Topological transformation and free-space transport of photonic hopfions

Yijie Shen; Bingshi Yu; Haijun Wu; Chunyu Li; Zhihan Zhu; Anatoly V. Zayats

doi:10.1117/1.AP.5.1.015001

[1] N. Manton, P. Sutcliffe. Topological Solitons(2004).

[2] S. S. Parkin, M. Hayashi, L. Thomas. Magnetic domain-wall racetrack memory. Science, 320, 190-194(2008).

[3] X. Wang et al. Domain wall propagation through spin wave emission. Phys. Rev. Lett., 109, 167209(2012).

[4] J. Han et al. Mutual control of coherent spin waves and magnetic domain walls in a magnonic device. Science, 366, 1121-1125(2019).

[5] S. Tsesses et al. Optical skyrmion lattice in evanescent electromagnetic fields. Science, 361, 993-996(2018).

[6] L. Du et al. Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum. Nat. Phys., 15, 650-654(2019).

[7] T. J. Davis et al. Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution. Science, 368, eaba6415(2020).

[8] Y. Shen et al. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun., 12, 5891(2021).

[9] H. Jani et al. Antiferromagnetic half-skyrmions and bimerons at room temperature. Nature, 590, 74-79(2021).

[10] Y. Dai et al. Plasmonic topological quasiparticle on the nanometre and femtosecond scales. Nature, 588, 616-619(2020).

[11] Y. Shen. Topological bimeronic beams. Opt. Lett., 46, 3737-3740(2021).

[12] Y. Shen, E. C. Martínez, C. Rosales-Guzmán. Generation of optical skyrmions with tunable topological textures. ACS Photonics, 9, 296-303(2022).

[13] B. Göbel, I. Mertig, O. A. Tretiakov. Beyond skyrmions: review and perspectives of alternative magnetic quasiparticles. Phys. Rep., 895, 1-28(2021).

[14] A. Fert, N. Reyren, V. Cros. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater., 2, 17031(2017).

[15] B. A. Bernevig, C. Felser, H. Beidenkopf. Progress and prospects in magnetic topological materials. Nature, 603, 41-51(2022).

[16] P. J. Ackerman, I. I. Smalyukh. Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids. Nat. Mater., 16, 426-432(2017).

[17] J. Tang et al. Magnetic skyrmion bundles and their current-driven dynamics. Nat. Nanotechnol., 16, 1086-1091(2021).

[18] F. Zheng et al. Magnetic skyrmion braids. Nat. Commun., 12, 5316(2021).

[19] L. Faddeev. Some comments on the many-dimensional solitons. Lett. Math. Phys., 1, 289-293(1976).

[20] T. H. R. Skyrme. A non-linear field theory. Proc. R. Soc. A, 260, 127-138(1961).

[21] T. H. R. Skyrme. A unified field theory of mesons and baryons. Nucl. Phys., 31, 556-569(1962).

[22] J. Hietarinta, P. Salo. Faddeev-Hopf knots: dynamics of linked un-knots. Phys. Lett. B, 451, 60-67(1999).

[23] P. Sutcliffe. Knots in the Skyrme–Faddeev model. Proc. R. Soc. A: Math. Phys. Eng. Sci., 463, 3001-3020(2007).

[24] D. W. Lyons. An elementary introduction to the Hopf fibration. Math. Mag., 76, 87-98(2003).

[25] J. Whitehead. An expression of Hopf’s invariant as an integral. Proc. Natl. Acad. Sci. U.S.A., 33, 117-123(1947).

[26] L. Faddeev, A. J. Niemi. Stable knot-like structures in classical field theory. Nature, 387, 58-61(1997).

[27] J.-S. B. Tai et al. Static Hopf solitons and knotted emergent fields in solid-state noncentrosymmetric magnetic nanostructures. Phys. Rev. Lett., 121, 187201(2018).

[28] X. Wang, A. Qaiumzadeh, A. Brataas. Current-driven dynamics of magnetic hopfions. Phys. Rev. Lett., 123, 147203(2019).

[29] Y. Liu et al. Three-dimensional dynamics of a magnetic hopfion driven by spin transfer torque. Phys. Rev. Lett., 124, 127204(2020).

[30] I. Luk’yanchuk et al. Hopfions emerge in ferroelectrics. Nat. Commun., 11, 2433(2020).

[31] B. Göbel et al. Topological hall signatures of magnetic hopfions. Phys. Rev. Res., 2, 013315(2020).

[32] N. Kent et al. Creation and observation of hopfions in magnetic multilayer systems. Nat. Commun., 12, 1562(2021).

[33] D. S. Hall et al. Tying quantum knots. Nat. Phys., 12, 478-483(2016).

[34] W. Lee et al. Synthetic electromagnetic knot in a three-dimensional skyrmion. Sci. Adv., 4, eaao3820(2018).

[35] E. Babaev. Dual neutral variables and knot solitons in triplet superconductors. Phys. Rev. Lett., 88, 177002(2002).

[36] Y. Kawaguchi, M. Nitta, M. Ueda. Knots in a spinor Bose-Einstein condensate. Phys. Rev. Lett., 100, 180403(2008).

[37] R. Bisset et al. Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates. Phys. Rev. A, 92, 063611(2015).

[38] S. Zou et al. Formation of vortex rings and hopfions in trapped Bose–Einstein condensates. Phys. Fluids, 33, 027105(2021).

[39] M. Cruz et al. A cosmic microwave background feature consistent with a cosmic texture. Science, 318, 1612-1614(2007).

[40] A. Thompson et al. Classification of electromagnetic and gravitational hopfions by algebraic type. J. Phys. A: Math. Theor., 48, 205202(2015).

[41] D. Kleckner, W. T. Irvine. Creation and dynamics of knotted vortices. Nat. Phys., 9, 253-258(2013).

[42] P. J. Ackerman, I. I. Smalyukh. Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions. Phys. Rev. X, 7, 011006(2017).

[43] P. J. Ackerman, J. Van De Lagemaat, I. I. Smalyukh. Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals. Nat. Commun., 6, 6012(2015).

[44] D. Sugic et al. Particle-like topologies in light. Nat. Commun., 12, 6785(2021).

[45] M. R. Dennis et al. Isolated optical vortex knots. Nat. Phys., 6, 118-121(2010).

[46] Y. Intaravanne et al. Color-selective three-dimensional polarization structures. Light Sci. Appl., 11, 302(2022).

[47] C. Wan et al. Scalar optical hopfions. eLight, 2, 22(2022).

[48] M. Kobayashi, M. Nitta. Torus knots as hopfions. Phys. Lett. B, 728, 314-318(2014).

[49] Y. Shen et al. Topological quasiparticles of light: optical skyrmions and beyond(2022).

[50] Y. Shen. Rays, waves, SU(2) symmetry and geometry: toolkits for structured light. J. Opt., 23, 124004(2021).

[51] Y. Shen, C. Rosales-Guzmán. Nonseparable states of light: from quantum to classical. Laser Photonics Rev., 16, 2100533(2022).

[52] C. He, Y. Shen, A. Forbes. Towards higher-dimensional structured light. Light Sci. Appl., 11, 205(2022).

[53] S. Gao et al. Paraxial skyrmionic beams. Phys. Rev. A, 102, 053513(2020).

[54] R.-Y. Zhong et al. Gouy-phase-mediated propagation variations and revivals of transverse structure in vectorially structured light. Phys. Rev. A, 103, 053520(2021).

[55] G. Poy et al. Interaction and co-assembly of optical and topological solitons. Nat. Photonics, 16, 454-461(2022).

[56] J.-S. B. Tai, I. I. Smalyukh. Three-dimensional crystals of adaptive knots. Science, 365, 1449-1453(2019).