Nikolay I. Zheludev

Toroidal electromagnetic pulses are non-transverse free-space wave packets with coupled spatial, temporal, and polarization structure. We show that balanced superpositions of transverse-electric (TE) and transverse-magnetic (TM) toroidal pulses generate compact, propagating regions of nonzero E · B in the real physical fields, even though each constituent pulse has E · B = 0. The sign and symmetry of this localized E · B distribution are controlled by the intermodal phase between the TE and TM components. Since E · B enters as the source term in axion electrodynamics, we also calculate the corresponding classical pseudoscalar response in the weak-coupling, negligible-backreaction limit. The results identify toroidal pulses as an analytically tractable platform for shaping propagating electromagnetic pseudoscalar structures; they do not constitute a prediction of axion-particle generation or photon–axion conversion.

Label-free, far-field super-resolution imaging can be achieved by exploiting prior knowledge about an object, such as sparsity, or by using information accumulated from similar object classes. Here we show that simply knowing that an object is confined within a limited spatial extent is sufficient to surpass the Abbe–Rayleigh diffraction limit: for a fixed photon budget, smaller objects can be resolved with higher spatial resolution. To demonstrate this, we develop a limited-size object microscopy (LSOM) technique. The method relies on representing the coherently scattered field from the object within a limited field of view with Slepian–Pollak functions, a family of prolate spheroidal wavefunctions. The coefficients of such functions can then be recovered from diffraction-limited measurements. We experimentally demonstrate down to λ /8 resolution (where λ is the wavelength) for subwavelength structures and analyse the performance limits of the method using information theory. The technique requires no assumptions about the object’s shape or complexity and does not rely on labels, making it broadly applicable to the study of isolated nano-objects.

Superoscillation (SO) refers to the phenomenon in which a wavefield locally oscillates at a rate exceeding its highest spatial or temporal Fourier component. SO has enabled light to be focused into arbitrarily small hotspots, forming the basis of superresolution imaging and metrology far beyond the Abbe-Rayleigh diffraction limit. Here we show that spatial and temporal superoscillations can occur simultaneously at the same point in space-time, a phenomenon we term space-time superoscillation (STSO). We demonstrate STSOs in a band-limited version of supertoroidal light pulses, a recently introduced family of space–time nonseparable finite-energy solutions of Maxwell’s equations. Our results reveal a new regime of extreme spatiotemporal field structuring, with implications for ultrafast metrology, light–matter interactions, and deep-subwavelength control of electromagnetic waves.

It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, a significant advantage in measurement precision can be gained from exploiting phase singularities in a topologically structured incident light field. Here, we demonstrate that this advantage, derived from the dependence of scattered intensity profiles on strong local (subwavelength-scale) intensity and phase variations in the incident field, can be extended towards imaging applications: analysis of scattering patterns from arbitrary binary gratings under superoscillatory illumination successfully resolves feature sizes down to ∼λ/6.6 in single-shot measurements (a factor of 1.3× smaller than is achieved with plane wave illumination), and ∼λ/10.5 in positionally-displaced few-shot measurements (which yields no improvement in the plane wave case). Interestingly, there are circumstances in which more complex objects are better resolved than simple structures, because interference effects increase the information content of their scattering patterns.

Toroidal pulses, also known as Focused or Flying Doughnuts (FDs), are few-cycle pulses of doughnut-like topology that exhibit space-polarization and space-time couplings resulting in skyrmionic field configurations and regions of energy backflow, while their light-matter interactions involve toroidal and non-radiating (anapole) excitations. In this work, we experimentally generate optical toroidal pulses and analyze their space-polarization and space-time couplings using tomographic techniques. Using tandem projective measurements in the space and polarization degrees of freedom, we characterize the spatially varying polarization of the pulses, whereas space-time nonspeparability is characterized by measuring the angular divergence of the pulse monochromatic components. Space-time and space-polarization nonseparabilty are quantified by concurrence and fidelity (with respect to the ideal pulses). Experimentally generated pulses show high fidelity values of 0.88 and 0.72 for their space-polarization and space-time couplings, respectively. The reported results will be of interest to the fundamental study of toroidal pulses and spatiotemporally structured light more broadly, enabling applications in telecommunications, spectroscopy, metrology, and imaging.

Unprecedented atomic‐scale measurement resolution has recently been demonstrated in single‐shot optical localization measurements based on deep‐learning analyses of diffraction patterns of topologically structured light scattered from objects. Here, we show that variations in the diffraction patterns caused by positional changes of an object depend upon the spatial derivatives of the amplitude and phase of the incident field, most strongly around phase singularities. Despite lower intensity near the singularity, an orders‐of‐magnitude increase in Fisher information contained in the diffraction patterns can be achieved when a nano‐object is illuminated by light containing phase singularities, rather than a plane wave. Our work provides a fundamental explanation and motivation for singularity‐based metrology with deeply subwavelength precision.

We show that the continuous time crystal state can arise in an ensemble of linear oscillators from nonconservative coupling via optical radiation pressure forces. This new mechanism comprehensively explains observations of the time crystal state in an array of nanowires illuminated with light [T. Liu et al., Nat. Phys. 19, 986 (2023).]. Being fundamentally different from regimes of nonlinear synchronization, it has relevance to a wide range of interacting many-body systems, including in the realms of chemistry, biology, weather, and nanoscale matter.

Toroidal electromagnetic pulses have been recently reported as nontransverse, space-time nonseparable topological excitations of free space. However, their propagation dynamics and topological configurations have not been comprehensively experimentally characterized. In addition, the existing generators were limited in optical and terahertz domains; however, the feasibility and significance of generating such pulses at microwave frequencies have been overlooked. Here, we report that microwave toroidal pulses can be launched by a transient finite-aperture broadband horn antenna emitter, as an electromagnetic counterpart of “air vortex cannon.” Applying this effective generator, we experimentally map the toroidal pulses' topological skyrmionic textures in free space and demonstrate their resilient propagation dynamics, i.e., how that, during propagation, the pulses evolve toward stronger space-time nonseparability and closer proximity to the canonical Hellwarth–Nouchi toroidal pulses. Our work offers a practical opportunity for using topologically robust toroidal pulses as information carriers in high-capacity telecom, cell phone technology, remote sensing, and global positioning, especially where microwave frequencies are predominant.

Supertoroidal light pulses, as space-time nonseparable electromagnetic waves, exhibit unique topological properties including skyrmionic configurations, fractal-like singularities, and energy backflow in free space, which however do not survive upon propagation. Here, we introduce the non-diffracting supertoroidal pulses (NDSTPs) with propagation-robust skyrmionic and vortex field configurations that persists over arbitrary propagation distances. Intriguingly, the field structure of NDSTPs has a similarity with the von Kármán vortex street, a pattern of swirling vortices in fluid and gas dynamics with staggered singularities that can stably propagate forward. NDSTPs will be of interest as directed channels for information and energy transfer applications.