Experimental Evidence of Vortex γ Photons in All-Optical Inverse Compton Scattering.

P lasmonic systems have been shown to be resonantly excited when the linear momentum selection rule is fulfi lled.1 However, conservation of total angular momentum (AM) in a closed physical system results in additional selection rules. e AM of an optical beam comprises the intrinsic component—the spin, associated with the handedness of the circular polarization—and the extrinsic component— orbital AM (OAM), associated with a spiral phase front.2 Here, we demonstrate a plasmonic nanostructure that exhibits a crucial role of an AM selection rule in a lightsurface plasmon scattering process. In our experiment, the intrinsic AM of the incident radiation was coupled to the extrinsic momentum of the surface plasmons via spin-orbit interaction, which was manifested by a geometric Berry phase.3 Due to this eff ect, we achieved a symmetry breaking that resulted in a spin-dependent enhanced transmission through coaxial nanoapertures, even in rotationally symmetric structures.4 In an optical paraxial beam with a spiral phase distribution (= –l, where  is the azimuthal angle in polar coordinates, and the integer number l is the topological charge), the total AM per photon, in units of h– (normalized AM), was shown to be j=(+l), where =1 is the right-handed circular polarization and =–1 is the left-handed circular polarization.2 In accordance with fundamental physical principles, resonant excitation of the nanoaperture eigenmode requires that the exciting wave match the excited mode, both with its linear and angular momentum. is matching imposes restrictions, or selection rules, on the excitation process. e coaxial nanoaperture was milled by a focused ion beam into a 200-nmthick gold fi lm evaporated onto a glass wafer. e inner and the outer radii of the ring slit were 250 and 350 nm, respectively. e aperture was designed to be a single mode system—in other words, to possess a single allowed excitation with OAM of lGM=±1. e aperture was surrounded by an annular coupling grating with a period of 500 nm. is element was illuminated by a green laser light (532 nm) whose phase was modulated by a spatial light modulator to achieve a spiral phase corresponding to an OAM of lext=0, ±2. e incident spin (in=±1) induced a spiral phase of the excited surface plasmons via spinorbit interaction, and, therefore, was converted to the OAM.5 e surface mode then acquired OAM of lSM= in+ lext. e best overlapping of the surface mode and guided modes was obtained when lSM= lGM, i.e. (a) Mechanism of the nanoaperture’s excitation controlled by AM selection rules. Incident beam bears the intrinsic AM of in and the extrinsic AM of lext. Excited surface mode acquires the OAM of lSM as a result of spin-orbit interaction. Guided mode with lGM is excited only if selection rule is satis ed. (Inset) Scanning electron microscope image of the structure. (b) Intensity distribution cross-sections for different lext. Blue dashed lines correspond to in=1 and red solid lines to in=–1. Intensity was normalized by the transmission measured via coaxial aperture without the surrounding corrugation. (Horizontal dimension was scaled according to the optical magni cation.) (a)

Presented during my PhD defense at ICFO - The institute of Photonic Sciences. Barcelona (Spain), March 12 (2010) This talk shows that * The two-photon mode function, for photons generated in SPDC, can be written in a matrix form which is not as computational demanding as other ways to describe the downconverted state. * The internal correlations in the two-photon state can be suppress or enhance by tailoring the SPDC parameters. * The OAM content of the pump is completely transferred to the signal and idler photons, emitted all over a cone. It is only possible to introduce a selection rule that always holds if all possible emission directions are considered.<br>* The SPDC parameters and the detection system determine the portion of the cone that is detected in a noncollinear configuration, and therefore the amount of OAM that can be detected.

All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of spin of the gauge field particle -- the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) $\boldsymbol{S}_{M}=(1/c)\int d^{3}x\boldsymbol{\pi}\times\boldsymbol{A}$ and orbital angular momentum (OAM) $\boldsymbol{L}_{M}=-(1/c)\int d^{3}x\pi^{\mu}\boldsymbol{x}\times\boldsymbol{\nabla}A_{\mu}$ of the photon, where $\pi^{\mu}$ is the conjugate canonical momentum of the gauge field $A^{\mu}$. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above defined quantum operators. Our work shows that the spin and OAM operators commute which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon have applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.

In this paper, a microlens array with sector sub-aperture (MLA-S) is proposed to measure the orbital angular momentum (OAM) of the vortex beam. This device has a circularly symmetric structure, which can well match the spiral phase, whose phase slope is also circularly symmetric. Furthermore, the spiral phase is split by the MLA-S, and each sub-wavefront can be approximated as a tilted wavefront. Thus, in the far field, the spot position can characterize the OAM information, and the displacement and displacement direction of the spot can determine the magnitude and sign of the OAM. In the experiments, perfect vortex beams are generated as measurement objects, and the measurement range can be up to ± 112 orders, with absolute measurement errors around 0.1. Meanwhile, for a multi-ring perfect vortex beam, in which each ring is loaded with a different OAM mode, these rings can be separated by MLA-S, and the OAM of each ring can be measured simultaneously, which is well demonstrated in the experiments. In addition, owing to the circular symmetry structure of the MLA-S, the partial error can be counteracted as the beam deviates from the center of the MLA-S. This research introduces a new technical way to measure the OAM, which is promising for some OAM-based applications.

Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.

Vortex electromagnetic (EM) waves exhibit spiral wavefront phase distributions, owing to their orbital angular momentum (OAM). Thus, the scattered waves from targets contain OAM characteristics, demonstrating novel scattering properties. Although researchers have carried out both theoretical and experimental studies on the target scattering characteristics of vortex EM waves, a comprehensive and standardized characterization framework is still lacking. This paper proposes and defines an EM vortex scattering matrix (EVSM), which can be used as a characterization method for the target scattering characteristics in the OAM dimension of vortex EM waves. Since vortex EM waves carry both OAM and spin angular momentum (SAM), the EM vortex-polarization joint scattering matrix (EVPJSM) is defined by extending EVSM. This joint matrix simultaneously describes the target scattering characteristics in both OAM and SAM dimensions of vortex EM waves. And it can offer a thorough framework of target scattering characteristics for arbitrary OAM–SAM combinations in new-dimensional EM waves. Numerical simulations are performed to compute each element in EVPJSM for two typical targets under twelve different pairs of OAM modes and two SAM polarization combinations. The numerical results can be used as an example of the characterization method in new dimensions for the targets’ scattering characteristics.

By the theory of paraxial approximation for optical beam, the analytical expression of orbital angular momentum (OAM) of off axial Gaussian vortex beam is derived in the coordinates of centroid, based on which distribution of OAM of off axial vortex beam and its propagation are investigated. Numerical calculations show that the OAM of off axial vortex beam is not circularly symmetric. The contour of zero OAM is a close curve, inside which the OAM is positive and outside which the OAM is negative. With the increment of propagation length, the distribution of OAM of off axial vortex beam tends to be approximately right and left symmetric, and the bigger the topological charge is, the faster the distribution of OAM tends to form the characteristic of symmetry. Besides, the off axial distance also has influence on the distribution of OAM. On a certain observation plane, the absolute value of the minimum OAM (in negative area) will become closer to the absolute value of the maximum OAM (in positive area) if the off axial distance increases. The conclusion can provide guidance during the research on the interaction between off axial vortex beam and particles.

Similar to other physical dimensions of light such as amplitude, phase, frequency, time and polarization, orbital angular momentum (OAM), which refers to the spatial structure of light (a spiral wavefront), is an additional degree of freedom to modulate or multiplex information in optical communication systems [1, 2]. Theoretically, OAM and linear-polarization (LP) modes in few mode fibers (FMFs) are both spatial orthogonal basis that can be chosen for carrying data streams simultaneously, to greatly increase the capacity and spectrum efficiency of communication systems. Here we review recent progress in free-space optical (FSO) systems employing OAM multiplexing, including: (1) using 16-QAM signals over polarization division multiplexed (PDM) 8 OAM modes in two groups of concentric rings to achieve a spectral efficiency of 95.7 bit/s/Hz [3]; (2) using OFDM/OQAM 64-QAM signals over 22 OAM modes with PDM to achieve a spectral efficiency of 230 bit/s/Hz [4]; (3) using Nyquist 32-QAM signals over 52 orbital angular momentum (OAM) modes with PDM to achieve an ultra-high spectral efficiency of 435 bit/s/Hz [5]; (4) using 30 Gbaud PAM-4 signals over 12 OAM modes with PDM to achieve a single wavelength terabit intensity modulation direct detection (IM-DD) system and the spectrum efficiency is 29.8 bit/s/Hz [6]. The above mentioned systems utilize spatial light modulators (SLMs) to convert Gaussian beams into OAM beams, making the whole systems bulky and unscalable. Therefore, one valuable goal is to realize compact and efficient integrated devices for generating, multiplexing and demultiplexing OAM modes. We will review some promising work in this area: (1) using angular gratings and a microring resonator to realize a silicon optical vortex emitter [7]; (2) fabricating micro-scale spiral phase plates within the aperture of a vertical-cavity surface-emitting laser (VCSEL) [8]; (3) using Dammann optical vortex gratings to achieve the parallel detection of massive individual OAM modes [9].

We report the method of producing a spatio-temporal (ST) wave packet carrying pure transverse orbital angular momentum (OAM) with subwavelength spatial sizes. Due to the lack of temporal focusing, an ST wave packet focused by a high numerical aperture (NA) objective lens experiences a "spatio-temporal astigmatism" effect similar to the focusing action of a cylindrical lens on the transverse profile of optical field. Thus an ST vortex with a spiral phase in the ST domain focused through a high NA objective will be distorted and lose the ST characteristic spiral phase pattern. With the understanding of such an ST astigmatism, the ST wave packet can be pre-conditioned such that an ST vortex carrying OAM with subwavelength transverse sizes can be obtained after strong focusing. This is the first revelation that a tightly focused ST vortex beam with transverse OAM can be realized, paving the way for potential applications including microscopy, optical trapping, laser machining, nonlinear light-matter interactions, and so on. The ST astigmatism effect also offers insights for the focusing and propagation studies of other types of ST wave packets.

An investigation into the orbital angular momentum (OAM) cross talk of multiple coaxial terahertz vortex beams propagating through an inhomogeneous unmagnetized plasma slab was conducted using the vector angular spectrum expansion method. For the double Gaussian distribution model of plasma sheath, considering the incidence of coherent vortex beams with single topological charge (TC), double, and four TCs, numerical simulations of the amplitude and OAM spectra of the reflected and transmitted beams were carried out and discussed in detail. The results showed that, as an oblique incidence of vortex beams, the effects of an inhomogeneous plasma slab on the distortions of the magnitude profiles and OAM spectra of the reflected and transmitted beams were critical, and due to the effects of several reflections between interfaces, the effects on the reflected beam were more serious. The distribution of the contours of the electric fields in transverse planes was closely related to the TCs of the incident beams. For coaxial incidence of multiple coherent vortex beams, the additional mutual cross talk, which was caused by interference, decreased with the increasing difference in the TCs and needed to be considered during OAM multiplexing. The selection of the radial integral distance had an obvious impact on the weights of the primary OAM states. This work provides an important theoretical reference for terahertz OAM multiplexing technology in solving the communication blackout caused by the plasma sheath.

Quark orbital angular momentum (OAM) in the nucleon can be evaluated directly by constructing the simultaneous distribution of parton transverse position and momentum in a rapidly propagating nucleon, and using it to perform the appropriate average over these parton characteristics. The aforementioned distribution can be accessed via a generalization of the nucleon matrix elements of quark bilocal operators which have been used previously in the lattice evaluation of transverse momentum dependent parton distributions (TMDs). By supplementing these matrix elements with a nonzero momentum transfer, mixed transverse position and momentum information is generated. In the quark bilocal operators, a gauge connection between the quarks must be specified; a staple-shaped gauge link path, as used in TMD calculations, yields Jaffe-Manohar OAM, whereas a straight path yields Ji OAM. A lattice calculation at a pion mass of 518 MeV is presented which demonstrates that the difference between Ji and Jaffe-Manohar OAM can be clearly resolved. The obtained Ji OAM is confronted with the traditional evaluation utilizing Ji's sum rule. Jaffe-Manohar OAM is enhanced in magnitude compared to Ji OAM.

Orbital angular momentum (OAM) beams, have attracted great attention in recent years. An OAM beam with a phase singularity is characterized by a helical phase front which provides an additional degree of freedom for wide amount of classical and quantum optical applications. However, despite many attempts to generate and manipulate OAM beams, a robust, reliable and scalable technique to directly address generation, multiplexing and low-loss transmission of the distinct OAM beams is still in great demand. Here, we review the development of all-fiber, ring core photonics lantern mode multiplexer to generate high quality OAM beams up to the second order within a broad spectral range of >550 nm. Our device is a 5-mode mode selective photonic lantern (MSPL) with an annular refractive index profile which is fully compatible with well-established ring core and vortex transmission fibers. Through the excitation of pairs of degenerate linearly polarized (LP) modes of the MSPL, we demonstrate the generation of high quality OAM beams up to the second order. In addition, we demonstrate multiplexing of two OAM modes (OAM+1+ OAM-2) to verify complex beam pattern generation of our all fiber devices. Furthermore, by splicing the end-facet of the photonic lantern to a ring core fiber, we achieve low-loss coupling of OAM modes while maintaining high contrast spiral phase patterns. These results demonstrate the potential of photonic lanterns for generating complex optical beams.

The discovery of optical transverse orbital angular momentum (OAM) has broadened our understanding of light and is expected to promote optics and other physics. However, some fundamental questions concerning the nature of such OAM remain, particularly whether they can survive from observed mode degradation and hold OAM values higher than 1. Here, we show that the strong degradation actually origins from inappropriate time-delayed kx–ω modulation, instead, for transverse OAM having inherent space-time coupling, immediate modulation is necessary. Thus, using immediate x–ω modulation, we demonstrate theoretically and experimentally degradation-free spatiotemporal Bessel (STB) vortices with transverse OAM even beyond 102. Remarkably, we observe a time-symmetrical evolution, verifying pure time diffraction on transverse OAM beams. More importantly, we quantify such nontrivial evolution as an intrinsic dispersion factor, opening the door towards time diffraction-free STB vortices via dispersion engineering. Our results may find analogues in other physical systems, such as surface plasmon-polaritons, superfluids, and Bose-Einstein condensates.

In underwater wireless optical communication (UWOC), a vortex beam carrying orbital angular momentum has a spatial spiral phase distribution, which provides spatial freedom for UWOC and, as a new information modulation dimension resource, it can greatly improve channel capacity and spectral efficiency. In a case of the disturbance of a vortex beam by ocean turbulence, where a Laguerre–Gaussian (LG) beam carrying orbital angular momentum (OAM) is damaged by turbulence and distortion, which affects OAM pattern recognition, and the phase feature of the phase map not only has spiral wavefront but also phase singularity feature, the convolutional neural network (CNN) model can effectively extract the information of the distorted OAM phase map to realize the recognition of dual-mode OAM and single-mode OAM. The phase map of the Laguerre–Gaussian beam passing through ocean turbulence was used as a dataset to simulate and analyze the OAM recognition effect during turbulence caused by different temperature ratios and salinity. The results showed that, during strong turbulence , when different = −1.75, the recognition rate of dual-mode OAM ( = ±1~±5, ±1~±6, ±1~±7, ±1~±8, ±1~±9, ±1~±10) had higher recognition rates of 100%, 100%, 100%, 100%, 98.89%, and 98.67% and single-mode OAM ( = 1~5, 1~6, 1~7, 1~8, 1~9, 1~10) had higher recognition rates of 93.33%, 92.77%, 92.33%, 90%, 87.78%, and 84%, respectively. With the increase in , the recognition accuracy of the CNN model will gradually decrease, and in a fixed case, the dual-mode OAM has stronger anti-interference ability than single-mode OAM. These results may provide a reference for optical communication technologies that implement high-capacity OAM.

Orbital angular momentum mode multiplexing communication in multimode fibers