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Optical polarization analogue in free electron beams


Spectromicroscopy techniques with fast electrons can quantitatively measure the optical response of excitations with unri- valled spatial resolution. However, owing to their inherently scalar nature, electron waves cannot access the polarization-related quantities. Despite promising attempts based on the conversion of concepts originating from singular optics (such as vortex beams), the definition of an optical polarization analogue for fast electrons has remained an open question. Here we establish such an analogue using the dipole transition vector of the electron between two well-chosen singular wave states. We show that electron energy loss spectroscopy allows the direct measurement of the polarized electromagnetic local density of states. In particular, in the case of circular polarization, it directly measures the local optical spin density. This work establishes electron energy loss spectroscopy as a quantitative technique to tackle fundamental issues in nano-optics, such as super-chirality, local polarization of dark excitations or polarization singularities at the nanoscale. Read more »

Self-hybridization within non-Hermitian localized plasmonic systems

Figure 1 : Left : Energy variation of two modes of silver nano-daggers as a function of the vertical arm length L. A clear anti-

In a recent paper published in Nature Physics, we show that electron energy loss spectroscopy in a scanning transmission electron microscope reveals the possibility for two eigenmodes from the same nanoparticle to hybridize – a physical effect that cannot be observed in day-to-day (Hermitian) linear physics Read more »


Lourenço-Martins, H., Gérard, D. & Kociak, M. Optical polarization analogue in free electron beams. Nature Physics (2021).doi:10.1038/s41567-021-01163-w Download: OpticalPolarizationAnalog.pdf (5.54 MB)
Di Giulio, V., Kociak, M. & de Abajo, J.G.F. Probing quantum optical excitations with fast electrons. Optica 6, 1524 (2019). Download: 
Lourenço-Martins, H., Das, P., Tizei, L.H.G., Weil, R. & Kociak, M. Self-hybridization within non-Hermitian localized plasmonic systems. Nature Physics 89, (2018). Download: LM2018.pdf (3.41 MB)
Guzzinati, G., et al. Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nature Communications 14999 (2017).doi:10.1038/ncomms14999 Download: Nature Communications 2017 eacute.pdf (1.55 MB)
Losquin, A. & Kociak, M. Link between Cathodoluminescence and Electron Energy Loss Spectroscopy and the radiative and full ElectroMagnetic Local Density of States. ACS Photonics 151006180224009 (2015).doi:10.1021/acsphotonics.5b00416 Download: acsphotonics.5b00416.pdf (1.71 MB)
Kociak, M., et al. Seeing and measuring in colours: Electron microscopy and spectroscopies applied to nano-optics. Comptes Rendus Physique 15, 158 - 175 (2014). Download: 1-s2.0-S1631070513001515-main.pdf (2.66 MB)
Kociak, M. & Stéphan, O. Mapping plasmons at the nanometer scale in an electron microscope. Chemical Society Reviews (2014).doi:10.1039/c3cs60478k Download: Chem. Soc. Rev. 2014 Kociak.pdf (2.86 MB)
de Abajo, F.J.G., Asenjo-Garcia, A. & Kociak, M. Multiphoton Absorption and Emission by Interaction of Swift Electrons with Evanescent Light Fields. Nano Letters 10, 1859–1863 (2010).
de Abajo, F.J.G. & Kociak, M. Probing the Photonic Local Density of States with Electron Energy Loss Spectroscopy. Physical Review Letters 100, 106804 (2008). Download: Phys. Rev. Lett. 2008 García de Abajo.pdf (540.82 KB)
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