The editorial introduces the theme issue on orbital angular momentum.

The article comments on the the impact on diverse fields of R. A. Beth’s direct detection of the angular momentum of light.

The optical angular momentum is ubiquitous to the science of light, especially whenever the polarization state and the spatial distribution of the phase are involved, which are most often associated with the spin and orbital parts of the total angular momentum, respectively. Notably, the independent introduction of these two contributions to the total optical angular momentum was accompanied by suggestions regarding the possible detection of their mechanical effects using a torsion pendulum. Today, the classical and quantum mechanical aspects of spin and orbital angular momentum of light and their mutual coupling remain active research topics offering exciting perspectives for photonic technologies. Our brief historical overview shows how the torsion pendulum has accompanied scientific advances on mechanical effects based on the angular degrees of freedom of light since Beth’s pioneering contribution published in 1935.

The recently proposed extreme-ultraviolet beams with time-varying orbital angular momentum (OAM) realized by high-harmonic generation provide extraordinary tools for quantum excitation control and particle manipulation. However, such an approach is not easily scalable to other frequency regimes. We design a space-time-coding digital metasurface operating in the microwave regime to experimentally generate time-varying OAM beams. Due to the flexible programmability of the metasurface, a higher-order twist in the envelope wavefront structure of time-varying OAM beams can be further designed as an additional degree of freedom. The time-varying OAM field patterns are dynamically mapped by developing a two-probe measurement technique. Our approach in combining the programmability of space-time-coding digital metasurfaces and the two-probe measurement technique provides a versatile platform for generating and observing time-varying OAM and other spatiotemporal excitations in general. The proposed time-varying OAM beams have application potentials in particle manipulation, time-division multiplexing, and information encryption.

Spatiotemporal optical vortex (STOV) pulses can carry transverse orbital angular momentum (OAM) that is perpendicular to the direction of pulse propagation. For a STOV pulse, its spatiotemporal profile can be significantly distorted due to unbalanced dispersive and diffractive phases. This may limit its use in many research applications, where a long interaction length and a tight confinement of the pulse are needed. The first demonstration of STOV pulse propagation through a few-mode optical fiber is presented. Both numerical and experimental analysis on the propagation of STOV pulse through a commercially available SMF-28 standard telecommunication fiber is performed. The spatiotemporal phase feature of the pulse can be well kept after the pulse propagates a few-meter length through the fiber even with bending. Further propagation of the pulse will result in a breakup of its spatiotemporal spiral phase structure due to an excessive amount of modal group delay dispersion. The stable and robust transmission of transverse photonic OAM through optical fiber may open new opportunities for transverse photonic OAM studies in telecommunications, OAM lasers, and nonlinear fiber-optical research.

Explosive growth in demand for data traffic has prompted exploration of the spatial dimension of light waves, which provides a degree of freedom to expand data transmission capacity. Various techniques based on bulky optical devices have been proposed to tailor light waves in the spatial dimension. However, their inherent large size, extra loss, and precise alignment requirements make these techniques relatively difficult to implement in a compact and flexible way. In contrast, three-dimensional (3D) photonic chips with compact size and low loss provide a promising miniaturized candidate for tailoring light in the spatial dimension. Significantly, they are attractive for chip-assisted short-distance spatial mode optical interconnects that are challenging to bulky optics. Here, we propose and fabricate femtosecond laser-inscribed 3D photonic chips to tailor orbital angular momentum (OAM) modes in the spatial dimension. Various functions on the platform of 3D photonic chips are experimentally demonstrated, including the generation, (de)multiplexing, and exchange of OAM modes. Moreover, chip-chip and chip–fiber–chip short-distance optical interconnects using OAM modes are demonstrated in the experiment with favorable performance. This work paves the way to flexibly tailor light waves on 3D photonic chips and offers a compact solution for versatile optical interconnects and other emerging applications with spatial modes.

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

Engineering single-photon states endowed with orbital angular momentum (OAM) is a powerful tool for quantum information photonic implementations. Indeed, due to its unbounded nature, OAM is suitable for encoding qudits, allowing a single carrier to transport a large amount of information. Most of the experimental platforms employ spontaneous parametric down-conversion processes to generate single photons, even if this approach is intrinsically probabilistic, leading to scalability issues for an increasing number of qudits. Semiconductor quantum dots (QDs) have been used to get over these limitations by producing on-demand pure and indistinguishable single-photon states, although only recently they have been exploited to create OAM modes. Our work employs a bright QD single-photon source to generate a complete set of quantum states for information processing with OAM-endowed photons. We first study hybrid intraparticle entanglement between OAM and polarization degrees of freedom of a single photon whose preparation was certified by means of Hong–Ou–Mandel visibility. Then, we investigate hybrid interparticle OAM-based entanglement by exploiting a probabilistic entangling gate. The performance of our approach is assessed by performing quantum state tomography and violating Bell inequalities. Our results pave the way for the use of deterministic sources for the on-demand generation of photonic high-dimensional quantum states.

X-ray beams carrying orbital angular momentum (OAM) are an emerging tool for probing matter. Optical elements, such as spiral phase plates and zone plates, have been widely used to generate OAM light. However, due to the high impinging intensities, these optics are challenging to use at X-ray free-electron lasers (XFELs). Here, we propose a self-seeded free-electron laser (FEL) method to produce intense X-ray vortices. Unlike passive filtering after amplification, an optical element will be used to introduce the helical phase to the radiation pulse in the linear regime, significantly reducing thermal load on the optical element. The generated OAM pulse is then used as a seed and significantly amplified. Theoretical analysis and numerical simulations demonstrate that the power of the OAM seed pulse can be amplified by more than two orders of magnitude, reaching peak powers of several tens of gigawatts. The proposed method paves the way for high-power and high-repetition-rate OAM pulses of XFEL light.

Laguerre-Gaussian (LG) modes, carrying the orbital angular momentum of light, are critical for important applications, such as high-capacity optical communications, superresolution imaging, and multidimensional quantum entanglement. Advanced developments in these applications demand reliable and tunable LG mode laser sources, which, however, do not yet exist. Here, we experimentally demonstrate highly efficient, highly pure, broadly tunable, and topological-charge-controllable LG modes from a Janus optical parametric oscillator (OPO). The Janus OPO featuring a two-faced cavity mode is designed to guarantee an efficient evolution from a Gaussian-shaped fundamental pump mode to a desired LG parametric mode. The output LG mode has a tunable wavelength between 1.5 and 1.6 μm with a conversion efficiency >15 % , a controllable topological charge up to 4, and a mode purity as high as 97%, which provides a high-performance solid-state light source for high-end demands in multidimensional multiplexing/demultiplexing, control of spin-orbital coupling between light and atoms, and so on.

A phase-only method is proposed to transform an optical vortex field into desired spiral diffraction–interference patterns. Double-ring phase apertures are designed to produce a concentric high-order vortex beam and a zeroth-order vortex beam, and the diffracted intensity ratio of two beams is adjustable between 0 and 1. The coherent superposition of the two diffracted beams generates a brighter Airy spot (or Poisson spot) in the middle of the spiral pattern, where the singularity for typical vortex beam is located. Experiments employing circular, triangular, and rectangular phase apertures with topological charges from 3 to 16 demonstrate a stable, compact, and flexible apparatus for vortex beam conversion. By adjusting the parameters of the phase aperture, the proposed method can realize the optical Gaussian tweezer function and the optical vortex tweezer function simultaneously along the same axis or switch the experimental setup between the two functions. It also has potential applications in light communication through turbulent air by transmitting an orbital angular momentum-coded signal with a concentric beacon laser.

Optical orbital angular momentum (OAM) multiplexed holography has been implemented as an effective method for information encryption and storage. Multiramp helicoconical-OAM multiplexed holography is proposed and experimentally implemented. The mode selectivity of the multiramp mixed screw-edge dislocations, constant parameter K, and normalized factor are investigated, respectively, which demonstrates that those parameters can be used as additional coding degrees of freedom for holographic multiplexing. The combination of the topological charge and the other three parameters can provide a four-dimensional multiplexed holography and can enhance information capacity.

Recently, structured light beams have attracted substantial attention in many applications, including optical communications, imaging, optical tweezers, and quantum optics. We propose and experimentally demonstrate a reconfigurable structured light beam generator in order to generate diverse structured light beams with adjustable beam types, beam orders, and beam sizes. By controlling the sizes of generated free-space structured light beams, free-space orbital angular momentum (OAM) beams and vector beams are coupled into an air–core fiber. To verify that our structured light generator enables generating structured light with high beam quality, polarization distributions and mode purity of generated OAM beams and vector beams in both free space and air–core fiber are characterized. Such a structured light generator may pave the way for future applications based on higher-order structured light beams.