Abstract 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. 

/pdf/towards-higher-dimensional-structured-light-1aqzgjjk.pdf

Towards higher-dimensional structured light

Controlling the various degrees‐of‐freedom (DoFs) of structured light at both quantum and classical levels is of paramount importance in optics. It is a conventional paradigm to treat diverse DoFs separately in light shaping. While, the more general case of nonseparable states of light, in which two or more DoFs are coupled in a nonseparable way, has become topical recently. Importantly, classical nonseparable states of light are mathematically analogue to quantum entangled states. Such similarity has hatched attractive studies in structured light, for example, the spin‐orbit coupling in vector beams. However, nonseparable classical states of light are still treated in a fragmented fashion, while its forms are not limited by vector beams and its potential is certainly not fully exploited. For instance, exotic space‐time coupled pulses open nontrivial light shaping toward ultrafast time scales, and ray‐wave geometric beams provide new dimensions in optical manipulations. Here, a bird's eye view on the rapidly growing but incoherent body of work on general nonseparable states involving various DoFs of light is provided and a unified framework for their classification and tailoring, providing a perspective on new opportunities for both fundamental science and applications, is introduced.

Nonseparable States of Light: From Quantum to Classical

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.

/pdf/creation-and-control-of-high-dimensional-multi-partite-2xikfbeunn.pdf

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

Structured light recently highlighted the higher-dimensional control with many tailored degrees of freedom (DoFs) such as amplitude, wavelength, polarization, and orbital angular momentum (OAM), spurring the extension of fundamental science and advanced applications, especially as the novel information carrier to meet the requirement of everlastingly increasing communication bandwidth and security. In addition to the basic DoFs in light, there are also several complex DoFs hidden in spin–orbital coupled vector beams, ray-wave geometric modes, spatiotemporal vortex rings, etc., extending the structured light manipulation. In this Review, we summarize a systematic technical roadmap on how to extend multiple DoFs step-by-step beyond the conventional OAM beams, creating new forms of ultra-DoF structured light, and present a tutorial on how to exploit multiple DoFs of light as advanced information carriers, especially with the recent assistance of artificial intelligence or deep learning method, enhancing the capacity, security, and dimension for the next-generation information technologies. 

https://pubs.acs.org/doi/pdf/10.1021/acsphotonics.2c01640

Ultra-Degree-of-Freedom Structured Light for Ultracapacity Information Carriers

/pdf/towards-higher-dimensional-structured-light-3j9p08qm.pdf

Structured-light lasers are highly topical due to not only their ability to tailor customized distribution of intensity, phase, orbital angular momentum (OAM), and other optical properties, but also the compact and simple at-the-source generation scheme. Here we propose a form of structured-light laser, intracavity mode convertor laser, with the ability to generate two-dimensional (2D) tunable high-order Hermite-Gaussian (HG) modes with a large indice range (up to 15). The mode convertor constituted by two cylindrical lenses is always used for external OAM conversion, but here we show that it can be inserted into a laser cavity as an intracavity element for symmetry-breaking control, which we also demonstrate with a complete matrix optics theory. The generated 2D HG modes can also be converted into Laguerre-Gaussian (LG) vortex beams with both tunable OAM and radial momentum. Moreover, we also show the ability to directly generate vortex beam from our laser cavity. Our approach meets the urgent necessity for a practical laser device for more versatile light, providing more alternative parametric space for structure control and fostering extended applications.

/pdf/index-tunable-structured-light-beams-from-a-laser-with-an-36o5fuzv2g.pdf

Index-Tunable Structured-Light Beams from a Laser with an Intracavity Astigmatic Mode Converter

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.

Advances of Yb:CALGO Laser Crystals

We present a novel scheme of structured light laser with an astigmatic mode converter (AMC) as intracavity element, first enabling the generation of Hermite-Gaussian (HG) modes with fully controlled two-dimensional (2D) indices (m,n) and vortex beams carrying orbital angular momentum (OAM) directly from cavity. The 2D tunability was realized by controlling the off-axis displacements of both pump and intracavity AMC. The output HGm,n beam could be externally converted into OAM beam with 2D tunable radial and azimuthal indices (p,l). With the certain parameter control, vortex beam carrying OAM also could be directly generated from the cavity. Our setup provides a compact and concise structured light source. It has great potential in extending various applications of optical tweezers, communications, and nonlinearity.

Two-dimensional-controlled high-order modes and vortex beams from an intracavity mode converter laser

The astigmatic mode converter is exploited as an intracavity element to establish a structured-light laser scheme, realizing free control of two-dimensional indices of laser modes and large-range tunability of radial- and orbital-angular-momenta (p-to-4ℏ and l-to-±15ℏ).

Intracavity-Mode-Conversion Structured-Light Laser

Structured light with customized complex topological pattern inspires diverse classical and quantum investigations underpinned by accurate detection techniques. However, the current detection schemes are limited to vortex beam with simple phase singularity. The precise recognition of general structured light with multiple singularities remains elusive. Here, we report a 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 captured via a camera, thus unleashing intuitive information of twisted photons. The DL toolbox can also acquire phases of Laguerre-Gaussian (LG) modes with single singularity and other general phase objects likewise. Leveraging 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 vortex beam communications, laser mode analysis, microscopy, Bose-Einstein condensates characterization, etc.

Deep-learning-based recognition of multi-singularity structured light

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