ИССЛЕДОВАНИЯ ЗАКРУЧЕННЫХ ЭЛЕКТРОМАГНИТНЫХ ВОЛН
За последние пару лет в разных, даже далеких от науки СМИ стали регулярно появляться новости про «закрученный свет». В подавляющем большинстве случаев эти новости воспринимаются скорее как новости технологии, поскольку они касаются лишь одного узкоспециального прикладного вопроса — увеличения информационной емкости световых импульсов или радиоволн за счет закрученности. Между тем, реальная физика закрученного света намного богаче, в ней есть разнообразные задачи как фундаментальной, так и практической физики.
Немецким физикам удалось получить яркий пучок закрученного рентгена с энергией фотонов 99 эВ. Это открывает новые возможности как в фундаментальной физике, так и для многочисленных приложений.
Б. А. Князев, В. С. Павельев, В. Г. Сербо, Ю. Ю. Чопорова, Б. О. Володкин
ЗАКРУЧЕННЫЕ ПУЧКИ: ОТ РЕНТГЕНА ДО РАДИОДИАПАЗОНА (2015) (pdf)
Представлен обзор исследований и применений пучков с орбитальным угловым моментом (оптических вихрей или закрученных пучков). Приведены результаты первых экспериментов по формированию закрученных пучков в терагерцовом спектральном диапазоне с помощью лазера на свободных электронах.
Ю. А. Портнов
ИНТЕРФЕРЕНЦИЯ ДВУХ ПРОТИВОПОЛОЖНО ЗАКРУЧЕННЫХ СВЕТОВЫХ ВОЛН (2015) (pdf)
Последние исследования в области классической и квантовой оптики, позволили установить, что электромагнитная волна способна не только нести энергию и импульс, но и угловой момент. Для доказательства этого были проведены эксперименты по созданию и детектированию закрученности электромагнитных волн (twisted light). В настоящей работе теория электромагнетизма Максвелла обобщается на пространство с вращением. Для этого используется разработанная автором модель семимерного пространства-времени, в которой наряду с поступательными координатами и временем используются вращательные координаты. На основе обобщенных уравнений электромагнитного поля получены решения, описывающие закрученную электромагнитную волну. Таким образом, в статье предлагается неквантовый подход для описания закрученной электромагнитной волны без использования понятия спина. Также в работе рассматривается суперпозиция двух разнозакрученных электромагнитных волн. Как показано, результатом такого сложения становится волна с необычным профилем амплитуды, зависящим от направления. Автор предполагает, что подобный подход для описания закрученных волн может помочь по-новому взглянуть на некоторые вопросы классической и квантовой оптики.
THE INTERFERENCE OF TWO OPPOSITELY TWISTED LIGHT WAVES (2015)
Recent researches in the ﬁeld of classical and quantum optics, have established the fact that the light can carry not only energy and linear momentum, but also angular momentum. To prove this, experiments were carried out on the creation and detection of twisted light. In the present work, the Maxwell theory of electromagnetism is generalized to the space with rotation. For this purpose the seven-dimensional model of space-time developed by the author is used. In this model the translational coordinates and time as well as the rotational coordinates are used. On the basis of generalized equations of electromagnetic ﬁeld, solutions describing the twisted light are obtained. Thus, the article proposes non-quantum approach to describe the twisted light, without using the concept of spin. We also consider the superposition of two diﬀerently twisted light waves. It is shown that the result this superposition is a wave with an unusual proﬁle of the amplitude that depends on the direction. The author suggests that such approach to describe the twisted waves can help to look diﬀerently at some of the issues of classical and quantum optics.
P. Miao, Z. Zhang, J. Sun, W. Walasik, N.M. Litchinitser, and L. Feng
Structured light provides an additional degree of freedom for modern optics and practical applications. The effective generation of orbital angular momentum (OAM) lasing, especially at a micro- and nanoscale, could address the growing demand for information capacity. By exploiting the emerging non-Hermitian photonics design at an exceptional point, we demonstrate a microring laser producing a single-mode OAM vortex lasing with the ability to precisely define the topological charge of the OAM mode. The polarization associated with OAM lasing can be further manipulated on demand, creating a radially polarized vortex emission.
Dunzhao Wei, Yongmei Wang, Dongmei Liu, Yunzhi Zhu, Weihao Zhong, Xinyuan Fang, Yong Zhang, Min Xiao
NONDESTRUCTIVE ON-CHIP DETECTION OF OPTICAL ORBITAL ANGULAR MOMENTUM THROUGH A SINGLE PLASMONIC NANOHOLE (2016) (pdf)
Optical orbital angular momentum (OAM) provides an additional dimension for photons to carry information in high-capacity optical communication. Although the practical needs have intrigued the generations of miniaturized devices to manipulate the OAM modes in various integrated platforms, the on-chip OAM detection is still challenging to match the newly-developed compact OAM emitter and OAM transmission fiber. Here, we demonstrate an ultra-compact device, i.e., a single plasmonic nanohole, to efficiently measure an optical beam's OAM state in a nondestructive way. The device size is reduced down to a few hundreds of nanometers, which can be easily fabricated and installed in the current OAM devices. It is a flexible and robust way for in-situ OAM monitoring and detection in optical fiber networks and long-distance optical communication systems. With proper optimization of the nanohole parameters, this approach could be further extended to discriminate the OAM information multiplexed in multiple wavelengths and polarizations.
Producing light with a controlled spin in a laser has been known for decades, but producing OAM beams inside a laser is not so simple. Light carrying OAM is created by twisting the phase of light into a helical shape, forming a spiral. Because the twisting of the pattern gets tighter and tighter as you move towards the centre of the beam, the light disappears and such beams are often called doughnut beams or vortex beams.
The novelty was to realise that by using custom-geometric phase optics to map polarisation to OAM, the laser could be designed to tell the difference between the clockwise and anticlockwise light. The control is achieved by simply rotating a single optical element inside the laser, without any need for realignment.
Importantly, the same laser can produce any combination of these OAM beams and various polarisations of light. The team was able to show that the outcome was the generation of arbitrary vector vortex beams, known as higher-order Poincaré sphere beams.
Производить свет с контролируемой спина в лазере была известна на протяжении десятилетий, но производить балки ОАМ внутри лазера не так просто. Свет несущий ОАМ создается путем скручивания фазы света в спиральную форму, образуя спираль. Потому что перекручивание узор туже и туже, как вы двигаться по направлению к центру пучка, свет исчезает, и такие пучки часто называют балки пончик или вихревых Пучков.
Новинка должна была понимать, что, используя пользовательские геометрические фазы оптики на карте поляризации в ОАМ, лазер может быть создан, чтобы рассказать разницу между по часовой стрелке и против часовой стрелки света. Управление осуществляется простым поворотом одного оптического элемента внутри лазера, без необходимости перестройки.
Главное, тот же лазер может производить любые комбинации этих ОАМ балки и различные поляризации света. Команда смогла показать, что результат генерации произвольных векторных вихревых Пучков, известный как высокого Пучков сфере Пуанкаре.
Christina J. Naify, Charles A. Rohde, Theodore P. Martin, Michael Nicholas, Matthew D. Guild, Gregory J. Orris
GENERATION OF TOPOLOGICALLY DIVERSE ACOUSTIC VORTEX BEAMS USING A COMPACT METAMATERIAL APERTURE (2016) (pdf)
Here, we present a class of metamaterial-based acoustic vortex generators which are both geometrically simple and broadly tunable. The aperture overcomes the significant limitations of both active phasing systems and existing passive coded apertures. The metamaterial approach generates topologically diverse acoustic vortex waves motivated by recent advances in leaky wave antennas by wrapping the antenna back upon itself to produce an acoustic vortex wave antenna. We demonstrate both experimentally and analytically that this single analog structure is capable of creating multiple orthogonal orbital angular momentum modes using only a single transducer. The metamaterial design makes the aperture compact, with a diameter nearly equal to the excitation wavelength and can thus be easily integrated into high-density systems. Applications range from acoustic communications for high bit-rate multiplexing to biomedical devices such as microfluidic mixers.
Xiaomei Zhang, Baifei Shen, Yin Shi, Lingang Zhang, Liangliang Ji, Xiaofeng Wang, Zhizhan Xu, Toshiki Tajima
An optical vortex with orbital angular momentum (OAM) enriches the light and matter interaction process, and helps reveal unexpected information in relativistic nonlinear optics. A scheme is proposed for the first time to explore the origin of photons in the generated harmonics, and produce relativistic intense harmonics with expected frequency and an optical vortex. When two counterpropagating Laguerre–Gaussian laser pulses impinge on a solid thin foil and interact with each other, the contribution of each input pulse in producing harmonics can be distinguished with the help of angular momentum conservation of photons, which is almost impossible for harmonic generation without an optical vortex. The generation of tunable, intense vortex harmonics with different photon topological charge is predicted based on the theoretical analysis and three-dimensional particle-in-cell simulations. Inheriting the properties of OAM and harmonics, the obtained intense vortex beam can be applied in a wide range of fields, including atom or molecule control and manipulation.
R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taïeb & T. Ruchon
Infrared and visible light beams carrying orbital angular momentum (OAM) are currently thoroughly studied for their extremely broad applicative prospects, among which are quantum information, micromachining and diagnostic tools. Here we extend these prospects, presenting a comprehensive study for the synthesis and full characterization of optical vortices carrying OAM in the extreme ultraviolet (XUV) domain. We confirm the upconversion rules of a femtosecond nfrared helically phased beam into its high-order harmonics, showing that each harmonic order carries the total number of OAM units absorbed in the process up to very high orders (57). This allows us to synthesize and characterize helically shaped XUV trains of attosecond pulses. To demonstrate a typical use of these new XUV light beams, we show our ability to generate and control, through photoionization, attosecond electron beams carrying OAM. These breakthroughs pave the route for the study of a series of fundamental phenomena and the development of new ultrafast diagnosis tools using either photonic or electronic vortices.
J. Luo, M. Chen, M. Zeng, J. Vieira, L.L. Yu, S.M. Weng, L.O. Silva, D.A. Jaroszynski, Z.M. Sheng, J. Zhang
Laser wakefield accelerators have great potential as the basis for next generation compact radiation sources because of their extremely high accelerating gradients. However, X-ray radiation from such devices still lacks tunability, especially of the intensity and polarization distributions. Here we propose a tunable polarized radiation source based on a helical plasma undulator in a plasma channel guided wakefield accelerator. When a laser pulse is initially incident with a skew angle relative to the channel axis, the laser and accelerated electrons experience collective spiral motions, which leads to elliptically polarized synchrotron-like radiation with flexible tunability on radiation intensity, spectra and polarization. We demonstrate that a radiation source with millimeter size and peak brilliance of 2×1019 photons/s/mm2/mrad2/0.1% bandwidth can be made with moderate laser and electron beam parameters. This brilliance is comparable with third generation synchrotron radiation facilities running at similar photon energies, suggesting that laser plasma based radiation sources are promising for advanced applications.
Alberto A. Lutman, James P. MacArthur, Markus Ilchen, Anton O. Lindahl, Jens Buck, Ryan N. Coffee, Georgi L. Dakovski, Lars Dammann, Yuantao Ding, Hermann A. Dürr, Leif Glaser, Jan Grünert, Gregor Hartmann, Nick Hartmann, Daniel Higley, Konstantin Hirsch, Yurii I. Levashov, Agostino Marinelli, Tim Maxwell, Ankush Mitra, Stefan Moeller, Timur Osipov, Franz Peters, Marc Planas, Ivan Shevchuk et al.
POLARIZATION CONTROL IN AN X - RAY FREE - ELECTRON LASER (2016) (pdf)
X-ray free-electron lasers are unique sources of high-brightness coherent radiation. However, existing devices supply only linearly polarized light, precluding studies of chiral dynamics. A device called the Delta undulator has been installed at the Linac Coherent Light Source (LCLS) to provide tunable polarization. With a reverse tapered planar undulator line to pre-microbunch the beam and the novel technique of beam diverting, hundreds of microjoules of circularly polarized X-ray pulses are produced at 500–1,200eV. These X-ray pulses are tens of femtoseconds long, have a degree of circular polarization of 0.98–0.04+0.02 at 707eV and may be scanned in energy. We also present a new two-colour X-ray pump–X-ray probe operating mode for the LCLS. Energy differences of ΔE/E=2.4% are supported, and the second pulse can be adjusted to any elliptical polarization. In this mode, the pointing, timing, intensity and wavelength of the two pulses can be modified.
Junxiao Zhou, Wenshuai Zhang, Yachao Liu, Yougang Ke, Yuanyuan Liu, Hailu Luo, Shuangchun Wen
We examine the spin-dependent manipulating of vector beams by tailoring the inhomogeneous polarization. The spin-dependent manipulating is attributed to the spin-dependent phase gradient in vector beams, which can be regarded as the intrinsic feature of inhomogeneous polarization. The desired polarization can be obtained by establishing the relationship between the local orientation of polarization and the local orientation of the optical axis of waveplate. We demonstrate that the spin-dependent manipulating with arbitrary intensity patterns can be achieved by tailoring the inhomogeneous polarization. It should be note that the varying polarization with a full period can be regard as spanning the equator of the Poincaré sphere.
Weixing Shu, Yachao Liu, Yougang Ke, Xiaohui Ling, Zhenxing Liu, Bin Huang, Hailu Luo, and Xiaobo Yin
A propagation model of vector beams generated by metasurfaces based on vector diffraction theory is established theoretically and verified experimentally. Considering the Pancharatnam-Berry phase introduced by the metasurface, analytical forms of vector beams for arbitrary incident polarization and topological charge of metasurfaces are found in the Fresnel and Fraunhofer diffraction regions, respectively. The complex amplitude of the resultant vector beam can be described in terms of a confluent hypergeometric function, with an intensity profile that manifests concentric rings in the Fresnel region and a single ring in the Fraunhofer one. Fraunhofer diffraction provides a method to create vector beams with simultaneously high purity and modal power. Further experiments verify the theoretical results.
Yi Zhang, Peng Li, Sheng Liu, Lei Han, Huachao Cheng, and Jianlin Zhao
We report the realization of spin-dependent splitting of vector abruptly autofocusing beam (AAB) by encoding cosine-azimuthal variant phases. By employing the local spatial frequency (LSF), we reveal an approximation mapping relationship between focal field intensity of the two spin components and the pertinent phase distribution of input field. As well as theoretical analysis, we present experimental demonstrations of this guidance. Special focal field intensity, polarization and phase are realized by consciously managing the cosine-azimuthal variant phase. This distinctive focal field of vector AAB may have a broad range of applications in harnessing the spin-orbit coupling, optical trapping and laser machining.
Zi-Yu Chen & Alexander Pukhov
Ultrafast extreme ultraviolet (XUV) sources with a controllable polarization state are powerful tools for investigating the structural and electronic as well as the magnetic properties of materials. However, such light sources are still limited to only a few free-electron laser facilities and, very recently, to high-order harmonic generation from noble gases. Here we propose and numerically demonstrate a laser–plasma scheme to generate bright XUV pulses with fully controlled polarization. In this scheme, an elliptically polarized laser pulse is obliquely incident on a plasma surface, and the reflected radiation contains pulse trains and isolated circularly or highly elliptically polarized attosecond XUV pulses. The harmonic polarization state is fully controlled by the laser–plasma parameters. The mechanism can be explained within the relativistically oscillating mirror model. This scheme opens a practical and promising route to generate bright attosecond XUV pulses with desirable ellipticities in a straightforward and efficient way for a number of applications.
Darryl Naidoo, Filippus S. Roux, Angela Dudley, Igor Litvin, Bruno Piccirillo, Lorenzo Marrucci, Andrew Forbes
CONTROLLED GENERATION OF HIGHER - ORDER POINCARE SPHERE BEAMS FROM A LASER (2015) (pdf)
The angular momentum state of light can be described by positions on a higher-order Poincaré (HOP) sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have found many applications, including optical communication, quantum information processing, microscopy, optical trapping and tweezing and materials processing. Many techniques exist to create such beams but none to date allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the HOP sphere. We exploit geometric phase control with a non-homogenous polarization optic and a wave-plate inside a laser cavity to map spin angular momentum (SAM) to orbital angular momentum (OAM). Rotation of these two elements provides the necessary degrees of freedom to traverse the entire HOP sphere. As a result, we are able to demonstrate that the OAM degeneracy of a standard laser cavity may be broken, producing pure OAM modes as the output, and that generalized vector vortex beams may be created from the same laser, for example, radially and azimuthally polarized laser beams. It is noteworthy that all other aspects of the laser cavity follow a standard design, facilitating easy implementation.
Christian Schulze, Filippus S. Roux, Angela Dudley, Ronald Rop, Michael Duparré, and Andrew Forbes
We introduce a class of light field that angularly accelerates during propagation. We show that the acceleration (deceleration) may be controlled by adjustment of a single parameter, and tuned continuously, down to no acceleration at all. As the angular acceleration takes place in a bounded space, the azimuthal degree of freedom, such fields accelerate periodically as they propagate. Notably, the amount of angular acceleration is not limited by paraxial considerations, may be tailored for large accelerations over arbitrarily long distances, and can be engineered independently of the beam's spatial extent. We discuss how such angularly accelerating light fields can maintain the conservation of angular momentum through an energy exchange mechanism across the field.
C. Hernández-García, J. San Román, L. Plaja and A. Picón
High-order harmonic generation (HHG) driven by beams carrying orbital angular momentum has been recently demonstrated as a unique process to generate spatio-temporal coherent extreme ultraviolet (XUV)/x-ray radiation with attosecond helical structure. We explore the details of the mapping of the driving vortex to its harmonic spectrum. In particular we show that the geometry of the harmonic vortices is complex, arising from the superposition of the contribution from the short and long quantum paths responsible of HHG. Transversal phase-matching and quantum path interferences provide an explanation of the dramatic changes in the XUV vortex structure generated at different relative positions of the target respect to the laser beam focus. Finally, we show how to take advantage of transversal phase-matching to select helical attosecond beams generated from short or long quantum paths, exhibiting positive or negative temporal chirp respectively.
Jérémie Harris, Vincenzo Grillo, Erfan Mafakheri, Gian Carlo Gazzadi, Stefano Frabboni, Robert W. Boyd, Ebrahim Karimi
The study of structured optical waves has enhanced our understanding of light and numerous experimental methods now enable the control of the angular momentum and radial distributions. Recently, these wavestructuring techniques have been successfully applied to the generation and shaping of electron beams, leading to promising practical and fundamental advances. Here, we discuss recent progress in the emerging field of electron beam shaping, and explore the unique attributes that distinguish electron beams from their photonic analogues.
It is well known that light propagating as an electromagnetic wave or photon carries momentum along the direction of the wave's propagation, and that this momentum is independent of polarization. In addition, light can carry an intrinsic angular momentum, called spin, that is proportional to the degree of circular polarization (helicity), and aligned with the propagation direction.
Surprisingly, the researchers found that evanescent waves carry momentum and spin components that are orthogonal to the direction of wave propagation. Moreover, the transverse spin turns out to be independent of polarization and helicity, while the transverse momentum is proportional to the wave helicity.
Konstantin Y. Bliokh, Aleksandr Y. Bekshaev, Franco Nori
Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante’s spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of ‘impossible’ properties of light and of a fundamental field-theory quantity, which was previously considered as ‘virtual’.
For the past few decades, physicists have been studying the phenomenon of "twisted light," which is light that is twisted like a corkscrew along its axis of travel. Due to the twisting, the light waves at the center of the axis cancel out, resulting in a ring of light with a dark spot in the center. As the physicists show in 3D simulations and analytical modeling, a light fan can be generated by using a relativistic laser pulse.
Yin Shi, Baifei Shen, Lingang Zhang, Zhizhan Xu
LIGHT FAN DRIVEN BY A RELATIVISTIC LASER PULSE (2014) (pdf)
When a relativistic laser pulse with high photon density interacts with a specially tailored thin foil target, a strong torque is exerted on the resulting spiral-shaped foil plasma, or light fan. Because of its structure, the latter can gain significant orbital angular momentum (OAM), and the opposite OAM is imparted to the reflected light, creating a twisted relativistic light pulse. Such an interaction scenario is demonstrated by particle-in-cell simulation as well as analytical modeling, and should be easily verifiable in the laboratory. As important characters, twisted relativistic light pulse has strong torque and ultra-high OAM density.
Erik Hemsing, Andrey Knyazik, Michael Dunning, Dao Xiang, Agostino Marinelli, Carsten Hast & James B. Rosenzweig
COHERENT OPTICAL VORTICES FROM RELATIVISTIC ELECTRON BEAMS (2013) (pdf)
Recent advances in the production and control of high-brightness electron beams (e-beams) have enabled a new class of intense light sources based on the free electron laser (FEL) that can examine matter at ångstrom length and femtosecond time scales1. The free, or unbound, electrons act as the lasing medium, which provides unique opportunities to exquisitely control the spatial and temporal structure of the emitted light through precision manipulation of the electron distribution. We present an experimental demonstration of light with orbital angular momentum (OAM; ref. 2) generated from a relativistic e-beam rearranged into an optical scale helix by a laser. With this technique, we show that a Gaussian laser mode can be effectively up-converted to an OAM mode in an FEL using only the e-beam as a mode-converter. Results confirm theoretical predictions3, 4, and pave the way for the production of coherent OAM light with unprecedented brightness down to hard X-ray wavelengths for wide ranging applications in modern light sources.
J. Bahrdt, K. Holldack, P. Kuske, R. Müller, M. Scheer, and P. Schmid
Photon beams of 99 eV energy carrying orbital angular momentum (OAM) have been observed in the 2nd harmonic off-axis radiation of a helical undulator at the 3rd generation synchrotron radiation light source BESSY II. For detection, the OAM carrying photon beam was superimposed with a reference beam without OAM. The interference pattern, a spiral intensity distribution, was recorded in a plane perpendicular to the propagation direction. The orientation of the observed spiral structure is related to the helicity of the undulator radiation. Excellent agreement between measurements and simulations has been found.
Vortex beams, rotating like a tornado, offer completely new possibilities for electron microscopy. A new breakthrough in research now allows scientists to produce much more intense vortex beams than ever before.
The first successes were achieved two years ago: at the time, the electron beam was shot through a minuscule grid mask, whereby it split into three partial beams: one turning right, one turning left and one beam that did not rotate.
Now researchers use a screen, half of which is covered by a layer of silicon nitride. This layer is so thin that the electrons can penetrate it with hardly any absorption, however they can be suitably phase-shifted. After focusing using a specially adapted astigmatic lens, an individual vortex beam is obtained.
P. Schattschneider, M. Stöger-Pollach, and J. Verbeeck
NOVEL VORTEX GENERATOR AND MODE CONVERTER FOR ELECTRON BEAMS (2012) (pdf)
A mode converter for electron vortex beams is described. Numerical simulations, confirmed by experiment, show that the converter transforms a vortex beam with a topological charge m=±1 into beams closely resembling Hermite-Gaussian HG10 and HG01 modes. The converter can be used as a mode discriminator or filter for electron vortex beams. Combining the converter with a phase plate turns a plane wave into modes with topological charge m=±1. This combination serves as a generator of electron vortex beams of high brilliance.
Fabrizio Tamburini, Elettra Mari, Anna Sponselli, Bo Thidé, Antonio Bianchini and Filippo Romanato
We have shown experimentally, in a real-world setting, that it is possible to use two beams of incoherent radio waves, transmitted on the same frequency but encoded in two different orbital angular momentum states, to simultaneously transmit two independent radio channels.
Benjamin James McMorran, Amit K. Agrawal, Ian M. Anderson, Andrew A. Herzing, Henri J. Lezec, Jabez J. McClelland, John Unguris
ELECTRON VORTEX BEAMS WITH HIGH QUANTA OF ORBITAL ANGULAR MOMENTUM (2011) (pdf)
Electron beams with helical wavefronts carrying orbital angular momentum are expected to provide new capabilities for electron microscopy and other applications. We used nanofabricated diffraction holograms in an electron microscope to produce multiple electron vortex beams with well-defined topological charge. Beams carrying quantized amounts of orbital angular momentum (up to 100ħ) per electron were observed. We describe how the electrons can exhibit such orbital motion in free space in the absence of any confining potential or external field, and discuss how these beams can be applied to improved electron microscopy of magnetic and biological specimens.
Alison M. Yao and Miles J. Padgett
As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.