Experimental demonstration of fractional orbital angular momentum entanglement of two photons

Generation of integer and fractional vortex beams based on liquid crystal electronically reconfigurable spiral phase plates

The manufacturing and characterization of a large-size 72-electrode liquid crystal-based reconfigurable spiral phase plate (SPP) is presented. The SPP is addressed by a custom-made driver with 72 independent channels, which allows for the generation of any arbitrary integer or fractional optical vortex beam with topological charges ranging from -24 to +24. The 25 mm diameter device is fabricated using direct laser writing, leading to a fill factor over 99%. The device performance and flexibility exceed previous transparent reconfigurable SPP in terms of size, tuning range, and fill factor. The device and the light path have been simulated using the angular spectrum propagation method, showing excellent correspondence.

Spiral fractional vortex beams

A new type of spatially structured light field carrying orbital angular momentum (OAM) mode with any non-integer topological order, referred to as the spiral fractional vortex beam, is demonstrated using the spiral transformation. Such beams have a spiral intensity distribution and a phase discontinuity in the radial direction, which is completely different from an opening ring of the intensity pattern and an azimuthal phase jump, common features that all previously reported non-integer OAM modes (referred to as the conventional fractional vortex beams) shared. The intriguing properties of a spiral fractional vortex beam are studied both in simulations and experiments in this work. The results show that the spiral intensity distribution will evolve into a focusing annular pattern during its propagation in free space. Furthermore, we propose a novel scheme by superimposing a spiral phase piecewise function on spiral transformation to convert the radial phase jump to the azimuthal phase jump, revealing the connection between the spiral fractional vortex beam and its conventional counterpart, of which OAM modes both share the same non-integer order. Thus this work is expected to inspire opening more paths for leading fractional vortex beams to potential applications in optical information processing and particle manipulation.

Supercontinuum Induced by Filamentation of Bessel-Gaussian and Laguerre-Gaussian Beams in Water

In this paper, we study the characteristics of the supercontinuum (SC) induced by the filamentation of two typical vortex beams (i.e., Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams) in water. By moving the cuvette filled with water along the laser propagation path, we measure the SC induced by the filamentation of the two vortex beams at different positions in water. The results show that the degree of spectral broadening induced by the filamentation of LG beams hardly changes with the change of position, while for BG beams, the spectral broadening induced by filamentation is weak on both sides and strong in the middle. The value of topological charge (TC) affects the length of the filament formed by BG beams; however, its effect on the spectral broadening induced by the filamentation of LG and BG beams is negligible.

Precise measurement of trapping and manipulation properties of focused fractional vortex beams

Fractional vortex beams (FVBs) were believed to be hard to rotate microparticles at a half-integer topological charge due to the unique radial opening (low-intensity gap) in their intensity ring. However, recent research discovered more symmetric intensity structures with less intensity inhomogeneity of practical FVBs at the focal plane. Here, we experimentally demonstrated the manipulation of trapped microparticles and precisely measured their rotation periods at the focal plane of practical FVBs by using a high-speed camera. We verified that the measured orbital angular momentum (OAM) derived from the collective microparticle rotation is roughly proportional to the fractional OAM of practical FVBs. Furthermore, we also experimentally obtained the trapped microparticles' power spectra under the illumination of FVBs, from which we achieved the average trap stiffness to evaluate the two-dimensional trapping strength of the practical focused FVB intensity ring. Our results provide a new insight and an efficient tool on finely trapping and rotating microparticles and bio-cells by using fractional vortex beams.

Wideband and high-order microwave vortex-beam launcher based on spoof surface plasmon polaritons

The electromagnetic vortex carrying orbital angular momentum (OAM), which is first studied at optical frequency, has begun to attract widespread attention in the field of radio-frequency/microwave. However, for the OAM mode generated by traditional single antennas, there are problems such as low order and narrow bandwidth, and complex structures such as dual-fed networks may be required. In this paper, based on spoof surface plasmon polariton (SSPP) mode leaky-wave antenna, a single-port traveling-wave ring is proposed to radiate high-order OAM modes working near the cut-off frequency of SSPP state. The achieved 12-order OAM mode within 9.1–10.1 GHz (relative bandwidth of 10.4%) has the main radiation direction close to the antenna surface, forming a plane spiral OAM (PSOAM) wave, which reduces the requirements for mode purity in practical applications. This SSPP ring using periodic units as radiating elements can be an effective radiator for broadband and large-capacity OAM multiplexing communications. The structural characteristics of single feed contribute to the integration of microwave circuits.

Generation of perfect helical Mathieu vortex beams

We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.

Measuring dimensionality and purity of high-dimensional entangled states

High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

The Limits of Effective Degrees of Freedom in UCA based Orbital Angular Momentum Multiplexed Communications

Orbital angular momentum (OAM) multiplexing technique has recently emerged and generated widespread interests since the OAM was discovered as a property of electromagnetic wave and acoustic wave. It was widely acknowledged that OAM multiplexing can achieve very high effective degrees of freedom (EDOF) and improve the spectral efficiency in optical, radio and acoustic communications. However, in the field of free-space optical (FSO) communications, it was demonstrated that OAM multiplexing is not the optimal multiplexing technique and the spatial bandwidth product (SBP) limits the EDOF. Is there any EDOF limits of OAM multiplexing in radio and acoustic communications? Could OAM multiplexing be safely scaled to far field? Here, we discover that the azimuthal resolution of OAM mode generator in OAM multiplexing limits its EDOF. Furthermore, we also verify that the OAM multiplexing in radio and acoustic communication fails to enable a long distance transmission and high EDOF simultaneously incurred by the inherently imperfect OAM mode generator.

Deterministic Generation of Orbital-Angular-Momentum Multiplexed Tripartite Entanglement

We demonstrate the experimental generation of orbital angular momentum (OAM) multiplexed multipartite entanglement with cascaded four-wave mixing processes in a continuous variable (CV) system. In particular, we implement the simultaneous generation of 9 sets of OAM multiplexed tripartite entanglement over 27 Laguerre-Gauss (LG) modes, as well as 20 sets of OAM multiplexed bipartite entanglement over 40 LG modes, which show the rich entanglement structure of the system. In addition, we also generate tripartite entanglement of three types of coherent OAM superposition modes. Such OAM multiplexed multipartite entanglement opens the avenue to construct CV parallel quantum network for realizing parallel quantum information protocols.

Fractional vortex ultrashort pulsed beams with modulating vortex strength

In most papers about the fractional vortex continuous beams (FVCBs), the relationship between the total vortex strength S_α and the propagation distance is not analyzed since the vortex structure is not stable in the near field. In this paper, we theoretically study the fractional vortex ultrashort pulsed beams (FVUPBs) possessing non-integer topological charges α at arbitrary plane and find that the vortex structure is propagation-distance-dependent. Both the intensity and phase distributions are calculated to analyze the vortex structure. To evaluate the propagation properties of FVUPBs, we focus on the total vortex strength (TVS) of FVUPBs to investigate the number of vortex, and demonstrate that the birth of a vortex is at α = m + ɛ, where m is an integer, ɛ is a changing fraction depending on the pulse durations, peak wavelengths and propagation distances. Furthermore, we discover that the FVUPBs carry decreasing TVS along the propagation axis in free space. This special vortex structure for FVUPBs appears due to the mixture weight of vortex pulsed beam with different integer topological charges (TCs) n. However, the total orbital angular momentum is invariant during propagation. The above phenomenon presented in our paper are totally particular and intriguing compared with the FVCBs.

Superhigh-Resolution Recognition of Optical Vortex Modes Assisted by a Deep-Learning Method

Orbital angular momentum (OAM) has demonstrated great success in the optical communication field, which theoretically allows an infinite increase of the transmitted capacity. The resolution of a receiver to precisely recognize OAM modes is crucial to expand the communication capacity. Here, we propose a deep learning (DL) method to precisely recognize OAM modes with fractional topological charges. The minimum interval recognized between adjacent modes decreases to 0.01, which as far as we know is the first time this superhigh resolution has been realized. To exhibit its efficiency in the optical communication process, we transfer an Einstein portrait by a superhigh-resolution OAM multiplexing system. As the convolutional neuron networks can be trained by data up to an infinitely large volume in theory, this work exhibits a huge potential of generalized suitability for next generation DL based ultrafine OAM optical communication, which might even be applied to microwave, millimeter wave, and terahertz OAM communication systems.

Orbital-Angular-Momentum Multiplexed Continuous-Variable Entanglement from Four-Wave Mixing in Hot Atomic Vapor

Multiplexing is crucial for the data-carrying capacity of information communication systems. Orbital angular momentum (OAM) with a topological charge ℓ (ℓ integer) provides a degree of freedom to realize multiplexing. In this Letter, we report an experimental implementation of OAM multiplexed continuous variables (CV) entanglement based on a four-wave mixing (FWM) process, in which 13 pairs of entangled Laguerre-Gauss (LG) modes, LG_{ℓ,pr} and LG_{-ℓ,conj}, are simultaneously and deterministically generated, where ℓ (ℓ integer) is the topological charge corresponding to the OAM mode and pr (conj) indicates a probe (conjugate) beam. In the meanwhile, we experimentally show that there is no entanglement between the modes of LG_{ℓ,pr} and LG_{ℓ,conj} (ℓ≠0). These results clearly confirm the conservation of OAM in the FWM process from the viewpoint of a CV system. In addition, we investigate the entanglement properties of three types of coherent superposition of OAM modes. In the end, we also study the effect of the pump beam radius on the number of OAM multiplexing. Such OAM multiplexed CV entanglement provides a new perspective and platform to study CV quantum information protocols.

Orbital angular momentum transformation of optical vortex with aluminum metasurfaces

The orbital angular momentum (OAM) transformation of optical vortex is realized upon using aluminum metasurfaces with phase distributions derived from the caustic theory. The generated OAM transformation beam has the well-defined Bessel-like patterns with multiple designed topological charges from −1 to +2.5 including both the integer-order and fractional-order optical vortices along the propagation. The detailed OAM transformation process is observed in terms of the variations of both beam intensity and phase profiles. The dynamic distributions of OAM mode density in the transformation are further analyzed to illustrate the conservation of the total OAM. The demonstration of transforming OAM states arbitrarily for optical vortex beams will lead to many new applications in optical manipulation, quantum optics, and optical communication.

Gouy phase-assisted topological transformation of vortex beams from fractional fork holograms

The topological transformation of optical vortex beams from fractional fork holograms induced by the modulation of controlled Gouy phase (GP) is demonstrated. The GP change is tuned by varying the wavefront curvature of the input beam on the plane of the fractional phase generating optic. The locus of the point of singularity traces a semi-circle about the beam axis for maximum possible change of the associated GP. The morphology parameters describing the anisotropic vortex phases of generated optical vortices are tuned in the experiment by varying the input wavefront curvature. Through the transformation of the transverse Poynting vector of the fractional vortex beams, control of the extrinsic orbital angular momentum is demonstrated for the first time, to the best of our knowledge. This could enable better manipulation of an optically trapped micro-particle and be used in optically driven micro-machines.

Asymmetrical hyperentanglement concentration for entanglement of polarization and orbital angular momentum

We propose two hyperentanglement concentration protocols (hyper-ECPs) for two-photon entangled states in the polarization and orbital angular momentum degrees of freedom. The two cases distilling a maximally hyperentangled state from partially entangled pure state with unknown parameters and known parameters are dissected respectively. Both of the protocols require only linear optical elements which make our protocols more feasible for current technologies. In our protocols, the remote parties perform different local operations, which will reduce everyone's operation and improve the total efficiency. Each of them has the theoretical maximum success probability in the corresponding situation. The hyper-ECPs can be exploited simply to hyperentangled Greenberger-Horne-Zeilinger states.

Vortex strength and beam propagation factor of fractional vortex beams

Fractional vortex beams (FVBs) with non-integer topological charges attract much attention due to unique features of propagations, but different viewpoints still exist on the change of their total vortex strength. Here we have experimentally demonstrated the distribution and number of vortices contained in FVBs at the Fraunhofer diffraction region. We have verified that the jumps of total vortex strength for FVBs happen only when non-integer topological charge is before and after (but very close to) any even integer number that originates from two different mechanisms for generation and movement of vortices on focal plane. Meanwhile, we have also measured the beam propagation factor (BPF) of such FVBs and have found that their BPF values almost increase linearly in the x component (along the initial edge dislocation) and oscillate increasingly in the y component (vertical to the initial edge dislocation). Our experimental results are in good agreement with numerical results.

Conservation of orbital angular momentum for high harmonic generation of fractional vortex beams

This work demonstrates conservation of average orbital angular momentum for high harmonic generation of fractional vortex beams. High harmonics are generated in reflected light beams in a three-dimensional particle-in-cell simulation. The average orbital angular momentum of the beam is calculated when a relativistic linearly polarized fractional vortex beam impinges on a solid foil. The harmonic generation progress can be well explained by using the vortex oscillating mirror model. Both simulation and theoretical analysis show that the average orbital momentum of the nth harmonic is n times that of the fundamental frequency beam. This provides evidence that the average orbital angular momentum obeys momentum conservation during the harmonic generation of fractional vortex beams.

Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum

Quantum entanglements between integer-order and fractional-order orbital angular momentums (OAMs) have been previously discussed. However, the entangled nature of arbitrary rational-order OAM has long been considered a myth due to the absence of an effective strategy for generating arbitrary rational-order OAM beams. Therefore, we report a single metadevice comprising a bilaterally symmetric grating with an aperture, creating optical beams with dynamically controllable OAM values that are continuously varying over a rational range. Due to its encoded spiniform phase, this novel metagrating enables the production of an average OAM that can be increased without a theoretical limit by embracing distributed singularities, which differs significantly from the classic method of stacking phase singularities using fork gratings. This new method makes it possible to probe the unexplored niche of quantum entanglement between arbitrarily defined OAMs in light, which could lead to the complex manipulation of microparticles, high-dimensional quantum entanglement and optical communication. We show that quantum coincidence based on rational-order OAM-superposition states could give rise to low cross-talks between two different states that have no significant overlap in their spiral spectra. Additionally, future applications in quantum communication and optical micromanipulation may be found.

Polarization-entangled photon generation using partial spatially coherent pump beam

The generation of two photon fields, to date, has been demonstrated utilizing a fully coherent pump beam. In this paper we demonstrate, the theoretical and experimental generation of polarization entangled single photon pairs by varying the spatial coherence of the pump beam. The effect of the pump beam spatial coherence on the visibility of a polarization-entangled single photon source is investigated. A comparison of the visibility measurements using a fully coherent and partially coherent pump beam is performed. It is shown that the partial coherence of the pump beam contributes to an increase in the visibility. The coherence properties of the beam are significant for free-space optical transmission in particular for long range free-space quantum communication.

Optical angular momentum derivation and evolution from vector field superposition

Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or/and spiraling the electric-field vector. We employ vectorial formulation derivation to comprehensively study all angular momentum contents of optical vector fields in arbitrary superposition states, including the longitudinal and transverse, spin and orbital (SAM and OAM) components. As for the orthogonal superposition fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM, and the whole local spin flow manifests local multiple-fold helical trajectories. Especially, both the spin-orbit shift and transverse SAM could become considerable in the non-paraxial condition. Our studies here provide an explicit insight into the derivation and evolution, intrinsic correlations and salient features of various types of angular momentum components.

Synthetic-lattice enabled all-optical devices based on orbital angular momentum of light

All-optical photonic devices are crucial for many important photonic technologies and applications, ranging from optical communication to quantum information processing. Conventional design of all-optical devices is based on photon propagation and interference in real space, which may rely on large numbers of optical elements, and the requirement of precise control makes this approach challenging. Here we propose an unconventional route for engineering all-optical devices using the photon’s internal degrees of freedom, which form photonic crystals in such synthetic dimensions for photon propagation and interference. We demonstrate this design concept by showing how important optical devices such as quantum memory and optical filters can be realized using synthetic orbital angular momentum (OAM) lattices in degenerate cavities. The design route utilizing synthetic photonic lattices may significantly reduce the requirement for numerous optical elements and their fine tuning in conventional design, paving the way for realistic all-optical photonic devices with novel functionalities.

Design of all-optical devices rely on large numbers of optical elements and precise control makes this approach challenging. The authors demonstrate that optical devices such as quantum memory and optical filters can be realized using synthetic orbital angular momentum lattices in a single main degenerate cavity.

Digital spiral object identification using random light

Photons that are entangled or correlated in orbital angular momentum have been extensively used for remote sensing, object identification and imaging. It has recently been demonstrated that intensity fluctuations give rise to the formation of correlations in the orbital angular momentum components and angular positions of random light. Here we demonstrate that the spatial signatures and phase information of an object with rotational symmetries can be identified using classical orbital angular momentum correlations in random light. The Fourier components imprinted in the digital spiral spectrum of the object, as measured through intensity correlations, unveil its spatial and phase information. Sharing similarities with conventional compressive sensing protocols that exploit sparsity to reduce the number of measurements required to reconstruct a signal, our technique allows sensing of an object with fewer measurements than other schemes that use pixel-by-pixel imaging. One remarkable advantage of our technique is that it does not require the preparation of fragile quantum states of light and operates at both low- and high-light levels. In addition, our technique is robust against environmental noise, a fundamental feature of any realistic scheme for remote sensing.

Orthogonal quasi-phase-matched superlattice for generation of hyperentangled photons

A crystal superlattice structure featuring nonlinear layers with alternating orthogonal optic axes interleaved with orthogonal poling directions, is shown to generate high-quality hyperentangled photon pairs via orthogonal quasi-phase-matched spontaneous parametric downconversion. We demonstrate that orthogonal quasi-phase matching (QPM) processes in a single nonlinear domain structure correct phase and group-velocity mismatches concurrently. Compared with the conventional two-orthogonal-crystals source and the double-nonlinearity single-crystal source, the orthogonal QPM superlattice is shown to suppress the spatial and temporal distinguishability of the generated photon pairs by several orders of magnitude, depending on the number of layers. This enhanced all-over-the-cone indistinguishability enables the generation of higher fluxes of photon-pairs by means of the combined use of (a) long nonlinear crystal in noncollinear geometry, (b) low coherence-time pumping and ultra-wide-band spectral detection, and (c) focused pumping and over-the-cone detection. While each of these three features is challenging by itself, it is remarkable that the orthogonal QPM superlattice meets all of these challenges without the need for separate spatial or temporal compensation.

Orbital angular momentum 25 years on [Invited]

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.

Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes

The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.

Transmission of fractional topological charges via circular arrays of anisotropic fibers

We demonstrate that in circular arrays of anisotropic fibers at certain distribution of anisotropy directors robust transmission of optical fields with half-integer topological charges is possible. We show that this is possible because the supermodes of such arrays may contain in their circularly polarized components half-integer topological charges of opposite values. We also study the structure of singularities in these supermodes.

Spin-to-orbital angular momentum conversion in dielectric metasurfaces

Vortex beams are characterized by a helical wavefront and a phase singularity point on the propagation axis that results in a doughnut-like intensity profile. These beams carry orbital angular momentum proportional to the number of intertwined helices constituting the wavefront. Vortex beams have many applications in optics, such as optical trapping, quantum optics and microscopy. Although beams with such characteristics can be generated holographically, spin-to-orbital angular momentum conversion has attracted considerable interest as a tool to create vortex beams. In this process, the geometrical phase is exploited to create helical beams whose handedness is determined by the circular polarization (left/right) of the incident light, that is by its spin. Here we demonstrate high-efficiency Spin-to-Orbital angular momentum-Converters (SOCs) at visible wavelengths based on dielectric metasurfaces. With these SOCs we generate vortex beams with high and fractional topological charge and show for the first time the simultaneous generation of collinear helical beams with different and arbitrary orbital angular momentum. This versatile method of creating vortex beams, which circumvents the limitations of liquid crystal SOCs and adds new functionalities, should significantly expand the applications of these beams.

Comparing the information capacity of Laguerre-Gaussian and Hermite-Gaussian modal sets in a finite-aperture system

Using a spontaneous parametric down-conversion process to create entangled spatial states, we compare the information capacity associated with measurements in the Hermite-Gaussian and Laguerre-Gaussian modal basis in an optical system of finite aperture. We show that the cross-talk imposed by the aperture restriction degrades the information capacity. However, the Laguerre-Gaussian mode measurements show greater resilience to cross talk than the Hermite-Gaussian, suggesting that the Laguerre-Gaussian modal set may still offer real-world advantages over other modal sets.

Dynamically sculpturing plasmonic vortices: from integer to fractional orbital angular momentum

As a fundamental tool for light-matter interactions, plasmonic vortex (PV) is extremely useful due to the unique near field property. However, it is a pity that, up to now, the orbital angular momentum (OAM) carried by PVs could not be dynamically and continuously tuned in practice as well as the properties of fractional PVs are still not well investigated. By comparing with two previously reported methods, it is suggested that our proposal of utilizing the propagation induced radial phase gradient of incident Laguerre-Gaussian (LG) beam is a promising candidate to sculpture PVs from integer to fractional OAM dynamically. Consequently, the preset OAM of PVs could have four composing parts: the incident spin and orbital angular momentum, the geometric contribution of chiral plasmonic structure, and the radial phase gradient dependent contribution. Moreover, an analytical expression for the fractional PV is derived as a linear superposition of infinite numbers of integer PVs described by Bessel function of the first kind. It is also shown that the actual mean OAM of a fractional PV would deviate from the preset value, which is similar with previous results for spatial fractional optical vortices.

Arbitrarily tunable orbital angular momentum of photons

Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrarily tunable OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrarily tunable OAM we presented has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrarily tunable OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.

Coding/decoding two-dimensional images with orbital angular momentum of light

We investigate encoding and decoding of two-dimensional information using the orbital angular momentum (OAM) of light. Spiral phase plates and phase-only spatial light modulators are used in encoding and decoding of OAM states, respectively. We show that off-axis points and spatial variables encoded with a given OAM state can be recovered through decoding with the corresponding complimentary OAM state.

Electro-optic analyzer of angular momentum hyperentanglement

Characterizing a high-dimensional entanglement is fundamental in quantum information applications. Here, we propose a theoretical scheme to analyze and characterize the angular momentum hyperentanglement that two photons are entangled simultaneously in spin and orbital angular momentum. Based on the electro-optic sampling with a proposed hyper-entanglement analyzer and the simple matrix operation using Cramer rule, our simulations show that it is possible to retrieve effectively both the information about the degree of polarization entanglement and the spiral spectrum of high-dimensional orbital angular momentum entanglement.

Quantum simulation of 2D topological physics in a 1D array of optical cavities

Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration.

A wide variety of interesting phenomena arise in 2D systems subject to external gauge fields, but these are sometimes challenging to verify experimentally. Here the authors propose a setup to simulate 2D physics with a 1D arrangement of cavities, by exploiting the orbital angular momentum of trapped photons.

One exposure processing to fabricate spiral phase plate with continuous surface

An economical method for fabricating spiral phase plate (SPP) with continuous surface is proposed in this paper. We use an interval to quantize a three dimensional surface of an SPP into two dimensional bars to form a binary mask. The exposure dose can be precisely distributed through this mask in the exposure process. We discuss the select criterion of the quantization interval and the fabricating processes of SPP in detail. In the results, we present the fabrication of four kinds of high quality SPPs with different topological charges. The morphology analysis and the corresponding optical measurements verify the reliability of our fabrication method.

Light's twist

That light travels in straight lines is a statement of the obvious. However, the energy and momentum flow within light beams can twist to form vortices such as eddies in a stream. These twists carry angular momentum, which can make microscopic objects spin, be used to encode extra information in communication systems, enable the design of novel imaging systems and allow new tests of quantum mechanics.

Mimicking Faraday rotation to sort the orbital angular momentum of light

The efficient separation of the orbital angular momentum (OAM) is essential to both the classical and quantum applications with twisted photons. Here we devise and demonstrate experimentally an efficient method of mimicking the Faraday rotation to sort the OAM based on the OAM-to-polarization coupling effect induced by a modified Mach-Zehnder interferometer. Our device is capable of sorting the OAM of positive and negative numbers, as well as their mixtures. Furthermore, we report the first experimental demonstration to sort optical vortices of noninteger charges. The possibility of working at the photon-count level is also shown using an electron-multiplying CCD camera. Our scheme holds promise for quantum information applications with single-photon entanglement and for high-capacity communication systems with polarization and OAM multiplexing.

Ray transfer matrix for a spiral phase plate

We present a ray transfer matrix for a spiral phase plate. Using this matrix we determine the stability of an optical resonator made of two spiral phase plates and trace stable ray orbits in the resonator. Our results should be relevant to laser physics, optical micromanipulation, quantum information, and optomechanics.

Position measurement of non-integer OAM beams with structurally invariant propagation

We present a design to generate structurally propagation invariant light beams carrying non-integer orbital angular momentum (OAM) using Hermite-Laguerre-Gaussian (HLG) modes. Different from previous techniques, the symmetry axes of our beams are fixed when varying the OAM; this simplifies the calibration technique for beam positional measurement using a quadrant detector. We have also demonstrated analytically and experimentally that both the OAM value and the HLG mode orientation play an important role in the quadrant detector response. The assumption that a quadrant detector is most sensitive at the beam center does not always hold for anisotropic beam profiles, such as HLG beams.

Measurement of the entanglement between photonic spatial modes in optical fibers

We experimentally demonstrate the entanglement of spatial modes between two photons propagating through separate few-mode optical fibers. Quantum states over the two lowest-order spatial modes are measured with highly efficient spatial-mode analyzers based on acousto-optics. Quantum state tomography verifies the entanglement of the spatial-domain Bell state.

Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system

Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property can be singled out using graph theory. Here we report the experimental observation of an impossible-to-beat quantum advantage on a four-dimensional quantum system defined by the polarization and orbital angular momentum of a single photon. The results show pristine evidence of the quantum advantage and are compatible with the maximum advantage allowed using postquantum resources.

Entanglement and classical polarization states

We identify classical light fields as physical examples of nonquantum entanglement. A natural measure of degree of polarization emerges from this identification, and we discuss its systematic application to any optical field, whether beamlike or not.

Fiber transport of spatially entangled photons

Entanglement in the spatial degrees of freedom of photons is an interesting resource for quantum information. For practical distribution of such entangled photons, it is desirable to use an optical fiber, which in this case has to support multiple transverse modes. Here we report the use of a hollow-core photonic crystal fiber to transport spatially entangled qubits.

Visualization of the birth of an optical vortex using diffraction from a triangular aperture

The study and application of optical vortices have gained significant prominence over the last two decades. An interesting challenge remains the determination of the azimuthal index (topological charge) ℓ of an optical vortex beam for a range of applications. We explore the diffraction of such beams from a triangular aperture and observe that the form of the resultant diffraction pattern is dependent upon both the magnitude and sign of the azimuthal index and this is valid for both monochromatic and broadband light fields. For the first time we demonstrate that this behavior is related not only to the azimuthal index but crucially the Gouy phase component of the incident beam. In particular, we explore the far field diffraction pattern for incident fields incident upon a triangular aperture possessing non-integer values of the azimuthal index ℓ. Such fields have a complex vortex structure. We are able to infer the birth of a vortex which occurs at half-integer values of ℓ and explore its evolution by observations of the diffraction pattern. These results demonstrate the extended versatility of a triangular aperture for the study of optical vortices.

The creation and annihilation of optical vortices using cascade conical diffraction

Internal conical diffraction produces a superposition of orthogonally polarised zero- and first-order Bessel like beams from an incident circularly polarised Gaussian beam. For right-circularly polarised light, the first-order beam has an optical vortex of charge -1. Upon propagation of the first-order beam through a second biaxial crystal, a process which is termed cascade conical refraction, the generated beam is a superposition of orthogonally polarised fields of charge 0 and -1 or 0 and -2. This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness.

Generation of hybrid polarization-orbital angular momentum entangled states

Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair and thus could be useful for asymmetric optical quantum network where the communication channels are characterized by different properties. We report the first experimental realization of hybrid polarization-orbital angular momentum (OAM) entangled states by adopting a spontaneous parametric down conversion source of polarization entangled states and a polarization-OAM transferrer. The generated quantum states have been characterized through quantum state tomography. Finally, the violation of Bell's inequalities with the hybrid two photon system has been observed.

Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction

When a left-circularly polarised Gaussian light beam, which has spin angular momentum (SAM) J(sp) = sigmah = 1h per photon, is incident along one of the optic axes of a slab of biaxial crystal it undergoes internal conical diffraction and propagates as a hollow cone of light in the crystal. The emergent beam is a superposition of equal amplitude zero and first order Bessel like beams. The zero order beam is left-circularly polarised with zero orbital angular momentum (OAM) J(orb) = [see text]h = 0, while the first order beam is right-circularly polarized but carries OAM of J(orb) = 1h per photon. Thus, taken together the two beams have zero SAM and J(orb) = (1/2)h per photon. In this paper we examine internal conical diffraction of an elliptically polarised beam, which has fractional SAM, and demonstrate an all-optical process for the generation light beams with fractional OAM up to +/- 1h.

Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion

We present a study of the propagation of higher-order spatial modes in a waveguided parametric down-conversion photon-pair source. Observing the multimode photon-pair spectrum from a periodically poled KTiOPO(4) waveguide allowed us to isolate individual spatial modes through their distinctive spectral properties. We have measured directly the spatial distribution of each mode of the photon pairs, confirming the findings of our waveguide model, and demonstrated by coincidence measurements that the total parity of the modes is conserved in the nonlinear interaction. Furthermore, we show that we can combine the advantages of a waveguide source with the potential to generate spatially entangled photon pairs as in bulk-crystal down-converters.

Polarization control of single photon quantum orbital angular momentum states

The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum m degree of freedom within the subspaces of |m| = 2h and |m| = 4h per photon.