Spontaneous Generation of Magnetically-Active Optical Vortices in Topological Media

Vortices, swirling textures with singularities, have been observed in various physical entities. In condensed matter, the emergence of the vortices originates from exotic physical phenomena, such as Bose-Einstein condensation and magnetic flux quantization, that provides quasi-particle nature to the textures. The optical vortex (OV) is an optical analogy to the vortices in other physical entities, exhibiting zero-intensity point with spiral phase distribution in the electromagnetic field. OVs support the orbital angular momentum of light, which provides an extra degree of freedom in fundamental studies and applications, such as optical manipulation, forbidden electronic transition, and classical/quantum information processing. However, the generation of OVs has relied on structural singularities, such as spiral phase plates and metasurfaces, rather than critical phenomena, which prevents the OVs from possessing quasiparticle-like behavior, such as dynamic and interactive characteristics.<br/>In this study, we propose and demonstrate the spontaneous generation of real-space optical vortex and anti-vortex and their active control using an external magnetic field based on a gradient-thickness optical cavity (GTOC) [1]. The GTOC consists of a magneto-optic Ni layer, between two SiO₂ layers, on top of an Al mirror. We found singular solutions in the calculated optical reflection of GTOC depending on the Ni layer thickness (<i>h</i>_Ni) in the generalized parameter space of top and bottom SiO₂ layer thicknesses (<i>h</i>₁, <i>h</i>₂), which correspond to the OVs with winding number of <i>w</i> = ±1. Regarding to the emergence of the OVs, topological phase of given system can be classified as trivial (<i>h</i>_Ni &lt; <i>h</i>_c1 and <i>h</i>_Ni &gt; <i>h</i>_c2) and non-trivial phase (<i>h</i>_c1 &lt; <i>h</i>_Ni &lt; <i>h</i>_c2), where <i>h</i>_c1 = 6.34 nm and <i>h</i>_c2 = 13.15 nm correspond to the critical points.<br/>We experimentally realized the topological phases of GTOC in an actual media by the bijective projection of the generalized parameter space (<i>h</i>₁, <i>h</i>₂) into real space (<i>x</i>, <i>y</i>). The thickness changes of the top and bottom SiO₂ layers are achieved by non-uniform sputtering in the order of tens of nanometer variation in centimeter-scale distances. We fabricated GTOC samples at trivial (<i>h</i>_Ni = 5, 15 nm) and non-trivial (<i>h</i>_Ni = 10 nm) phases and characterized them using confocal reflectance scanning and off-axis holography. For the non-trivial phase, the OVs are observed in the reflection distribution as singular minima and phase singularities. For the trivial phases, weak single minimum and continuous phase distributions are observed.<br/>The most striking point of our topological media is the magnetic field activity. The magneto-optic effect applies an effective change to the optical thickness of the Ni layer, which can perturb the topological phase of GTOC. Under the external magnetic field (<i>B</i>), we observed magneto-optically-driven vortex dynamics, which induce topology- and polarization-dependent movement of the OVs. From <i>B</i> = -0.5 to +0.5 T, the displacements showed (Δx, Δy) = (0.649 mm, -0.344 mm) and (-0.385 mm, 0.010 mm) for the optical vortex (<i>w</i> = +1) and antivortex (w = -1), respectively, under the right circularly polarized incidence. The displacement directions were reversed when the incidence polarization changed into left circular. Finally, we demonstrated the magnetic-field-induced generation of the optical vortex-antivortex pair at the critical point (<i>h</i>_Ni ~ <i>h</i>_c2) of the topological phase. This is the first observation of field-induced topological phase transition in photonic media. We believe that our findings will pave a way to study topological photonic interactions and inspire the exploration of quasiparticle-like nature in various topological photonic textures, such as toroidal vortices, polarization/vortex knots, and optical skyrmions.<br/><br/>[1] Kim, D., et al., Spontaneous generation and active manipulation of real-space optical vortex. arXiv:2202.02335 (2022). (Accepted in <i>Nature</i>)