techniques is their ability to probe heterogeneity of free energy states across a molecular population, too challenging in general for conventional ensemble average approaches. Parallel developments in experimental and computational techniques have catalysed the birth of multiplexed, correlative techniques to tackle previously intractable biological questions. Experimentally, progress has been driven by improvements in sensitivity and speed of detectors, and the stability and efficiency of light sources, probes and microfluidics. We discuss the motivation and requirements for these recent experiments, including the underpinning mathematics. These methods are broadly divided into tools which detect molecules and those which manipulate them. For the former we discuss the progress of super-resolution microscopy, transformative for addressing many longstanding questions in the life sciences, and for the latter we include progress in 'force spectroscopy' techniques that mechanically perturb molecules. We also consider in silico progress of single-molecule computational physics, and how simulation and experimentation may be drawn together to give a more complete understanding. Increasingly, combinatorial techniques are now used, including correlative atomic force microscopy and fluorescence imaging, to probe questions closer to native physiological behaviour. We identify the trade-offs, limitations and applications of these techniques, and discuss exciting new directions.

155 citations

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TL;DR: In this paper, Turunen and Friberg dealt with a class of fields with propagation-invariant properties such as the optical intensity distribution and applied them to scalar and electromagnetic approaches.

Abstract: The first article by Turunen and Friberg deals with a class of fields with propagation-invariant properties such as the optical intensity distribution. Coherent and partially coherent stationary and pulsed solutions are treated in view of scalar and electromagnetic approaches. Approximations of ideal propagation-invariant fields and methods for their generation are discussed. Finally, some application areas are covered.

149 citations

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TL;DR: This work describes the programmable spatial beam shaping of 100-kHz, 4-microJ amplified femtosecond pulses in a focal plane by wave-front modulation and obtains top-hat, doughnut, square, and triangle shapes of 20-microm size.

Abstract: We describe the programmable spatial beam shaping of 100-kHz, 4-?J amplified femtosecond pulses in a focal plane by wave-front modulation. Phase distributions are determined by a numerical iterative procedure. A nonpixelated optically addressed liquid-crystal light valve is used as a programmable wave-front tailoring device. Top-hat, doughnut, square, and triangle shapes of 20-?m size are obtained in a focal plane. Their suitability for femtosecond laser machining is demonstrated.

148 citations

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TL;DR: Helico-conical optical beams, different from higher-order Bessel beams, are generated with a parallel-aligned nematic liquid crystal spatial light modulator by multiplying helical and conical phase functions leading to a nonseparable radial and azimuthal phase dependence.

Abstract: Helico-conical optical beams, different from higher-order Bessel beams, are generated with a parallel-aligned nematic liquid crystal spatial light modulator (SLM) by multiplying helical and conical phase functions leading to a nonseparable radial and azimuthal phase dependence. The intensity distributions of the focused beams are explored in two- and three-dimensions. In contrast to the ring shape formed by a focused optical vortex, a helico-conical beam produces a spiral intensity distribution at the focal plane. Simple scaling relationships are found between observed spiral geometry and initial phase distributions. Observations near the focal plane further reveal a cork-screw intensity distribution around the propagation axis. These light distributions, and variations upon them, may find use for optical trapping and manipulation of mesoscopic particles.

100 citations

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TL;DR: This paper elucidates through both theory and experiment the behavior of silica microspheres moving under the influence of the periodic optical field provided by a Bessel beam, and compares two different computational models based on Mie scattering and geometrical ray optics to find good qualitative agreement.

Abstract: Spatially periodic optical fields can be used to sort dielectric microscopic particles as a function of size, shape or refractive index. In this paper we elucidate through both theory and experiment the behavior of silica microspheres moving under the influence of the periodic optical field provided by a Bessel beam. We compare two different computational models, one based on Mie scattering, the other on geometrical ray optics and find good qualitative agreement, with both models predicting the existence of distinct size-dependent phases of particle behavior. We verify these predictions by providing experimental observations of the individual behavioral phases.

89 citations

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TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.

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.

2,283 citations

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TL;DR: Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

Abstract: Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

1,251 citations

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TL;DR: This work shows by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram, and demonstrates experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.

Abstract: A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.

668 citations

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01 Jan 1993

TL;DR: Optical properties of liquid crystals electro-optical properties and nonlinear optical properties of nonlinear optics of liquid crystal nonlinear systems were studied in this paper, where liquid crystals were considered.

Abstract: Optical properties of liquid crystals electro-optical properties of liquid crystals nonlinear optical properties of liquid crystals nonlinear optics.

558 citations

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TL;DR: In this article, the properties of light beams carrying phase singularities, or optical vortices, were studied both in theory and experiment, and the general rule for angular-momentum density distribution in a combined beam was established.

Abstract: We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation.

491 citations