Abstract
Optical vortices are beams of light that carry orbital angular momentum1, which represents an extra degree of freedom that can be generated and manipulated for photonic applications2,3,4,5,6,7,8. Unlike vortices in other physical entities, the generation of optical vortices requires structural singularities9,10,11,12, but this affects their quasiparticle nature and hampers the possibility of altering their dynamics or making them interacting13,14,15,16,17. Here we report a platform that allows the spontaneous generation and active manipulation of an optical vortex–antivortex pair using an external field. An aluminium/silicon dioxide/nickel/silicon dioxide multilayer structure realizes a gradient-thickness optical cavity, where the magneto-optic effects of the nickel layer affect the transition between a trivial and a non-trivial topological phase. Rather than a structural singularity, the vortex–antivortex pairs present in the light reflected by our device are generated through mathematical singularities in the generalized parameter space of the top and bottom silicon dioxide layers, which can be mapped onto real space and exhibit polarization-dependent and topology-dependent dynamics driven by external magnetic fields. We expect that the field-induced engineering of optical vortices that we report will facilitate the study of topological photonic interactions and inspire further efforts to bestow quasiparticle-like properties to various topological photonic textures such as toroidal vortices, polarization and vortex knots, and optical skyrmions.
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Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Code availability
All codes generated during this study are available upon request from the corresponding authors.
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Acknowledgements
We thank S. Lee, D. Kim, S. Park and H. Oh for discussions. M.-K.S. acknowledges the support of the KAIST Cross-Generation Collaborative Lab project and the National Research Foundation of Korea (NRF) (2020R1A2C2014685 and 2020R1A4A2002828). J.S. acknowledges the support of the NRF (2021R1A2C200868711). D.K. acknowledges the support of the NRF (2015H1A2A1033753 and 2019R1A6A1A10073887). Y.-S.C. acknowledges the support of the NRF (2020R1I1A1A01069219).
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D.K. conceived the idea. A.B. and D.K. designed and fabricated the gradient-thickness optical cavity samples. D.K. and Y.-S.C. built the magneto-optic off-axis holography set-up. D.K. performed the magneto-optic measurements and the theoretical calculations. D.K. and M.-K.S. analysed the data and wrote the manuscript with input from all other authors.
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Extended data figures and tables
Extended Data Fig. 1 Amplitude and phase distribution of the calculated reflection coefficient components (r1 and r2) in the generalized parameter space (h1, h2).
a,b, Plot of the (a) amplitude and (b) phase of the reflection coefficient components r1 (the red curved surface) and r2 (the blue curved surface) near the reflection minima in the generalized parameter space for the GTOCs with hNi = 5, 10, and 15 nm. (Δh1, Δh2) represents the position away from the target reflection minimum in the generalized parameter space. The yellow and green solid curves represent the same amplitude (|r1| = |r2|) and out-of-phase conditions (arg(r1) = arg(−r2)), respectively. c, Projection of the same amplitude (the yellow curve) and out-of-phase (the green curve) conditions onto the generalized parameter space. The singular minimum of reflection for the non-trivial topological textures exists only when the two conditions intersect. The red and blue dots indicate the intersections for the optical vortex (w = +1) and antivortex (w = −1), respectively. The white circles indicate the positions of the weak reflection minima of the trivial topological phase (w = 0).
Extended Data Fig. 2 Polarization dependency of magneto-optically-driven optical vortex dynamics.
a,b, External magnetic-field-dependent behaviour of the complex reflection coefficient of the (a) optical vortex (Sample #2, w = +1) and (b) antivortex (Sample #3, w = −1) for the opposite handedness of the circular polarization (+σ and −σ) of the incident light.
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Supplementary Information
This file contains Supplementary Sections 1–13, including Supplementary Figs. 1–17 and References.
Supplementary Video 1
Plot of the same amplitude (the yellow curve) and out-of-phase (the green curve) conditions inside the GTOC unit cell (p × p) in the generalized parameter space depending on the thickness of the Ni layer. The red and blue dots indicate the intersections for the optical vortex (w = +1) and antivortex (w = −1), respectively.
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Kim, D., Baucour, A., Choi, YS. et al. Spontaneous generation and active manipulation of real-space optical vortices. Nature 611, 48–54 (2022). https://doi.org/10.1038/s41586-022-05229-4
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DOI: https://doi.org/10.1038/s41586-022-05229-4
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