Ince–Gaussian beams
TL;DR: The existence of the Ince-Gaussian beams is demonstrated that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation and has an inherent elliptical symmetry.
Abstract: We demonstrate the existence of the Ince-Gaussian beams that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation. Their transverse structure is described by the Ince polynomials and has an inherent elliptical symmetry. Ince-Gaussian beams constitute the exact and continuous transition modes between Laguerre and Hermite-Gaussian beams. The propagating characteristics are discussed as well.
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TL;DR: The authors survey the steady refinement of techniques used to create optical vortices, and explore their applications, which include sophisticated optical computing processes, novel microscopy and imaging techniques, the creation of ‘optical tweezers’ to trap particles of matter, and optical machining using light to pattern structures on the nanoscale.
Abstract: Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.
1,016 citations
TL;DR: In this article, the authors used an artificial neural network (ANN) to identify the characteristic mode patterns displayed on a screen at the receiver, and were able to distinguish between 16 different OAM superposition with only a 1.7% error rate.
Abstract: Transverse spatial modes of light offer a large state-space with interesting physical properties. For exploiting these special modes in future long-distance experiments, the modes will have to be transmitted over turbulent free-space links. Numerous recent lab-scale experiments have found significant degradation in the mode quality after transmission through simulated turbulence and consecutive coherent detection. Here, we experimentally analyze the transmission of one prominent class of spatial modes?orbital-angular momentum (OAM) modes?through 3 km of strong turbulence over the city of Vienna. Instead of performing a coherent phase-dependent measurement, we employ an incoherent detection scheme, which relies on the unambiguous intensity patterns of the different spatial modes. We use a pattern recognition algorithm (an artificial neural network) to identify the characteristic mode patterns displayed on a screen at the receiver. We were able to distinguish between 16 different OAM mode superpositions with only a ?1.7% error rate and to use them to encode and transmit small grayscale images. Moreover, we found that the relative phase of the superposition modes is not affected by the atmosphere, establishing the feasibility for performing long-distance quantum experiments with the OAM of photons. Our detection method works for other classes of spatial modes with unambiguous intensity patterns as well, and can be further improved by modern techniques of pattern recognition.
380 citations
TL;DR: In this paper, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields, namely, dielectrophoretic and photophoretic forces.
Abstract: Optical tweezers, a simple and robust implementa- tion of optical micromanipulation technologies, have become a standard tool in biological, medical and physics research labo- ratories. Recently, with the utilization of holographic beam shap- ing techniques, more sophisticated trapping configurations have been realized to overcome current challenges in applications. Holographically generated higher-order light modes, for exam- ple, can induce highly structured and ordered three-dimensional optical potential landscapes with promising applications in op- tically guided assembly, transfer of orbital angular momentum, or acceleration of particles along defined trajectories. The non- diffracting property of particular light modes enables the op- tical manipulation in multiple planes or the creation of axially extended particle structures. Alongside with these concepts which rely on direct interaction of the light field with particles, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields. Optoelectronic tweezers take advantage of dielectrophoretic forces for adaptive and flexible, massively parallel trapping. Photophoretic trapping makes use of thermal forces and by this means is perfectly suited for trapping ab- sorbing particles. Hence the possibility to tailor light fields holo- graphically, combined with the complementary dielectrophoretic and photophoretic trapping provides a holistic approach to the majority of optical micromanipulation scenarios.
338 citations
TL;DR: A new solution of the paraxial equation based on the Pearcey function, which is related to the Airy function and describes diffraction about a cusp caustic, is presented and the theory of propagating Pearcey beams is described.
Abstract: We present a new solution of the paraxial equation based on the Pearcey function, which is related to the Airy function and describes diffraction about a cusp caustic. The Pearcey beam displays properties similar not only to Airy beams but also Gaussian and Bessel beams. These properties include an inherent auto-focusing effect, as well as form-invariance on propagation and self-healing. We describe the theory of propagating Pearcey beams and present experimental verification of their auto-focusing and self-healing behaviour.
233 citations
TL;DR: An extensive overview of Microelectronechanical Systems (MEMS) scanning mirrors specifically for applications in LiDAR systems is presented, and a figure of merit (FoM) is defined for MEMS mirrors inLiDAR scanners in terms of aperture size, field of view (foV) and resonant frequency.
Abstract: In recent years, Light Detection and Ranging (LiDAR) has been drawing extensive attention both in academia and industry because of the increasing demand for autonomous vehicles. LiDAR is believed to be the crucial sensor for autonomous driving and flying, as it can provide high-density point clouds with accurate three-dimensional information. This review presents an extensive overview of Microelectronechanical Systems (MEMS) scanning mirrors specifically for applications in LiDAR systems. MEMS mirror-based laser scanners have unrivalled advantages in terms of size, speed and cost over other types of laser scanners, making them ideal for LiDAR in a wide range of applications. A figure of merit (FoM) is defined for MEMS mirrors in LiDAR scanners in terms of aperture size, field of view (FoV) and resonant frequency. Various MEMS mirrors based on different actuation mechanisms are compared using the FoM. Finally, a preliminary assessment of off-the-shelf MEMS scanned LiDAR systems is given.
182 citations
References
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TL;DR: Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum and an astigmatic optical system may be used to transform a high-order LaguERre- Gaussian mode into aHigh-order Hermite-Gaussia mode reversibly.
Abstract: Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.
7,918 citations
TL;DR: A computer-generated hologram is used to form an optical beam with a localized intensity null at its focus that will have applications in the optical trapping of macroscopic objects or atoms; hence the term optical bottle beam.
Abstract: A computer-generated hologram is used to form an optical beam with a localized intensity null at its focus. The beam is a superposition of two Laguerre-Gaussian modes that are phased so that they interfere destructively to give a beam focus that is surrounded in all directions by regions of higher intensity. Beams of this kind will have applications in the optical trapping of macroscopic objects or atoms; hence the term optical bottle beam.
404 citations
TL;DR: In this paper, the authors derived relation between Hermite (HG) and Laguerre (LG) Gaussian modes from addition identities between a pair of Hermite polynomials.
Abstract: Relations between Hermite (HG) and Laguerre (LG) Gaussian modes are derived. With these, a LG mode is written as a sum of HG modes, and vice versa. These mode relations are derived from addition identities between a Laguerre polynomial and a pair of Hermite polynomials. The addition relations are derived in two appendices. One figure illustrates the contents of a LG mode in terms of HG modes while a second figure shows the translation in the opposite direction. >
148 citations
TL;DR: In this paper, a reformulation of nondiffracting beams, based on more general (travelling wave) solutions of the nonparaxial wave equation, is presented.
99 citations
TL;DR: In this article, the authors theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, and proposed a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and transverse mode.
Abstract: We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, ${\mathrm{HG}}_{10},$ ${\mathrm{HG}}_{01},$ ${\mathrm{LG}}_{01},$ and ${\mathrm{LG}}_{0\ensuremath{-}1}$ (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the ${\mathrm{HG}}_{10}$ and ${\mathrm{HG}}_{01}$ components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.
96 citations