Plasmonic topological quasiparticle on the nanometre and femtosecond scales

Abstract

At the interface of classical and quantum physics, the Maxwell and Schrödinger equations describe how optical fields drive and control electronic phenomena to enable lightwave electronics at terahertz or petahertz frequencies and on ultrasmall scales1,2,3,4,5. The electric field of light striking a metal interacts with electrons and generates light–matter quasiparticles, such as excitons6 or plasmons7, on an attosecond timescale. Here we create and image a quasiparticle of topological plasmonic spin texture in a structured silver film. The spin angular momentum components of linearly polarized light interacting with an Archimedean coupling structure with a designed geometric phase generate plasmonic waves with different orbital angular momenta. These plasmonic fields undergo spin–orbit interaction and their superposition generates an array of plasmonic vortices. Three of these vortices can form spin textures that carry non-trivial topological charge8 resembling magnetic meron quasiparticles9. These spin textures are localized within a half-wavelength of light, and exist on the timescale of the plasmonic field. We use ultrafast nonlinear coherent photoelectron microscopy to generate attosecond videos of the spatial evolution of the vortex fields; electromagnetic simulations and analytic theory confirm the presence of plasmonic meron quasiparticles. The quasiparticles form a chiral field, which breaks the time-reversal symmetry on a nanometre spatial scale and a 20-femtosecond timescale (the ‘nano-femto scale’). This transient creation of non-trivial spin angular momentum topology pertains to cosmological structure creation and topological phase transitions in quantum matter10,11,12, and may transduce quantum information on the nano-femto scale13,14.

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Fig. 1: The plasmonic meron SAM texture.
Fig. 2: Ultrafast microscopy of the SPP vortex.
Fig. 3: The origin of the topological SAM texture.
Fig. 4: The topological charge.

Data availability

The data that support the reported findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

This research was supported by the NSF Center for Chemical Innovation on Chemistry at the Space-Time Limit, grant CHE-1414466. The authors thank L. Vuong for advice on the plasmonic flow analysis, A. Kosowsky for illuminating discussion of the role of phase transitions in cosmological structure formation and J. Chen at the Peterson Institute of NanoScience and Engineering for help in sample preparation.

Author information

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Authors

Contributions

Y.D. performed the experiments and simulations, processed and analysed the data, and generated the figures; Z.Z. helped with the sample preparation and performing the experiments; Y.D., Z.Z. and A.G. developed the analytical model for topological quasiparticles; R.S.K.M. advised on the topological properties of quasiparticles; A.K. explained the PEEM imaging of plasmonic phenomena; C.-B.H. supervised the research on plasmonic vortices, performed simulations of experiments and participated in the data interpretation, H.P. guided interpretation of the data as a realization of topological quasiparticles, wrote the manuscript and supervised the research; all authors contributed to the discussion.

Corresponding authors

Correspondence to Yanan Dai or Hrvoje Petek.

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Extended data figures and tables

Extended Data Fig. 1 Diagram of the nonlinear two-photon photoelectron emission process that forms the PEEM images.

The recorded photoelectron count images are created by electrons absorbing two energy quanta (2ħωL) from the total electric fields at the surface, EL + Elong + Ez, exciting them above Evac (left). The light quanta can be supplied either from a single pulse, or from a coherent superposition of fields from a pump–probe pulse pair with a variable time delay; the PEEM records the spatial distribution of photoelectrons excited by the total field. Right, the superposition of EL (shown as solid (dotted) grey lines) with wavelength λL and the parallel (anti-parallel) Elong (the tangential component of the SPP field at the vacuum/Ag interface, which oscillates between the Ez and Elong character; the solid and dotted curved lines signify a change in the SPP field sign in the same sense as for EL) fields with wavelength λSPP creates the total in-plane field with a modulation period of λSPP, as shown by the green curve. The PEEM signal is integrated over many excitation cycles, so the experimental time resolution is encoded by how interferences evolve with the pump–probe delay.

Extended Data Fig. 2 Raw static PEEM image of the plasmonic vortex.

Top, image presented on a logarithmic colour scale. The vertical dashed lines approximately delineate the regions dominated by self-interference and SPP interference, as described in the text. Bottom, the horizontal line intensity profile shows the vertically integrated signal within the white rectangle centred on the vortex. The interferences occur with λSPP and λSPP/2 periods.

Extended Data Fig. 3 Interferograms of photoemission (PE) yields.

a, 2PP yields recorded at single pixels from selected regions within the vortex (inset). The reference 2PP signal is recorded from a flat Ag surface region. The scans are translated vertically for easier viewing. b, Phase distribution (the red and blue colours signify opposite phases) of the y component of Elong relative to the excitation field. c, Fourier transform of the 2PP yield, as a function of polarization energy, which is defined by ħωL. The square filtering function of 1 eV width centred at 1ħωL indicates the selected energy range for the inverse Fourier transformation to obtain Supplementary Video 2. A second-order correlation process also includes the 2ħωL signal, which is not evaluated. The vertical scale is normalized at the 0ħωL peak maximum. Scale bars in a and b, λSPP.

Extended Data Fig. 4 ITR-PEEM images of the SPP vortex corresponding to the same time delays as in Fig. 2d.

The time delay increases from τ (leftmost image) to τ + 0.9 fs (rightmost image). a, The raw PEEM data; b, absolute values of the phase-independent 0ħωL Fourier component. c, The real part (amplitude) of the Ey component of the SPP field from the inverse Fourier transform of the 1ħωL signal. The asterisk and white lines mark the evolution of two components with the opposite phase as Δτ is advanced. Scale bars, λSPP.

Extended Data Fig. 5 The FDTD simulated field evolution in 1/2 an optical cycle at the SPP vortex excited by 550-nm y-polarized light.

The fields from top to bottom represent Ez and y and x components of Elong. For an m = 2 Archimedean spiral structure, the optical phase evolves by π from left to right. Note that the stronger Ez component is plotted with a different colour scale than the x and y components. Scale bars, λSPP/2.

Extended Data Fig. 6 Topological properties of plasmonic vortex system.

a, L-line map of a 2 μm × 2 μm region about the central vortex. The central domains are surrounded by apple-shaped toroids that are delimited by dashed lines and repeat with an approximate periodicity of λSPP (along the y direction) to infinity. Different domains of interest are coloured and labelled with the corresponding topological charge. Black dots mark the phase singularities, within these regions. b, Normalized spin texture overlapped by the L-line map in a. The colour map and arrows indicate the spin components, as in Supplementary Fig. 3b. c, d, Enlarged spin textures at side phase singularities indicated by the square shading in c. e, f, Spin texture in the same region as in c, d, but with the sign of positive Sz reversed, while conserving the topological charge. Black dots in c, d indicate positions of the phase singularities.

Extended Data Fig. 7 Phase change of the Ez associated with the phase singularities.

a, Phase change of Ez around the central and the two side phase singularities at y = 0 and ±λSPP/2 in the dumb-bell region. b, Phase change of Ez around of the phase singularities along the x and y axes shown in Extended Data Fig. 6c, d. The opposite phase change along the x and y axes results from the opposite vorticity causing the topological charges of apple toroid domains to be zero.

Extended Data Fig. 8 Selected slices of the experimental plasmonic flow illustrating L-line formation, persistence and decay.

The delay times given at the top of each panel are normalized by the optical cycle. They are obtained from ITR-PEEM images with the probe pulse interacting with the sample before, during and after the generation of the plasmonic vortex (labelled ‘Pre-vortex’, ‘Established vortex’ and ‘After vortex’, respectively).

Supplementary information

Supplementary Information

This file contains (A) Analytical formalism of the Plasmonic Vortex Fields; (B) Formalism of the Topological SAM Textures; Supplementary References; and Supplementary Figure 1-3.

Supplementary Video 1

. Raw ITR-PEEM movie of plasmonic vortex The experimental ITR-PEEM data showing the spatial distribution of the 2PP signal from the SPP plasmonic vortex; PEEM images are taken in pump-probe delay increments between identical pulses of ~100 as.

Supplementary Video 2

. Fourier filtered plasmon vortex at 1ω The component of the Fourier transformed signal (absolute value) from Video 1 at the laser driving frequency, 1ωL, is inverse Fourier transformed. This extracts the interference signal between the SPP and the probe optical pulse fields at the sample, enabling imaging of the vortex gyration about the vortex core. This SPP field gyration generates the spin angular momentum meron texture.

Supplementary Video 3

. The L-line singularity distribution The L-line distribution for a single pulse generated at the optical vortex. The bright contrast corresponds to high ellipticity of the x,y polarized SPP field, where the polarization is nearly linear and SAM points in the x,y plane orthogonal to the propagation k-vector. The central hourglass domain and the dumbbell region that are constant on ±20 fs time scale contain the meron-like SAM texture, and define the integration boundaries that obtain the topological charge of +1/2/per domain or +3/2 total. Time zero corresponds to maximum in the SPP vortex field.

Supplementary Video 4

. SAM quasiparticle density distribution. The video shows the evolution of SAM quasiparticle density. Integrating the density within the specified L-line domains in Video 3, gives topological charges of +1/2 and +3/2, respectively.

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Dai, Y., Zhou, Z., Ghosh, A. et al. Plasmonic topological quasiparticle on the nanometre and femtosecond scales. Nature 588, 616–619 (2020). https://doi.org/10.1038/s41586-020-3030-1

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