Dichroism in the Interaction between Vortex Electron Beams, Plasmons, and Molecules

A. Asenjo-Garcia and F. J. García de Abajo

Phys. Rev. Lett. 113, 066102 – Published 6 August 2014

Abstract

We study the transfer of orbital angular momentum between vortex electron beams and chiral samples, such as staircase plasmonic nanostructures and biomolecules. Inelastic electron scattering from these samples produces large dichroism in the momentum-resolved electron energy-loss spectra. We illustrate this phenomenon with calculations for chiral and nonchiral clusters of silver spheres using both focused and extended electron beams, which exhibit $\sim 10 %$ difference between channels of opposite angular momentum. In addition to its fundamental interest, this remarkably high dichroism suggests a way of spatially resolving chiral optical excitations, including dark plasmons. We also predict a dichroic response when probing a chiral biomolecule, which suggests the use of these electron beams for resolving different enantiomers.

Received 12 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.113.066102

Authors & Affiliations

A. Asenjo-Garcia¹ and F. J. García de Abajo^1,2,*

¹ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
²ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain

^*javier.garciadeabajo@icfo.es

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Vol. 113, Iss. 6 — 8 August 2014

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Images

Figure 1
(a) Sketch of the system under consideration. A 100 keV electron plane wave impinges on a cluster (left-handed tetramer) consisting of four 30 nm silver spheres separated by 5 nm gaps. The electron is subsequently passing through an orbital angular momentum (OAM) analyzer that splits the beam into different components $m_{f}$ along different transmission directions. These components are independently energy-analyzed by an angle-resolved spectrometer. The origin of OAM is made to coincide with the position of the electron arrow depicted in (a). The angular distribution of different $m_{f}$ components are represented at the bottom for a 3.5 eV energy loss. For visualization purposes, the intensities of the $m_{f} = \pm 1$ and $m_{f} = \pm 2$ components are multiplied by factors of 5 and 10, respectively. (b) Energy-loss $m_{f}$ -resolved cross-section spectra under the conditions of (a).
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Figure 2
(a) Dichroism between $m_{f} = \pm 1$ components in the spectrally resolved inelastic cross section of 100 keV electrons for different clusters of 30 nm silver spheres with gaps of 5 nm (see insets). The planar trimer does not exhibit any dichroism. (b) Same as (a), normalized to the sum of $m_{f} = \pm 1$ cross sections. (c) Extrinsic dichroism displayed by the trimer when it is tilted with respect to the direction of electron propagation. (d) Partial $m_{f} = \pm 1$ inelastic cross sections normalized to the $m_{f} = 0$ transmitted beam component for different electron energies in the left-handed tetramer [upper inset in (a)]. The inset of (d) shows the maximum of this ratio (left, red curve) and the energy loss at which this happens (right, blue curve) as a function of electron energy. The origin of OAM is the same as in Fig. 1
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Figure 3
(a),(b) Normalized maximum of the partial inelastic cross section $σ_{1}$ (a) and the dichroism $| σ_{1} - σ_{- 1} |$ (b) for a randomly oriented model point structure characterized by a chiral excitation of frequency $ω_{0}$ , width $γ_{0}$ , and associated electric and magnetic dipole moments $p$ and $m$ [see inset to (b)]. The cross section and dichroism spectra follow a Lorentzian profile [see inset to (a)]. The origin of OAM is displaced a distance $R_{0}$ with respect to the structure. The vertical axes are normalized to yield universal curves that only depend on the electron energy (see legend) and $ω_{0} R_{0} / v γ$ . (c),(d) Partial inelastic cross section (c) and normalized dichroism (d) for an $α$ -helix, parametrized as described in the Supplemental Material [24]). The optical dichroism with circularly polarized light is shown for reference. Different electron energies are considered with the same color code throughout the figure.
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