Periodic-trajectory-controlled, coherent-state-phase-switched, and wavelength-tunable SU(2) geometric modes in a frequency-degenerate resonator

Mathieu ray-wave structured light with self-healing elliptical accelerating vortices

Ray-wave structured vortex beams have attracted increasing attention due to their unique spatial geometric coupling to control complex orbital angular momentum (OAM). Still, current models were constrained by circular symmetry with limited modulation freedom. Herein, we propose a generalized class of ray-wave light fields called Mathieu geometric modes (MGMs) fulfilling the form of a stationary coherent state but based on a set of helical Mathieu modes (HMMs), in which geometrically tunable elliptical accelerating vortices are obtained by tuning their eccentricity-related parameters. MGMs also possess intriguing properties of coordinate transformation, self-healing, and multilayer tunable angular acceleration upon propagation. MGMs have higher degrees of freedom to control spatial accelerating vortices, paving the way for higher-dimensional optical tweezers and complex particle manipulation.

Complex structured beam direct generation by coherent superposition of a complete set of degenerate eigenmodes

Structured beams have played an important role in many fields due to their rich spatial characteristics. The microchip cavity with a large Fresnel number can directly generate structured beams with complex spatial intensity distribution, which provides convenience for further exploring the formation mechanism of structured beams and realizing low-cost applications. In this article, theoretical and experimental studies are carried out on complex structured beams directly generated by the microchip cavity. It is demonstrated that the complex beams generated by the microchip cavity can be expressed by the coherent superposition of whole transverse eigenmodes within the same order, thus forming the eigenmode spectrum. The mode component analysis of complex propagation-invariant structured beams can be realized by the degenerate eigenmode spectral analysis described in this article.

Multiaxial super-geometric mode laser

Structured light was usually studied by two-dimensional (2D) transverse eigenmodes. Recently, the three-dimensional (3D) geometric modes as coherent superposed states of eigenmodes opened new topological indices to shape light, that optical vortices can be coupled on multiaxial geometric rays, but only limited to azimuthal vortex charge. Here, we propose a new structured light family, multiaxial super-geometric modes, enabling full radial and azimuthal indices coupled to multiaxial rays, and they can be directly generated from a laser cavity. Exploiting combined intra- and extra-cavity astigmatic mode conversions, we experimentally verify the versatile tunability of complex orbital angular momentum and SU(2) geometry beyond the limit of prior multiaxial geometric modes, opening new dimensions to revolutionize applications such as optical trapping, manufacturing, and communications.

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes are originally and systematically investigated. The quantum theory of the coherent state is exploited to derive an analytical wave representation for the transformed output beams. The derived wave function is further employed to numerically analyze the propagation dependent orbital angular momentum densities. The parts of the negative and positive regions in the orbital angular momentum density are found to rapidly change in the Rayleigh range behind the transformation.

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers for free-space optical communication, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and data transmission by the conjugated modulation method, demonstrating lower error rates caused by center offset and coherent background noise, compared with OAM basis. Our work provides a potentially useful basis for the next generation of large-scale dense data communication.

Advances of Yb:CALGO Laser Crystals

Yb:CaGdAlO4, or Yb:CALGO, a new laser crystal, has been attracting increasing attention recently in a myriad of laser technologies. This crystal features salient thermal, spectroscopic and mechanical properties, which enable highly efficient and safe generation of continuous-wave radiations and ultrafast pulses with ever short durations. More specifically, its remarkable thermal-optic property and its high conversion efficiency allow high-power operation. Its high nonlinear coefficient facilitates study of optimized mode locking lasers. Besides, its ultrabroad and flat-top emission band benefits the generation of complex structured light with outstanding tunability. In this paper, we review the recent advances in the study of Yb:CALGO, covering its physical properties as well as its growing applications in various fields and prospect for future development.

Generating high-power Lissajous structured modes and trochoidal vortex beams by an off-axis end-pumped Nd:YVO4 laser with astigmatic transformation

High-power structured beams with the transverse morphologies as the Lissajous figures are generated by an Nd:YVO₄ laser under two-dimensional off-axis pumping. By fine-tuning the cavity length in the neighborhood around the condition of longitudinal-transverse coupling, different cases of accidental degeneracies from the intracavity astigmatism are achieved to lead the output emission to be various Lissajous modes with different transverse frequency ratios. The generated Lissajous modes reveals good power performance with slope efficiency up to 47% and optical-to-optical conversion efficiency to be higher than 37.5% at a pump power of 16 W. Moreover, by applying beam transformation via a single-lens astigmatic mode converter, the generated Lissajous modes are further converted into structured vortex beams with transverse patterns localized on the trochoidal curves. The transformed trochoidal vortex beams are confirmed to preserve well-defined mode structures even when the average output power has been scaled up to be higher than 4 W.

Creation and control of high-dimensional multi-partite classically entangled light

Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger-Horne-Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.

Astigmatic hybrid SU(2) vector vortex beams: towards versatile structures in longitudinally variant polarized optics

Structured light with more controllable degrees-of-freedom (DoFs) is an exciting topic with versatile applications. In contrast to conventional vector vortex beams (VVBs) with two DoFs of orbital angular momentum (OAM) and polarization, a hybrid ray-wave structure was recently proposed [Optica 7(7), 820-831 (2020)], which simultaneously manifests multiple DoFs such as ray trajectory, coherent state phase, trajectory combination, besides OAM and polarization. Here we further generalize this exotic structure as the astigmatic hybrid VVB by hatching a new DoF of astigmatic degree. Importantly, the transverse topology varies with propagation, e.g. a linearly distributed hybrid trajectory pattern can topologically evolve to a circularly polygonal star shape, where the number of singularity changes from zero to multiple in a single beam. The propagation-dependent evolution can be easily controlled by the astigmatic degree, including as a vector vortex state such that different astigmatic trajectories have different polarizations. We experimentally generate such beams from a simple laser with a special astigmatic conversion by combined spherical and cylindrical lenses, and the results agree well with our theoretical simulation. With our new structured light, the propagation-multiplexing multi-DoF patterns can be controlled in a single beam, which can largely extend related applications such as high-dimensional large-capacity optical communication, laser machining, and particle trapping.

Digitally tailoring arbitrary structured light of generalized ray-wave duality

Structured lights, particularly those with tunable and controllable geometries, are highly topical due to a myriad of their applications from imaging to communications. Ray-wave duality (RWD) is an exotic physical effect in structured light that the behavior of light can be described by both the geometric ray-like trajectory and a coherent wave-packet, thus providing versatile degrees of freedom (DoFs) to tailor more general structures. However, the generation of RWD geometric modes requires a solid-state laser cavity with strict mechanical control to fulfill the ray oscillation condition, which limits the flexiblility of applications. Here we overcome this confinement to generate on-demand RWD geometric modes by digital holographic method in free space without a cavity. We put forward a theory of generalized ray-wave duality, describing all previous geometric modes as well as new classes of RWD geometric modes that cannot be generated from laser cavities, which are verified by our free-of-cavity creation method. Our work not only breaks the conventional cavity limit on RWD but also enriches the family of geometric modes. More importantly, it offers a new way of digitally tailoring RWD geometric modes on-demand, replacing the prior mechanical control, and opening up new possibilities for applications of ray-wave structured light.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.