Abstract
The photonic spin Hall effect, a deep subdiffraction-limited shift between the opposite spin components of light, emerges when light undergoes an evolution of polarization or trajectory that induces the geometric phase. Here, we study a stochastic photonic spin Hall effect arising from space-variant Berry–Zak phases, which are generated by disordered magneto-optical effects. This spin shift is observed from a spatially bounded lattice of ferromagnetic meta-atoms displaying nanoscale disorders. A random variation of the radii of the meta-atoms induces the nanoscale fluctuation. The standard deviation of the probability distribution of the spin shifts is proportional to the fluctuation of the meta-atoms. This enables us to detect a five-nanometre fluctuation by measuring the probability distribution of the spin shifts via weak measurements. Our approach may be used for sensing deep-subwavelength disorders by actively breaking the photonic spin symmetry and may enable investigations of fluctuation effects in magnetic nanosystems.
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Data availability
The data for Figs. 2–4 are available as source data. Other data that support the conclusions of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
We gratefully acknowledge financial support from the Israel Science Foundation (ISF); the US Air Force Office of Scientific Research (FA9550-18-1-0208) through their programme on Photonic Metamaterials; the Israel Ministry of Science, Technology and Space; the United States−Israel Binational Science Foundation (BSF); and, in part, the Technion via an Aly Kaufman Fellowship. The fabrication was performed at the Micro-Nano Fabrication & Printing Unit (MNF&PU), Technion.
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Supplementary Information
Supplementary text, Figs. 1–10 and refs. 1–12.
Source data
Source Data Fig. 2
Source data for the simulation results of the Kerr effect and photonic spin Hall effect from disordered Kerr effects.
Source Data Fig. 3
Source data for the experimental results of weak measurements.
Source Data Fig. 4
Source data for the calculated and experimental results for stochastic photonic spin Hall effect.
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Wang, B., Rong, K., Maguid, E. et al. Probing nanoscale fluctuation of ferromagnetic meta-atoms with a stochastic photonic spin Hall effect. Nat. Nanotechnol. 15, 450–456 (2020). https://doi.org/10.1038/s41565-020-0670-0
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DOI: https://doi.org/10.1038/s41565-020-0670-0
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