Topological quasiparticles of light: Optical skyrmions and beyond

Abstract

Skyrmions are topologically stable quasiparticles that have been predicted and demonstrated in quantum fields, solid-state physics, and magnetic materials, but only recently observed in electromagnetic fields, triggering fast expanding research across different spectral ranges and applications. Here we review the recent advances in optical skyrmions within a unified framework. Starting from fundamental theories, including classification of skyrmionic states, we describe generation and topological control of different kinds of optical skyrmions in structured and time-dependent optical fields. We further highlight generalized classes of optical topological quasiparticles beyond skyrmions and outline the emerging applications, future trends, and open challenges. A complex vectorial field structure of optical quasiparticles with versatile topological characteristics emerges as an important feature in modern spin-optics, imaging and metrology, optical forces, structured light and topological and quantum technologies.

Topological transformation and free-space transport of photonic hopfions

“…in which i; j; k ¼ fx; y; zg, ε is the Levi-Civita tensor, and A is the vector potential satisfying ∇ × A ¼ F and is closely related to the skyrmion number (p and q correspond to the skyrmion numbers of the skyrmions in the x-z and x-y cross sections of a hopfion 43 ), which can be defined by the product of topological numbers of polarity Q P and vorticity Q V of the skyrmion spin texture. 13,49 The polarity Q P ¼ 1 2 ½cos βðrÞ r¼a r¼0 ¼ AE1 is defined by the vector direction down (up) at the center r ¼ 0 and up (down) at the skyrmion boundary r → r σ for Q P ¼ 1 (Q P ¼ −1), and the vorticity Q V ¼ 1 2π ½αðϕÞ ϕ¼2π ϕ¼0 can be an arbitrary integer that controls the azimuthal distribution of the transverse vector field components. For a fixed vorticity, an initial phase θ should be added to distinguish the helicity to completely decide the transverse distribution of the vector field, i.e., αðϕÞ ¼ mϕ þ θ, which is termed helicity.…”

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

“…Further special cases of this model can derive the focused single-cycle pulses, including both linearly polarized “flying pancakes”, and pulses of toroidal symmetry termed “flying doughnuts”, as shown in Figure a. Moreover, the DoF of polarization can be coupled, then extended to novel spatiotemporal vector pulses with ultrashort vector pulses based on optical skyrmions, − and topological quasiparticles , have been reported, as shown in Figure b. Recently, it was proposed that the focused single-cycle pulses can be characterized by the classically space-frequency entangled state, and the degree of nonseparability can be quantified by quantum-like measurement methods.…”

Nondiffractive three-dimensional polarization features of optical vortex beams

“…The interplay between spin and orbital angular momenta of light beams results in complex polarization textures of light fields with optical properties important in imaging, metrology, and quantum technologies. 1 For example, polarization variations appear in the structure of two-dimensional photonic spin-skyrmions at lengthscales much smaller than the wavelength of light because, in contrast to the field and intensity variations, the polarization structure is not influenced by the diffraction of electromagnetic waves. 2 Such polarization features often appear due to the spin-orbit interactions involving vector vortex beams and, in the case of evanescent fields, may be topologically protected by the optical spin-Hall effect.…”