Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

Abstract

A general orbital angular momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of spiral zone plate holograms and suggesting that naturally occurring rotationally symmetric patterns could be inadvertent sources of vortex beams, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks. 42.50.Tx Vortices are common to all wave phenomena [1], including tornadoes at the large scale and superfluid helium at the small scale. The prototypical example of these is the optical vortex beam [2], followed recently by the electron vortex beam [3][4][5] and there are early studies of neutron [6] and atom vortex beams [7]. Vortex beams are characterized by a phase singularity described by an exp ℓ azimuthal phase factor, where θ is the azimuthal angle and ℓ stands for the winding number and is also called the topological charge. Vortex beams are of special interest because of their quantized OAM of ℓħ per particle [1] and have led to various applications in the contexts of super-resolution microscopy [8], nano-manipulation [9], astronomy [10] and crystallography [11]. In contrast to the intrinsic (spin) angular momentum, OAM can be very large and, as such, vortex beams can lead to new physics [12,13] and have potential in multiplex free-space communication [14] and quantum information [15]. PACS:The establishment of a toolbox for flexible vortex beam generation is the key to the development of science and technology involving vortex beams. If the vortex beam wavefunctions are known exactly, they can be generated either by direct phase manipulation (or wavefront shaping) [16] using, for example, spiral phase plates [3,6,17], spinto-orbital angular momentum convertors [18], and by phase encoding techniques through diffraction involving computer-generated holograms (CGHs) [19], including fork grating [4,5] and spiral zone plates [20][21][22]. Other techniques require case by case analysis to identify the nature of the vortex beams produced, as in the case involving the Aharonov-Bohm effect experienced by a charged particle in a suitable magnetic field [23,24]. More recent methods make use of photon sieves [25][26][27] and Vogel spiral arrays [28,29] as diffractive elements for vortex beam generation.Here we put forward a general principle for vortex beam generation in rotationally symmetric systems. We examine the role of rotational symmetry, not only for the purpose of generating a specific vortex wavefunction, but also for the essential symmetry elements that must be possessed by any vortex-related state by virtue of its characteristic azimuthal phase factor exp ℓ . The principle would enable us to understand, in a novel deconstructive manner, the generation of individual pure vorte...

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Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wavefront manipulation

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Generation of Circular Optical Vortex Array

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