Plasmonic vortices host magnetoelectric interactions

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Plasmonic vortices host magnetoelectric interactions

Atreyie Ghosh, Sena Yang, Yanan Dai, W. Vincent Liu, and Hrvoje Petek

Phys. Rev. Research 6, 013163 – Published 13 February 2024

Abstract

The vector $E \times H$ and pseudoscalar $E \cdot H$ products of electric and magnetic fields are separately finite in vacuum transverse electric and magnetic (TEM) plane waves, and angular momentum structured light. Current theories of interactions beyond the standard model of particle physics invoke $E \cdot H \neq 0$ as the source term in the axion law that describes interactions with the cosmological dark matter axion particles outside of the quartet of Maxwell's equations. $E \cdot H \neq 0$ also drives relativistic spin-charge magnetoelectric excitations of axion quasiparticles at a distinctively higher condensed matter scale in magnetic and topological materials. Yet, how to drive coherent $E \cdot H$ response is unknown, and provides motivation to examine the field polarizations in structured light on a deep subdiffraction limited spatial scale and suboptical cycle temporal scale by ultrafast nonlinear photoemission electron microscopy. By analytical theory and ultrafast coherent photoemission electron microscopy, we image $E \cdot H$ fields in surface plasmon polariton vortex cores at subwavelength scales, where we find that the magnetoelectric relative to the dipole density is intensified on an ∼10-nm-diameter scale as a universal property of plasmonic vortex fields. The generation and nanoscale localization of $E \cdot H$ fields introduces the magnetoelectric symmetry class, having the parity $P$ and time reversal $T$ broken, but the joint $P T$ symmetry preserved. The ability to image the optical fields of plasmonic vortex cores opens the research of ultrafast microscopy of magnetoelectric responses and interactions with axion quasiparticles in solid state materials.

Received 2 October 2023
Revised 7 January 2024
Accepted 9 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013163

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Light-induced magnetic effects Magneto-dielectric effect Magneto-optics Plasmonics Plasmons Ultrafast magnetic effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Atreyie Ghosh ^1,2, Sena Yang ¹, Yanan Dai^1,3,4,*, W. Vincent Liu ¹, and Hrvoje Petek ^1,†

¹Department of Physics and Astronomy, University of Pittsburgh and IQ Initiative, Pittsburgh, Pennsylvania 15260, USA
²James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
³Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
⁴Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen 518045, China

^*daiyn@sustech.edu.cn
^†petek@pitt.edu

Article Text

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Supplemental Material

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References

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Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Optics

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Images

Figure 1
The focus region and rotation of $E \cdot H$ fields at the core of an $l = - 1$ surface plasmon vortex. (a) Color maps show how the relative $E ∡ H$ angle evolves between 0 and $π$ in 1/8 of an optical cycle step. For LCP generation, in the center $λ_{SPP} / 2$ diameter region (yellow), the $E$ and $H$ fields remain dominantly antiparallel as they jointly rotate about the vortex core (center) at frequency, $ω_{L}$ . Progressing outward by $λ_{SPP} / 2$ the fields become parallel (dark blue) and again antiparallel in a fourfold symmetric structure that repeats at $4 ω_{L}$ . (b) Averaging the angle over $ω_{L}$ illustrates that $E$ and $H$ fields form antiparallel and parallel rings with abrupt realignment for every increase in the radius by $λ / 4$ , outside of the central core. The field structure shows that the ME polarization is generated with singular variations of the sign passing through rings of orthogonal polarization (green). Ultrafast photoelectron microscopy measures the action of such field textures with subdiffraction limited resolution. The lateral side dimension of each image is $2 λ_{SPP}$ (1060 nm).
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Figure 2
The plasmonic fields generating the ME density in SPP vortex cores. (a) Color maps of the instantaneous $Re (E^{*} \cdot H)$ distribution with black and green arrows denoting the instantaneous SPP $E_{| |}$ and $H_{| |}$ fields, respectively, generated by illuminating circular and square CS with LCP light. The figures show that $R e (E^{*} \cdot H)$ has the maximum values at vortex cores where $E_{∥}$ and $H_{∥}$ are (anti-)parallel on $λ_{SPP} / 2$ length scale (black scale bars). $Re (E^{*} \cdot H)$ amplitude follows the envelope of the generation optical fields in time. (b) The amplitudes and widths of $A_{ME}$ for the same spatial regions displayed in (a) for $δ = 10^{- 4}$ in Eq. (2). The arrows emphasize that the red and blue spots mark strong $A_{ME}$ for the clockwise and counterclockwise rotating SPP vortices in (a) with parallel and antiparallel $E_{∥}$ and $H_{∥}$ field orientations. The black solid curves indicate horizontal line profiles of $A_{ME}$ along the black dashed lines. The amplitudes and the FWHM of $A_{ME}$ foci, $\pm 12.6$ and 10.3 nm, respectively, are the same for the circular and square CS. The thick solid lines mark the $λ_{SPP} / 2$ (265 nm) scale.
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Figure 3
ITR-PEEM experiment setup. In a typical PEEM experiment, a coupling structure is etched on a metal surface to compensate for the momentum mismatch for launching SPP waves. The metal surface is excited by an externally incident laser pulse (optical field) to generate photoemission so that the photoemitted electrons can be detected. In an ITR-PEEM setup a pair of identical, phase-locked left circularly polarized femtosecond pulses with pulse delay $τ$ illuminates a silver film at a normal incidence. The silver film has lithographically inscribed square (or circular) structure for generation of SPP fields as shown in the scanning electron microscope image of a square slit coupling structure.
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Figure 4
Ultrafast microscopy of $E \cdot H$ fields generated by a $Q = \infty$ CS. (a) The color scale represent $s | E^{*} \cdot H |$ distribution from ITR-PEEM data [22] surrounding an SPP vortex core generated by illuminating a polycrystalline Ag film with a circular CS with ultrafast LCP laser pulses (details in the Supplemental Material). The measured $E$ and $H$ fields give a FWHM of the $| E^{*} \cdot H |$ distribution of $0.35 λ_{SPP}$ , and (b) the ME density ( $| A_{ME} |$ ) (amplitude represented by color scale). The white line in (b) is a horizontal line profile of $| A_{ME} |$ that quantifies the measured FWHM of 74 nm and height of 3.5 of $| A_{ME} |$ . The line profile shows secondary maxima in $| A_{ME} |$ with a dip where the $E$ and $H$ field's orientations transition through orthogonal. The scale bars in (a) and (b) denote $λ_{SPP} / 2$ (265 nm).
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Figure 5
Ultrafast microscopy of $E$ , $H$ , and $E \cdot H$ fields for a square plasmonic vortex array. (a)–(e) Color maps represent the experimental relative $E_{∥} ∡ H_{∥}$ distribution evolving from 0 to 1/8 of an optical cycle (like Fig. 1). The vectorial $E_{∥}$ and $H_{∥}$ field components are extracted from the experimental data of a square array of SPP vortices [42] by the procedure in Fig. S5 and shown in Fig. S6. (b) The color map represents the experimental $Re (E^{*} \cdot H)$ distribution with red (positive) and blue (negative) values defined by respective parallel and antiparallel projections between $E_{∥}$ and $H_{∥}$ . (c) The extracted $A_{ME}$ distribution for the spatial region of (a) and (b) denoted through the red and blue color scheme. The sharp spots indicate strong localization of the ME driving fields at each plasmonic vortex core of the array shown in (a) and (b). Note, that within an optical cycle the fields rotate at frequency $ω_{L}$ ; the quantity $Re (E^{*} \cdot H)$ remains unchanged within the experimental uncertainty. The black line in (c) shows the line profile of $A_{ME}$ taken along the black dashed line. The average heights and FWHMs of the peaks shown are 1.4 and 55 nm, respectively. For comparison, the purple line in the same plot denotes the line profile of the $z$ component of the normalized SAM ( $S_{z n}$ ) [42] along the black dashed line. The scale bars in (a) and (b) indicate $λ_{SPP}$ /2 (265 nm).
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Figure 6
The SPP vortex fields. Color maps showing the phase angle variation from $- π$ to $π$ radians of the $E_{z}$ component of SPP field when generated by illuminating circular (left) and square (right) CSs with LCP light for the same spatial region that is shown in Fig. 2. The black arrows show the wave vector $k_{SPP}$ of the field circulation. At the center of each circulation there is a phase singularity where $E_{z} = 0$ and the phase is undefined. The thick black and green arrows indicate the instantaneous directions of the rotating $E_{∥}$ and $H_{∥}$ SPP fields at the vortex cores, respectively, as illustrated in Fig. 2. The scale bars indicate $λ_{SPP} / 2$ (265 nm). The details of $m = 0$ plasmonic vortex fields can be found in Refs. [22, 37, 42].
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