Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Changxu Liu, Shuang Zhang, Stefan A. Maier, and Haoran Ren

Phys. Rev. Lett. 129, 267401 – Published 23 December 2022

Abstract

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

Received 8 June 2022
Accepted 7 December 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.267401

Physics Subject Headings (PhySH)

Nanophotonics Skyrmions Topological effects in photonic systems

Disordered systems

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Changxu Liu ^*

Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle Upon Tyne NE1 8ST, United Kingdom and Chair in Hybrid Nanosystems, Nanoinstitute Munich, Faculty of Physics, Ludwig-Maximilians-Universitaet Muenchen, 80539 Muenchen, Germany

Shuang Zhang

Department of Physics, University of Hong Kong, Hong Kong, China and Department of Electrical Engineering, University of Hong Kong, Hong Kong, China

Stefan A. Maier

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia; Chair in Hybrid Nanosystems, Nanoinstitute Munich, Faculty of Physics, Ludwig-Maximilians-Universitaet Muenchen, 80539 Muenchen, Germany; and Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom

Haoran Ren ^†

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

^*changxu.liu@northumbria.ac.uk
^†haoran.ren@monash.edu

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Vol. 129, Iss. 26 — 23 December 2022

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Images

Figure 1
Realization of the Néel-type skyrmion. (a) Artistic view of a vectorial hologram for creating an optical skyrmion that is digitized by 3D vectorial fields in real space. Fluctuations in amplitude and phase can be introduced from the scattering medium. (b) An ideal Néel-type skyrmion ( $N_{sk} = 1$ , $ν = 1$ , $h = 0$ ). (c) The realized quasiparticle composed of vectorial electric field. (d)–(f) A comparison of the electric field in the symmetric axis. (g)–(j) The designed amplitude and phase on the hologram plane, i.e., the bottom plane shown in (a). The amplitude and phase polarized along the $x$ direction are shown in (g) and (h), while the amplitude and phase polarized along the $y$ direction are shown in (i) and (j).
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Figure 2
Realization of different classes of optical skyrmions based on vectorial hologram. The first row demonstrates the ideal textures and the second row shows the realized quasiparticles composed of vectorial electric fields. Five classes are included: (a)–(b) Bloch-type skyrmion ( $N_{sk} = 1$ , $ν = 1$ , and $h = (π / 2)$ ); (c)–(d) Néel-type anti-skyrmion ( $N_{sk} = 1$ , $ν = - 1$ , and $h = 0$ ); (e)–(f) Bloch-type anti-skyrmion ( $N_{sk} = 1$ , $ν = - 1$ , and $h = (π / 2)$ ); (g)–(h) Bloch-type half-skyrmion ( $N_{sk} = \frac{1}{2}$ , $ν = 1$ , and $h = (π / 2)$ ); (i)–(j) Bloch-type quarter-skyrmion ( $N_{sk} = \frac{1}{4}$ , $ν = 1$ , and $h = (π / 2)$ ).
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Figure 3
A demonstration of disorder introduced in amplitude (a)–(e) and phase (f)–(j) on the hologram plane. The amplitude and phase are selected from the central region in Figs. 1 and 1.
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Figure 4
Disorder-induced state transition of a Néel-type skyrmion. (a) The evolution of the skyrmion number $N_{sk}$ as the increment of disorder in phase $δ_{P}$ . $δ_{A}$ is set to 0. The insets show the vectorial electric field textures under different values of $δ_{P}$ . (b) The evolution of the skyrmion number $N_{sk}$ as the increment of disorder in amplitude $δ_{A}$ . $δ_{P}$ is set to 0. The insets show the vectorial electric field textures under different values of $δ_{A}$ . (c) The evolution of the skyrmion number $N_{sk}$ when disorder in phase and amplitude coexists. (d) Demonstration of the textures of vectorial electric field with hybrid disorder.
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Figure 5
The robustness of the optical skyrmions propagating through a random medium. (a) Demonstration of a discrete random medium. (b) The relationship between the absolute value of $N_{sk}$ and the permittivity of the scatters $ϵ_{sca}$ . (c) The vectorial electric field textures when $ϵ_{sca} = 2$ . (d) Demonstration of a continuous random medium. (e) The relationship between the absolute value of $N_{sk}$ and the standard deviation of dielectric function $Δ_{ϵ}$ . (f) The vectorial electric field textures when $Δ_{ϵ} = 0.25$ .
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