A general framework for conformal transformations in electron optics
TL;DR: In this paper, it is shown that it is a general property of those conformal transformations to be produced by harmonic phase elements and therefore to admit an electrostatic implementation in the electron optics scenario.
Abstract: The implementation of log-pol transformation has recently introduced a new boost in electron optics with charged matter vortices, allowing to map conformally between linear and orbital angular momentum (OAM) states and to measure them. That coordinate change belongs to the general framework of Hossack's transformations and it has been recently realized efficiently by means of electrostatic elements. In this letter we show that it is a general property of those conformal transformations to be produced by harmonic phase elements and therefore to admit an electrostatic implementation in the electron optics scenario. We consider a new kind of conformal mapping, the circular-sector transformation, which has been recently introduced for OAM multiplication and division in optics, and discuss how it represents a general solution of Laplace's equation, showing the analogy of the generating phase elements with projected multipole fields and linear charge distributions. Moreover, we demonstrate its capability to perform the sorting of multipole wavefronts, discovering a novel and effective method to measure the strength and orientation of a dipole field in a fast, compact and direct way.
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TL;DR: A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope and offers the possibility of real-time tuning of other electron optical devices and electron beam shaping configurations.
13 citations
Cites background from "A general framework for conformal t..."
...Recent research [40] suggests that it could be the first of many useful wave transformations to revolutionize the concept of measurement in electron microscopy....
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TL;DR: In this article, a ray-tracing assisted optimization scheme was proposed to improve the performance of OCT in the special case of log-polar coordinate transformation (LPCT), which is related to a Zernike polynomial based phase compensation.
Abstract: Optical coordinate transformation (OCT) has attracted widespread attention in the field of orbital angular momentum (OAM) (de)multiplexing or manipulation, but the performance of OCT would suffer from its distortion. In this paper, we quantitatively analyze the distortion of OCT from the perspective of ray optics and explain its rationality to work under non-normal incident light. For the special case of log-polar coordinate transformation (LPCT), we use a raytracing assisted optimization scheme to improve its distortion, which is related to a Zernike polynomial based phase compensation. After raytracing optimization, the root mean square error (RMSE) of the focused rays is reduced to 1/5 of the original value and the physical optic simulation also shows great improvement. In the experiment, we use three phase masks which are realized by metasurfaces, the measured results show well consistency with the simulation. Results in this paper have great potential to improve the performance of OCT related applications.
5 citations
TL;DR: In this paper, focused ion beam techniques are used to realize micrometer-sized Janus bimetallic cylinders acting as drift tube devices, which are able to impart a controlled phase shift to an electron wave.
Abstract: Modern nanotechnology techniques offer new opportunities for fabricating structures and devices at the micrometer and sub-micrometer level. Here, we use focused ion beam techniques to realize micrometer-sized Janus bimetallic cylinders acting as drift tube devices, which are able to impart a controlled phase shift to an electron wave. The phase shift results from the presence of contact potentials in the cylinders, in a similar manner to the electrostatic Aharonov–Bohm effect in bimetallic wires. We use electron Fraunhofer interference to demonstrate that such bimetallic structures introduce phase shifts that can be tuned to desired values by varying the dimensions of the pillars, in particular their heights. Such devices are promising for electron beam shaping and for the realization of electrostatic Zernike phase plates (i.e., devices that are able to impart a constant phase shift between an unscattered and a scattered electron wave) in electron microscopy, in particular, cryo-electron microscopy.
3 citations
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TL;DR: In this article, focused ion beam techniques were used to realize drift tube Zernike phase plates for electrons, whose operation is based on the presence of contact potentials in Janus bimetallic cylinders, in a similar manner to the electrostatic Aharonov-Bohm effect in Bimetallic wires.
Abstract: Modern nanotechnology techniques offer new opportunities for fabricating structures and devices at the micron and sub-micron level. Here, we use focused ion beam techniques to realize drift tube Zernike phase plates for electrons, whose operation is based on the presence of contact potentials in Janus bimetallic cylinders, in a similar manner to the electrostatic Aharonov-Bohm effect in bimetallic wires. We use electron Fraunhofer interference to demonstrate that such bimetallic pillar structures introduce phase shifts that can be tuned to desired values by varying their dimensions, in particular their heights.
3 citations
Cites background from "A general framework for conformal t..."
...[29] A two-dimensional array of such cylinders could be used to produce an arbitrary phase landscape without the problems that come with using material-based holograms....
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TL;DR: In this article , a non-orthogonal pattern set using ghost imaging is proposed to reduce the peak intensity of the electron beam during imaging, which is applicable at different spectral regions and robust to nonorthogonality.
Abstract: Solving challenges of enhanced imaging (resolution or speed) is a continuously changing frontier of research. Within this sphere, ghost imaging (and the closely related single-pixel imaging) has evolved as an alternative to focal plane detector arrays owing to advances in detectors and/or modulation devices. The interest in these techniques is due to their robustness to varied sets of patterns and applicability to a broad range of wavelengths and compatibility with compressive sensing. To achieve a better control of illumination strategies, modulators of many kinds have long been available in the optical regime. However, analogous technology to control of phase and amplitude of electron beams does not exist. We approach this electron microscopy challenge from an optics perspective, with a novel approach to imaging with non-orthogonal pattern sets using ghost imaging. Assessed first in the optical regime and subsequently in electron microscopy, we present a methodology that is applicable at different spectral regions and robust to non-orthogonality. The distributed illumination pattern sets also result in a reduced peak intensity, thereby potentially reducing damage of samples during imaging. This imaging approach is potentially translatable beyond both regimes explored here, as a single-element detector system.
2 citations
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TL;DR: In this article, it was shown that many of the symptoms of classicality can be induced in quantum systems by their environments, which leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information.
Abstract: as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
3,499 citations
TL;DR: A method to efficiently sort orbital angular momentum states of light using two static optical elements that perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient.
Abstract: We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.
926 citations
TL;DR: This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope, and it is demonstrated how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties.
Abstract: It has been possible to produce photon vortex beams — optical beams with spiralling wavefronts — for some time, and they have found widespread application as optical tweezers, in interferometry and in information transfer, for example. The production of vortex beams of electrons was demonstrated earlier this year (
http://go.nature.com/4H2xWR
) in a procedure involving the passage of electrons through a spiral stack of graphite thin films. The ability to generate such beams reproducibly in a conventional electron microscope would enable many new applications. Now Jo Verbeeck and colleagues have taken a step towards that goal. They describe a versatile holographic technique for generating these twisted electron beams, and demonstrate their potential use as probes of a material's magnetic properties. It was demonstrated recently that passing electrons through a spiral stack of graphite thin films generates an electron beam with orbital angular momentum — analogous to the spiralling wavefronts that can be introduced in photon beams and which have found widespread application. Here, a versatile holographic technique for generating these twisted electron beams is described. Moreover, a demonstration is provided of their potential use in probing a material's magnetic properties. Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum1,2, improving channel capacity in optical3 and radio-wave4 information transfer, astrophysics5 and so on6. Very recently, an experimental realization of vortex beams formed of electrons was demonstrated7. Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.
710 citations
Additional excerpts
...It has opened a new horizon of experiments and possibilities in electron microscopy including magnetic characterization of material [2][3], controlled diffraction, aberration and interferometry [4][5][6][7]....
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TL;DR: The generation of an electron beam with a phase singularity propagating in free space is reported by passing a plane electron wave through a spiral phase plate constructed naturally from a stack of graphite thin films.
Abstract: Light beams can be engineered to carry orbital angular momentum, with application as, for instance, optical 'spanners' — essentially a 'twisted' variant of the more familiar optical tweezers Here it is shown that it is, in principle, possible to engineer similar behaviour into an electron beam Such a beam could find use in a variety of spectroscopy and microscopy techniques
646 citations
"A general framework for conformal t..." refers background in this paper
...The revolution has been started with the introduction of electron vortex beams [8][9][10] carrying an azimuthal phase term ( ) exp i , which suggested the orbital angular momentum (OAM) (denoted by the quantum number l) as a new electron microscopy quantity....
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TL;DR: A brief review of the research in the field to date is examined and what future directions might hold is considered.
Abstract: Twenty-five years ago Allen, Beijersbergen, Spreeuw, and Woerdman published their seminal paper establishing that light beams with helical phase-fronts carried an orbital angular momentum. Previously orbital angular momentum had been associated only with high-order atomic/molecular transitions and hence considered to be a rare occurrence. The realization that every photon in a laser beam could carry an orbital angular momentum that was in excess of the angular momentum associated with photon spin has led both to new understandings of optical effects and various applications. These applications range from optical manipulation, imaging and quantum optics, to optical communications. This brief review will examine some of the research in the field to date and consider what future directions might hold.
551 citations