Volume 11, Issue 4 - Special Issue: Photonic Angular Momentum

The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ /2 π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.

Orbital angular momentum (OAM), which describes tailoring the spatial physical dimension of light waves into a helical phase structure, has given rise to many applications in optical manipulation, microscopy, imaging, metrology, sensing, quantum science, and optical communications. Light beams carrying OAM feature two distinct characteristics, i.e., inherent orthogonality and unbounded states in principle, which are suitable for capacity scaling of optical communications. In this paper, we give an overview of OAM and beyond in free-space optical communications. The fundamentals of OAM, concept of optical communications using OAM, OAM modulation (OAM modulation based on spatial light modulator, high-speed OAM modulation, spatial array modulation), OAM multiplexing (spectrally efficient, high capacity, long distance), OAM multicasting (adaptive multicasting, N -dimensional multicasting), OAM communications in turbulence (adaptive optics, digital signal processing, auto-alignment system), structured light communications beyond OAM (Bessel beams, Airy beams, vector beams), diverse and robust communications using OAM and beyond (multiple scenes, turbulence-resilient communications, intelligent communications) are comprehensively reviewed. The prospects and challenges of optical communications using OAM and beyond are also discussed at the end. In the future, there will be more opportunities in exploiting extensive advanced applications from OAM beams to more general structured light.

Complex vector light fields have become a topic of late due to their exotic features, such as their non-homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of freedom (DoF). In general, vector beams propagate in free space along straight lines, being the Airy-vector vortex beams the only known exception. Here, we introduce a new family of vector beams that exhibit novel properties that have not been observed before, such as their ability to freely accelerate along parabolic trajectories. In addition, their transverse polarisation distribution only contains polarisation states oriented at exactly the same angle but with different ellipticity. We anticipate that these novel vector beams might not only find applications in fields such as optical manipulation, microscopy or laser material processing but also extend to others.

Twist phase is a nontrivial second-order phase that only exists in a partially coherent beam. Such twist phase endows the partially coherent beam with orbital angular momentum (OAM) and has unique applications such as in super-resolution imaging. However, the manipulation and the detection of the twist phase are still far from easy tasks in experiment. In this work, we present a flexible approach to generate a famous class of twisted Gaussian Schell-model (TGSM) beam with controllable twist phase by the superposition of the complex field realizations using a single phase-only spatial light modulator. The precise control of the amplitude and phase of the field realizations allows one to manipulate the strength of the twist phase easily. In addition, we show that the twist factor, a key factor that determines the strength of twist phase and the amount of OAM, can be measured by extracting the real part of the complex degree of coherence of the TGSM beam. The experiment is carried out with the help of the generalized Hanbury Brown and Twiss experiment as the generated TGSM beam obeys Gaussian statistics. The flexible control and detection of the twist phase are expected to find applications in coherence and OAM-based ghost imaging.

We propose vector modes based on inhomogeneously polarized Hermite–Gaussian (HG) vector beams, providing complete structural conservation of the beams during propagation. Like uniformly polarized mode beams, these beams provide structural stability (or invariance) of both the intensity and the polarization state, in turn ensuring the stability of other field characteristics, including the angular momentum. We determine the conditions imposed on the HG mode composition in the transverse components of the electromagnetic field in order to control the three-dimensional characteristics of the field, such as intensity, polarization, and spin angular momentum (SAM). For the visual analysis of the polarization state of inhomogeneously polarized beams, we use the transverse distribution of the vector of three Stokes parameters. The correspondence of the third Stokes parameter to the distribution of the longitudinal component of the SAM is used for experimental measurements. The theoretical analysis is clearly illustrated by numerical simulations and confirmed by experimental results.

As a classical or quantum system undergoes a cyclic evolution governed by slow change in its parameter space, it acquires a topological phase factor known as the geometric or Berry phase. One popular manifestation of this phenomenon is the Gouy phase which arises when the radius of curvature of the wavefront changes adiabatically in a cyclic manner, for e.g., when focused by a lens. Here, we report on a new manifestation of the Berry phase in 3D structured light which arises when its polarization state adiabatically evolves along the optical path. We show that such a peculiar evolution of angular momentum, which occurs under free space propagation, is accompanied by an accumulated phase shift that elegantly coincides with Berry’s prediction. Unlike the conventional dynamic phase, which accumulates monotonically with propagation, the Berry phase observed here can be engineered on demand, thereby enabling new possibilities; such as spin-dependent spatial frequency shifts, and modified phase matching in resonators and nonlinear interactions. Our findings expand the laws of wave propagation and can be applied in optics and beyond.

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = ℓ + σ , where ℓ is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.

Transverse (Hall-effect) and Goos–Hänchen shifts of light beams reflected/refracted at planar interfaces are important wave phenomena, which can be significantly modified and enhanced by the presence of intrinsic orbital angular momentum (OAM) in the beam. Recently, optical spatiotemporal vortex pulses (STVPs) carrying a purely transverse intrinsic OAM were predicted theoretically and generated experimentally. Here we consider the reflection and refraction of such pulses at a planar isotropic interface. We find theoretically and confirm numerically novel types of OAM-dependent transverse and longitudinal pulse shifts. Remarkably, the longitudinal shifts can be regarded as time delays, which appear, in contrast to the well-known Wigner time delay, without temporal dispersion of the reflection/refraction coefficients. Such time delays allow one to realize OAM-controlled slow (subluminal) and fast (superluminal) pulse propagation without medium dispersion. These results can have important implications in various problems involving scattering of localized vortex states carrying transverse OAM.

We generate a spatiotemporal optical vortex (STOV) with tunable orbital angular momentum (OAM) orientation by a simple lens system. We utilize a cylindrical lens system, which is an astigmatic mode converter, to add longitudinal angular momentum to tilt the purely transverse OAM in an arbitrary direction. The amount of tilt is tunable by adjusting the lens system, and thus the OAM direction is continuously adjustable. STOVs with adjustable OAM directions have been verified theoretically and experimentally. We believe such direction controllable OAMs will enrich future applications.

Vectorial structured light fields have displayed properties advantageous in many disciplines ranging from communications, microscopy and metrology to laser cutting and characterizing quantum channels. The generation of these fields has been made convenient through the implementation of nanophotonic metasurfaces amongst other static and digital techniques. Consequently, the detection and characterisation of these fields is of equal importance. Most existing techniques involve using separate polarization optics and correlation filters to perform the projective measurements – or are only able to perform such measurements on a subset of possible vector states. We present a compact, fully automated measurement technique based on a digital micro-mirror device (DMD), which facilitates the complete, local and global, characterisation of the spatial mode and polarization degrees-of-freedom (DOFs) for arbitrary vectorial fields. We demonstrate our approach through the identification of relevant hybrid-order Poincaré spheres, the reconstruction of state vectors on these spheres, as well as the recovery of the non-separability and states-of-polarization for a variety of vector beams.

Stimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

We demonstrate the spin to orbital angular momentum transfer in frequency upconversion with structured light beams. A vector vortex is coupled to a circularly polarized Gaussian beam in noncollinear second harmonic generation under type-II phase match. The second harmonic beam inherits the Hermite–Gaussian components of the vector vortex; however, the relative phase between them is determined by the polarization state of the Gaussian beam. This effect creates an interesting crosstalk between spin and orbital degrees of freedom, allowing the angular momentum transfer between them. Our experimental results match the theoretical predictions for the nonlinear optical response.

Structured light with customized topological patterns inspires diverse classical and quantum investigations underpinned by accurate detection techniques. However, the current detection schemes are limited to vortex beams with a simple phase singularity. The precise recognition of general structured light with multiple singularities remains elusive. Here, we report deep learning (DL) framework that can unveil multi-singularity phase structures in an end-to-end manner, after feeding only two intensity patterns upon beam propagation. By outputting the phase directly, rich and intuitive information of twisted photons is unleashed. The DL toolbox can also acquire phases of Laguerre–Gaussian (LG) modes with a single singularity and other general phase objects likewise. Enabled by this DL platform, a phase-based optical secret sharing (OSS) protocol is proposed, which is based on a more general class of multi-singularity modes than conventional LG beams. The OSS protocol features strong security, wealthy state space, and convenient intensity-based measurements. This study opens new avenues for large-capacity communications, laser mode analysis, microscopy, Bose–Einstein condensates characterization, etc.

Structuring light–matter interaction at a deeply subwavelength scale is fundamental to optical metamaterials and metasurfaces. Conventionally, the operation of a metasurface is determined by the collective electric polarization response of its lithographically defined structures. The inseparability of electric polarization and current density provides the opportunity to construct metasurfaces from current elements instead of nanostructures. Here, we realize metasurfaces using structured light rather than structured materials. Using coherent control, we transfer structure from light to transient currents in a semiconductor, which act as a source for terahertz radiation. A spatial light modulator is used to control the spatial structure of the currents and the resulting terahertz radiation with a resolution of 5.6 ± 0.8  μm $5.6{\pm}0.8\mathrm{\,\mu m}$ , or approximately λ / 54 $\lambda /54$ at a frequency of 1 THz. The independence of the currents from any predefined structures and the maturity of spatial light modulator technology enable this metasurface to be reconfigured with unprecedented flexibility.

In linear optical processes, compact and effective wavefront shaping techniques have been developed with the artificially engineered materials and devices in the past decades. Recently, wavefront shaping of light at newly generated frequencies was also demonstrated using nonlinear photonic crystals and metasurfaces. However, the nonlinear wave-shaping devices with both high nonlinear optical efficiency and high wave shaping efficiency are difficult to realize. To circumvent this constraint, we propose the idea of metasurface decorated optical crystal to take the best aspects of both traditional nonlinear crystals and photonic metasurfaces. In the proof-of-concept experiment, we show that a silicon nitride metasurface decorated quartz crystal can be used for the wavefront shaping of the second harmonic waves generated in quartz. With this crystal-metasurface hybrid platform, the nonlinear vortex beam generation and nonlinear holography were successfully demonstrated. The proposed methodology may have important applications in nonlinear structured light generation, super-resolution imaging, and optical information processing, etc.

Modality is a generic concept of wave-optics at the basis of optical information and communications. One of the challenges of photonics technologies based on optical orbital angular momentum consists in the production of a modal content for both the azimuthal and radial degrees of freedom. This basically requires shaping the complex amplitude of an incident light beam, which is usually made up from adaptive spatial light modulators or bespoke devices. Here, we report on the experimental attempt of a recent theoretical proposal [ Opt. Lett. 42 , 1966 (2017)] toward the production of various optical vortex modes of the Laguerre–Gaussian type relying on the spin–orbit interaction of light. This is done in the visible domain from optical elements made out of silica glass. The idea consists in exploiting the combined effects of azimuthally-varying geometric phase with that of radially-varying propagation features. The proposed approach can be readily extended to any wavelength as well as to other families of optical modes, although some dynamic phase problems remain to be solved to make it a turnkey technology.

Polarimetry has been demonstrated essential in various disciplines, such as optical communications, imaging, and astronomy. On-chip nanostructures for polarization measurements are most expected to replace the conventional bulk elements, and hence minimize the polarimeter for integrated applications. Some on-chip nanophotonic polarimeter via polarization detection has been implemented, in which the separation of two spin polarized states is needed. However, due to the relatively low coupling efficiency or complicated photonic silicon circuits, on-chip polarimetry using a single device still remains challenging. Here, we introduce and investigate an on-chip polarimeter with nanostructures using the inverse design method. The developed device shows the ability to detect the four polarization components of light, two of which are the spin polarizations, and the other two are the linear polarizations. The retrieved Stokes parameters with experimentally tested data are in close agreement with the numerical results. We also show the proof of concept demonstration for high-speed Stokes vector optical signals detection. In the high-speed communication experiment with data rate up to 16 GBd, the detected optical signals via polarization measurements at multiple wavelengths in the C-band were recovered with the bit error rate below the 20% forward error correction threshold. The proposed on-chip polarimeter shows promising performance both in Stokes polarimetry and high-speed optical communication applications.

Light carrying orbital angular momentum constitutes an important resource for both classical and quantum information technologies. Its inherently unbounded nature can be exploited to generate high-dimensional quantum states or for channel multiplexing in classical and quantum communication in order to significantly boost the data capacity and the secret key rate, respectively. While the big potentials of light owning orbital angular momentum have been widely ascertained, its technological deployment is still limited by the difficulties deriving from the fabrication of integrated and scalable photonic devices able to generate and manipulate it. Here, we present a photonic integrated chip able to excite orbital angular momentum modes in an 800 m long ring-core fiber, allowing us to perform parallel quantum key distribution using two and three different modes simultaneously. The experiment sets the first steps towards quantum orbital angular momentum division multiplexing enabled by a compact and light-weight silicon chip, and further pushes the development of integrated scalable devices supporting orbital angular momentum modes.

We propose and experimentally demonstrate a laser-writing-induced selective chemical etching (LWISCE) technique for effective micro-fabrication of lithium niobate (LN) crystal. Laser writing of LN crystal produces negative domains and domain walls. Also, it causes local lattice defects, in which the etching rates are significantly increased in comparison to the original LN crystal. In experiment, we use the LWISCE technique to fabricate various fork gratings in an X-cut LN crystal for the generation of vortex beams. In comparison to etching an untreated X-cut LN crystal, the etching rates of the laser-writing-induced boundaries and the central laser-irradiated areas are enhanced by a factor of 26 and 16, respectively. The width and depth of fork grating structure can be precisely controlled by laser writing parameters. Our method provides an efficient mask-free micro-fabrication technique for LN crystal, which can be readily applied to other ferroelectric crystals such as lithium tantalate, potassium titanyl phosphate and barium calcium titanate.

We present the intracavity generation of beams with radial polarization at an average output power of 750 W and an optical efficiency of 43% from a continuous wave thin-disk laser. Circular grating waveguide output couplers (GWOC) were used to select the radial polarization. The sensitivity of the polarizing function of the GWOC with regards to the fabrication tolerances is also analysed in details with a particular emphasis on the effect of the duty cycle and the geometrical profile of the gratings. Furthermore, we present the conversion of femtosecond laser pulses from linear to azimuthal polarization using a nanograting-based polarization converter. Azimuthally polarized beams with an average power of up to 850 W, a pulse duration of 400 fs and a pulse repetition rate of 1 MHz were generated in this way with a conversion efficiency of >90%.

Numerous approaches have been developed to generate optical vortex beams carrying orbital angular momentum (OAM) over the past decades, but the direct intracavity generation of such beams with practical output powers in the femtosecond regime still remains a challenge. Here we propose and experimentally demonstrate the efficient generation of high-peak-power femtosecond optical vortex pulses from a Mamyshev oscillator (MO) based on few-mode polarization-maintaining (PM) ytterbium-doped fibers (YDFs). By employing an appropriate intracavity transverse spatial mode selection technique, ultrafast pulses carrying OAM with selectable topological charge of l  = ±1 are successfully generated with an average output power of ∼5.72 W at ∼24.35 MHz repetition rate, corresponding to a single pulse energy of ∼235 nJ. The chirped pulses can be compressed to ∼76 fs outside the cavity, leading to a pulse peak power of ∼2.2 MW. To the best of our knowledge, this is by far the highest pulse energy and peak power for optical vortex pulses ever generated directly from a fiber oscillator. This unprecedented level of performance should be of great interest for a variety of applications including materials processing and imaging.

An optical vortex possesses a ring-shaped spatial profile and orbital angular momentum (OAM) owing to its helical wavefront. This form of structured light has garnered significant attention in recent years, and it has enabled new investigations in fundamental physics and applications. One such exciting application is laser-based material transfer for nano-/micro-fabrication. In this work, we demonstrate the application of a single-pulse optical vortex laser beam for direct printing of ring-shaped structures composed of hexagonal close-packed, mono-/multi-layered nanoparticles which exhibit ‘structural color’. We compare and contrast the interaction of the vortex beam with both dielectric and metallic nanoparticles and offer physical insight into how the OAM of vortex beams interacts with matter. The demonstrated technique holds promise for not only photonic-based nano-/micro-fabrication, but also as a means of sorting particles on the nanoscale, a technology which we term ‘optical vortex nanoparticle sorting’.

Recently, orbital angular momentum (OAM) has been adopted to measure the shape of static objects and the translation motion of moving objects in optical remote sensing. Most of these studies rely on measuring the intensity variation of OAM beams. However, the OAM intensity does not change with the rotation of the spinning object, but its phase changes. The phase variation is proved to be proportional to the object’s angular velocity. Since a rotating object will cause the OAM phase dependent on time, the OAM phase needs to be measured instantaneously, to support the OAM-based angular velocity measurement. In this work, we report a scheme to measure the angular velocity of a spinning object using a photonic OAM phase spectrum. A phase-to-intensity strategy is implemented to enable the real-time multi-OAM phase measurement, in which the phase can be determined with the intensities of four focal spots in a two-dimensional array generated by a phase-only spatial light modulator. The experimental results show that the average error of the measured angular velocity could be under 2.45% by detecting the phase of two OAM modes. This OAM-based angular velocity detection method provides a complementary approach to characterize the rotational Doppler effect, especially for slow angular motion.

Spatial division multiplexed optical transmission over a multi-ring-core orbital angular momentum (OAM) fibre is reported for the first time. The seven cores in the fibre each supports OAM modes belonging to mode groups (MGs) of topological charge | l | = 0–4. The MGs of | l | = 1–4 each contains four near-degenerate OAM modes that carry the combinations of opposite orbital and spin angular momenta. The weak coupling between these higher-order MGs as well as between the cores enables the simultaneous transmission of 56 OAM mode channels (two MGs per core of the topological charges | l | = 2 and 3) over the 60-km span, while only requiring modular 4 × 4 multi-input multi-output (MIMO) signal processing to equalize the mixing among the four mode channels in each MG that are strongly coupled – a feature that also minimizes the number of filter taps. The mode channels are launched using seven-core single-mode fibre fan-in devices, with the light in all seven cores converted into OAM modes via specially designed plates that carry seven off-axis-compensated phase masks matching the hexagonal configuration of the multi-core fibres. Each mode channel carries 10 WDM wavelengths, equivalently aggregating to a capacity of 31.4 Tbit/s (net 25.1 Tb/s) and a spectral efficiency (SE) of 62.7 bit/s/Hz (net 50.2 bit/s/Hz) with 28-GBaud QPSK modulation per data channel.

When an orbital-angular-momentum (OAM) beam propagates through the dynamic air–water interface, the aerosol above the water and the water surface curvature could induce various degradations (e.g., wavefront distortion, beam wandering, scattering, and absorption). Such time-varying degradations could affect the received intensity and phase profiles of the OAM beams, resulting in dynamic modal power loss and modal power coupling. We experimentally investigate the degradation for a single OAM beam under dynamic aerosol, dynamic curvature, and their comprehensive effects. Our results show the following: (i) with the increase of the aerosol strength (characterized by the attenuation coefficient) from ∼0 to ∼0.7–1.3 dB/cm over ∼7 cm, the power coupling ratio from OAM −1 to +2 increases by 4 dB, which might be due to the amplitude and phase distortion caused by spatially dependent scattering and absorption. (ii) With the increase of the curvature strength (characterized by the variance of curvature slope over time) from ∼0 to ∼2 × 10 −5  rad 2 , the power coupling ratio from OAM −1 to +2 increases by 11 dB. This could be caused by both the wavefront distortion and the beam wandering. (iii) Under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10 −7  rad 2 ), there is an up to 2 dB higher modal power loss as compared with the single-effect cases. (iv) The received power on OAM −1 fluctuates in a range of ∼6 dB within a 220 ms measurement time under aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10 −7  rad 2 ) effects due to the dynamic degradations. We also demonstrate an OAM −1 and +2 multiplexed 2-Gbit/s on–off-keying link under dynamic aerosol and curvature effects. The results show a power penalty of ∼3 dB for the bit-error-rate at the 7% forward-error-correction limit under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10 −7  rad 2 ), compared with the no-effect case.