Acoustic vortex beams in synthetic magnetic fields (original) (raw)

Propagation of vortex electron wave functions in a magnetic field

Physical Review A, 2012

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.

Electron vortex beams subject to static magnetic fields

Physical Review A, 2015

The properties of electron vortex beams are examined when subject to static magnetic fields. The fields are assumed to be applied after the electron vortex beam carrying a well-defined orbital angular momentum has been created as a result of using a holographic mask. The shifts in the electron vortex beam energy momentum as well as its angular momentum due to the presence of an axial uniform magnetic field are evaluated. Order-of-magnitude estimates of the shifts are given with reference to typical electron vortex beams subject to moderate magnetic fields.

Spatiotemporal vortex beams and angular momentum

We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatio-temporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic), and can find applications in particle collisions, optics of moving media, quantum communications, and astrophysics.

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

2012

We examine the propagation of the recently discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux-and vortex-dependent probability distributions, stationary Landau states manifest themselves as nondiffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field-and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Interestingly, the nonrotating superpositions reproduce stable multivortex configurations that appear in rotating superfluids. Our results open an avenue for the direct electron-microscopy observation of fundamental properties of free quantum-electron states in magnetic fields.

Subwavelength Acoustic Vortex Beams Using Self-Demodulation

Physical Review Applied

Acoustic vortices with subwavelength dimensions and tunable topological charge are theoretically and experimentally synthesized at distances far beyond the Rayleigh diffraction length of the source, using self-demodulation. A dual helical acoustic source is used to generate two primary confocal vortex beams at different frequencies and different topological charges. As a consequence of the conservation of angular momentum during nonlinear wave mixing, a self-demodulated vortex beam at the difference frequency emerges, keeping the spatial features of the primary vortex beams and a topological charge that is the difference of their topological charges. We report subdiffractive vortices the characteristic size of which is 18 times smaller than its wavelength at a distance 2.8 times the Rayleigh diffraction length. The generation and focusing of subwavelength vortices paves the way for long-range communication, biomedical, and wave-matter interaction applications.

Mechanical Evidence of the Orbital Angular Momentum to Energy Ratio of Vortex Beams

Physical Review Letters, 2012

We measure, in a single experiment, both the radiation pressure and the torque due to a wide variety of propagating acoustic vortex beams. The results validate, for the first time directly, the theoretically predicted ratio of the orbital angular momentum to linear momentum in a propagating beam. We experimentally determine this ratio using simultaneous measurements of both the levitation force and the torque on an acoustic absorber exerted by a broad range of helical ultrasonic beams produced by a 1000-element matrix transducer array. In general, beams with helical phase fronts have been shown to contain orbital angular momentum as the result of the azimuthal component of the Poynting vector around the propagation axis. Theory predicts that for both optical and acoustic helical beams the ratio of the angular momentum current of the beam to the power should be given by the ratio of the beam's topological charge to its angular frequency. This direct experimental observation that the ratio of the torque to power does convincingly match the expected value (given by the topological charge to angular frequency ratio of the beam) is a fundamental result.

Electron vortices: Beams with orbital angular momentum

Reviews of Modern Physics

The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key di↵erences in the properties of the two kinds of vortex beams. This review is concerned primarily with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution as well as the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analysed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter. List of Symbols and Abbreviations 39 References 41 I. INTRODUCTION Electron vortex beams are a new member of an expanding class of experimentally realisable freely propa

Generating and analyzing non-diffracting vector vortex beams

Laser Beam Shaping XIV, 2013

We experimentally generate non-diffracting vector vortex beams by using a Spatial Light Modulator (SLM) and an azimuthal birefringent plate (q-plate). The SLM generates scalar Bessel beams and the q-plate converts them to vector vortex beams. Both single order Bessel beam and superposition cases are studied. The polarization and the azimuthal modes of the generated beams are analyzed. The results of modal decompositions on polarization components are in good agreement with theory. We demonstrate that the generated beams have cylindrical polarization and carry polarization dependent Orbital Angular Momentum (OAM).

Acoustic emissions by vortex motions

Journal of Fluid Mechanics, 1986

Fundamental aspects of the acoustic emission by vortex motions are considered by summarizing our recent work. Three typical cases are presented as illustrative examples: (i) head-on collision of two vortex rings, (ii) a vortex ring moving near a circular cylinder, and (iii) a vortex ring moving near a sharp edge of a semi-infinite plate. The theory of aerodynamic sound for low-Mach-number motion of an inviscid fluid predicts that the amplitude of the acoustic pressure in the far field is proportional to U4, U3 and U2.5 for (i)-(iii) respectively, where U is the translation velocity of a single vortex ring. Therefore the vortex-dge interaction generates the most powerful sound among the three cases at low Mach numbers. Our observations have confirmed these scaling laws. I n addition to the scaling properties, we show the wave profiles of the emission as well as the directionality pattern. The head-on collision radiates waves of quadrupole directionality, whereas waves of dipole property are originated by the vortex-cylinder interaction. The third, vortex-dge, interaction generates waves of a cardioid directionality pattern. The wave profiles of all three cases are related to the time derivatives of the volume flux (through the vortex ring) of an imaginary potential flow which is characteristic of each configuration, although the orders of the time derivatives are different for each case. The observed profiles are surprisingly well fitted to the curves predicted by the theory, except the final period of the first case, in which viscosity is assumed to play an important role. The observed wave profiles are shown in a perspective diagram. U C M = -< l .