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

In recent time, the optical-analogous skyrmions, topological quasiparticles with sophisticated vectorial structures, have received an increasing amount of interest. Here we propose theortically and experimentally a generalized family of these, the tunable optical skyrmion, unveiling a new mechanism to transform between various skyrmionic topologies, including N\'eel-, Bloch-, and antiskyrmion types, via simple parametric tuning. In addition, Poincar\'e-like geometric representation is proposed to visualize the topological evolution of tunable skyrmions, which we termed Skyrme-Poincar\'e sphere, akin to the spin-orbit representation of complex vector modes. To generate experimentally the tunable optical skyrmions we implemented a digital hologram system based on a spatial light modulator, showing great agreement with our theoretical prediction. 

Generation of Optical Skyrmions with Tunable Topological Textures

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

"Space-time"(ST) wave packets constitute a broad class of pulsed optical fields that are rigidly transported in linear media without diffraction or dispersion, and are therefore propagation-invariant in absence of optical nonlinearities or waveguiding structures. Such wave packets exhibit unique characteristics, such as controllable group velocities in free space and exotic refractive phenomena. At the root of these behaviors is a fundamental feature underpinning ST wave packets: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatio-temporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, deviation from this particular spatio-temporal structure yields novel behaviors that depart from propagation invariance in a precise manner, such as acceleration with an arbitrary axial distribution of the group velocity, tunable dispersion profiles, and Talbot effects in space-time. Although the basic concept of ST wave packets has been known since the 1980's, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatio-temporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics.

Space-time wave packets


 Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultra-fast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell’s equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird’s eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges.

https://iopscience.iop.org/article/10.1088/2040-8986/ace4dc/pdf

Roadmap on spatiotemporal light fields

Topological complex transient electromagnetic fields give access to nontrivial light-matter interactions and provide additional degrees of freedom for information transfer. An important example of such electromagnetic excitations are space-time non-separable single-cycle pulses of toroidal topology, the exact solutions of Maxwell’s equations described by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce an extended family of electromagnetic excitation, the supertoroidal electromagnetic pulses, in which the Hellwarth-Nouchi pulse is just the simplest member. The supertoroidal pulses exhibit skyrmionic structure of the electromagnetic fields, multiple singularities in the Poynting vector maps and fractal-like distributions of energy backflow. They are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics. Topology in electromagnetic fields can lead to a range of intriguing and unexpected phenomena. Here the authors describe a family of supertoroidal light pulses that exhibit skyrmionic topological structure flying in free space.

/pdf/supertoroidal-light-pulses-as-electromagnetic-skyrmions-4n6anjak67.pdf

Supertoroidal light pulses as electromagnetic skyrmions propagating in free space.

We report the generation of space-time non-separable toroidal pulses of complex topological structure. Such pulses, a formation of singularities propagating in free space, are ideal probes for toroidal and anapole modes in matter.

Generation of Topological Space-Time Non-Separable Light Pulses

Topological structures of electromagnetic fields could give access to nontrivial light-matter interactions and additional degrees of freedom for information and energy transfer. A characteristic example of such electromagnetic excitations are space-time non-separable single-cycle pulses, the exact solutions of Maxwell equation of toroidal topology predicted by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce a new family of electromagnetic excitation of toroidal topology with increasing complexity in which the Hellwarth-Nouchi pulse is just the simplest member. The electromagnetic excitations of the new family can be parametrised by a single real number and exhibit skyrmionic structures of various orders. They feature multiple singularities in the electromagnetic and Poynting vector fields are accompanied by the fractal-like distributions of energy backflow. The generalized family of toroidal electromagnetic excitation with salient topologies are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics.

/pdf/supertoroidal-light-pulses-propagating-electromagnetic-pde9wrznzc.pdf

Supertoroidal light pulses: Propagating electromagnetic skyrmions in free space

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Supertoroidal light pulses as electromagnetic skyrmions propagating in free space.

Generation of Topological Space-Time Non-Separable Light Pulses

Supertoroidal light pulses: Propagating electromagnetic skyrmions in free space