Toroidal vortices, also known as vortex rings, are whirling, closed-loop disturbances that form a characteristic ring shape in liquids and gases and propagate in a direction that is perpendicular to the plane of the ring. They are well-studied structures and commonly found in various fluid and gas flow scenarios in nature, for example in the human heart, underwater air bubbles and volcanic eruptions1–3. Here we report the experimental observation of a photonic toroidal vortex as a new solution to Maxwell’s equations, generated by the use of conformal mapping4–7. The resulting light field has a helical phase that twists around a closed loop, leading to an azimuthal local orbital angular momentum density. The preparation of such an intriguing state of light may offer insights for exploring the behaviour of toroidal vortices in other disciplines and find important applications in light–matter interactions, optical manipulation, photonic symmetry and topology, and quantum information8–17.
Conjugated microporous polymers (CMPs)
are promising electrode
materials for electrochemical energy storage, but their poor redox
activity and electric conductivity limit their practical applications.
Herein, CMPs obtained from the Buchwald–Hartwig coupling reaction
using a spirobifluorene bromide core and p-phenylenediamine
linker (SACMPs) are grafted onto the multiwalled carbon nanotube (MWCNT) via one-step in situ polymerization. The
as-prepared composite (MWCNT@SACMP) exhibits a high surface area of
514 m2 g–1, excellent redox activity,
and reasonable conductivity. As expected, MWCNT@SACMP presents a high
specific capacitance of 594 F g–1 at a current density
of 1.0 A g–1 when the content of MWCNTs is around
10 wt %, which is improved by 252% from the 236 F g–1 of SACMP. A symmetric two-electrode supercapacitor assembled with
MWCNT@SACMP shows an efficient specific capacitance of 254 F g–1 and an energy density of 28.53 W h kg–1 at a power density of 900 W kg–1 and can retain
84.38% of its initial capacitance after 6000 cycles. This work thus
presents a promising CMP/MWCNT composite material for supercapacitor
energy storage.
Vortices are whirling disturbances commonly found in nature ranging from tremendously small scales in Bose-Einstein condensates to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a result of this intersection, the wave packet hosts a tilted OAM that provides an additional degree of freedom to the applications that harness the OAM of photons.
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