Digitally tailoring arbitrary structured light of generalized ray-wave duality

Generating Multi-Depth 3D Holograms Using a Fully Convolutional Neural Network

Efficiently generating 3D holograms is one of the most challenging research topics in the field of holography. This work introduces a method for generating multi-depth phase-only holograms using a fully convolutional neural network (FCN). The method primarily involves a forward-backward-diffraction framework to compute multi-depth diffraction fields, along with a layer-by-layer replacement method (L2RM) to handle occlusion relationships. The diffraction fields computed by the former are fed into the carefully designed FCN, which leverages its powerful non-linear fitting capability to generate multi-depth holograms of 3D scenes. The latter can smooth the boundaries of different layers in scene reconstruction by complementing information of occluded objects, thus enhancing the reconstruction quality of holograms. The proposed method can generate a multi-depth 3D hologram with a PSNR of 31.8 dB in just 90 ms for a resolution of 2160 × 3840 on the NVIDIA Tesla A100 40G tensor core GPU. Additionally, numerical and experimental results indicate that the generated holograms accurately reconstruct clear 3D scenes with correct occlusion relationships and provide excellent depth focusing.

High-capacity and multi-dimensional orbital angular momentum multiplexing holography

Optical holography has been investigated for enhancing information capacity and encryption. Here, the multi-vortex geometric orbital angular momentum (MVG-OAM) multiplexing holography is proposed and experimentally implemented, which encodes information into MVG beams with different central OAM, sub-beam OAM, and coherent-state phase. The orthogonality of the above three parameters are analyzed, respectively, which point out the feasibility of using them for holographic multiplexing. A three-dimensional multiplexing holography is realized by combining these three parameters, which offers potential applications for information storage, optical encryption, and display.

Super-resolution orbital angular momentum holography

Computer-generated holograms are crucial for a wide range of applications such as 3D displays, information encryption, data storage, and opto-electronic computing. Orbital angular momentum (OAM), as a new degree of freedom with infinite orthogonal states, has been employed to expand the hologram bandwidth. However, in order to reduce strong multiplexing crosstalk, OAM holography suffers from a fundamental sampling criterion that the image sampling distance should be no less than the diameter of largest addressable OAM mode, which severely hinders the increase in resolution and capacity. Here we establish a comprehensive model on multiplexing crosstalk in OAM holography, propose a pseudo incoherent approach that is almost crosstalk-free, and demonstrate an analogous coherent solution by temporal multiplexing, which dramatically eliminates the crosstalk and largely relaxes the constraint upon sampling condition of OAM holography, exhibiting a remarkable resolution enhancement by several times, far beyond the conventional resolution limit of OAM holography, as well as a large scaling of OAM multiplexing capacity at fixed resolution. Our method enables OAM-multiplexed holographic reconstruction with high quality, high resolution, and high capacity, offering an efficient and practical route towards the future high-performance holographic systems.

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.

Holographic Tailoring of Structured Light Field with Digital Device

Structured light fields have attracted much attention due to rich spatial degrees of freedom. The tailoring of an arbitrary structured light field on demand is the precondition for the application of structured light. Therefore, the computer holography method used to reconstruct a coherent light field wavefront has been naturally applied for generating structured light. In this work, we comprehensively demonstrate the principles and procedures of pure-phase computer-generated holography (PP-CGH) and binary-amplitude computer-generated holography (BA-CGH) methods for tailoring structured light, realized by two digitally programmable devices: liquid-crystal spatial light modulators (Lc-SLM) and digital micromirror devices (DMD), respectively. Moreover, we first compare the two approaches in detail and clarify the recipe to obtain a high tailoring accuracy and efficiency, which will help researchers to better understand and utilize the holographic tailoring of structured optical fields.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

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.

Multipartite classically entangled scalar beams

Classically entangled light is used to refer to a class of structured beams with space-polarization, polarization-time, and space-time non-separable states akin to entangled states, which enable novel quantum-analog methods and applications in structured light. Here, we argue that classical entanglement is also available for pure scalar beams with multiple non-separable spatial degrees of freedom (DoFs). We theoretically and experimentally demonstrate a class of scalar ray-wave structured light with multiple controllable local DoFs to emulate multipartite entangled states, including the Greenberger-Horne-Zeilinger states. Our work unveils a rich parameter space for high-dimensional and multi-DoF control of structured light to extend applications in classical-quantum regimes.

Structural stability of spiral vortex beams to sector perturbations

Conditions of breaking down the structural stability of a spiral vortex beam subject to sector perturbations were considered. Employing methods of computer simulation and processing experimental results, we have shown that the spiral vortex beam has a caustic surface, the intersection of which sharply changes a shape of the Poynting vector streamlines and critical points of the spiral beam. Nevertheless, the beam propagation (scaling and rotation) does not change the perturbed streamline's shape and phase pattern. We also revealed that strong beam perturbations can cause the conversion of the circulation direction of streamlines in the perturbation region, which entails the appearance of a network of optical vortices with negative topological charges. However, the beam's orbital angular momentum remains unchanging, despite increasing the information entropy (growing a number of vortex modes), so that the perturbed beam keeps new stable states.

Ray-wave duality of electromagnetic fields: a Feynman path integral approach to classical vectorial imaging

We consider how vectorial aspects (polarization) of light propagation can be implemented and their origin within a Feynman path integral approach. A key part of this scheme is in generalizing the standard optical path length integral from a scalar to a matrix quantity. Reparametrization invariance along the rays allows a covariant formulation where propagation can take place along a general curve. A general gradient index background is used to demonstrate the scheme. This affords a description of classical imaging optics when the polarization aspects may be varying rapidly and cannot be neglected.

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.