High-Resolution Surface Plasmon Imaging http://physik.uni-graz.at/~atr, http://www.felmi-zfe.tugraz.atAndreas Trgler, Ulrich Hohenester, Bernhard Schaffer, and Ferdinand Hofer

W. Barnes et al., Surface plasmon subwavelength optics, Nature 424, 824 (2003).H. Atwater, The promise of plasmonics, Scientific American 296(4), 56 (2007).Flat lightParticle plasmonsMeta materialsThe promise of plasmonics...Agenda: Theoretical background and how to map a plasmon Simulation technique Comparison between experiment and theory

Theoretical background and how to map a plasmon

No! Because the wavelength of light is (much) larger than the nanoparticle but: What about other microscopy techniques?EELS Electron Energy Loss Spectroscopy

EFTEM Energy Filtered Transmission Electron MicroscopyCan one directly see surface plasmons?F. J. Garca de Abajo : Optical excitations in electron microscopy, arXiv:0903.1669v1 (2009)

Electron beam excites surface plasmon(evanescent source of radiation)Surface plasmonacts back on electron~ 100 keV electrons( approx. 70 % of c )Raster scanning of electron beamprobes dielectric environment of MNPElectron interaction

Maxwells equations:

Solution by Greens functions:

Structure of equations we want to solve:

Green function equation:

4-vector notation, .Linard-Wiechert potentials

Maxwells equations:

Solution by Greens functions:

Structure of equations we want to solve:

Solution for an arbitrary charge distribution:

4-vector notation, .Linard-Wiechert potentials

Solution for a relativistic moving charge:

Charge distribution of an electron moving along r(t):

Linard-Wiechert potentials

Solution for a relativistic moving charge:

Charge distribution of an electron moving along r(t):

Linard-Wiechert potentials

Solution for a relativistic moving charge:

Charge distribution of an electron moving along r(t):

Linard-Wiechert potentials

Solution for a relativistic moving charge:

Charge distribution of an electron moving along r(t):

Linard-Wiechert potentials

Solution for a relativistic moving charge:

Charge distribution of an electron moving along r(t):

Final potentials:

Linard-Wiechert potentials

Energy loss of the fast electron:

Energy loss can be related to the work against the induced electric field!Electron energy lossFourier transform~ 100 keV electronsProcess reminiscent of a self energy.

Probe of the electrost. potential of the SP!U. Hohenester, H. Ditlbacher, and J. R. Krenn: On the interpretation of electron energy loss spectra of plasmonic NPs(to be published)

Energy loss of the fast electron:

Energy loss can be related to the work against the induced electric field!Electron energy lossFourier transformLoss probability: The problem reduces to solving the electric field induced by the electron:

Change of the reference frameFourier transform:Time domain: Electron beam interacts with a SP oscillating in time.

Frequency domain: The SP oscillation becomes frozen, and interacts with a periodically modulated charge distribution of the electron beam.

(Interaction along the whole trajectory!)

Electric Green tensor:

The electromagnetic response of a structured material is fully captured in its electric Green tensor.

Green tensor - link to simulation

Simulation technique

Mie theoryAnalytic results for spherical particles to test the simulation.

Boundary Element Method (BEM)Approximate surface of scatterer by small surface elements. Works for scatterers which have a homogeneous dielectric function. Up to a few 1000surface elements.

Simulation of particle plasmons

1. Discretization of particle surfaceUsing standard triangulation techniques of Matlab with typically a few thousand surface elements Simulation of particle plasmons

2. Excitation of nanoparticle ( illumination, molecule, electron beam ... )Oscillating dipole Inside and outside the metallic nanoparticle Maxwells equation are the usual wave equations! The only non trivial contribution comes from the boundaries.ebemetal(w), Simulation of particle plasmons

Boundary Element Method approach (BEM ) Garcia de Abajo & Howie, PRB 65, 115418 (2002); Hohenester & Krenn, PRB 72, 195429 (2005). Oscillating dipole 3. Add surface charges and currents such that BC of Maxwells equations are fulfilledSimulation of particle plasmons

Results and comparisonbetween experiment and theory

TEM, HREM, EDAuger electronsSecondaryelectronsX-raysIncident high energy electrons60-300 kVElastically scatteredelectronsThin specimen10-200 nmTransmission electron microscopyFerdinand Hofer and Bernhard Schaffer, Austrian Centre for Electron Microscopy and Nanoanalysis (FELMI) , TU Graz

HAADFGold particles (low-loss)Monochromated STEM-EELS ZLP zero loss peak(energy resolution: FWHM)ZLP: Measures energy distribution of primary electron beam, defines resolutionplasmon peaks

J. Nelayah, M. Kociak , O. Stphan, F. J. Garca de Abajo, M. Tenc, L. Henrard , D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzn, and C. Colliex, Mapping surface plasmons on a single metallic nanoparticle, Nature Phys. 3, 348 (2007).ExperimentTheorySurface plasmon mapping with EELS

Narrow slit (0.3 eV) combined with monochromator gives an energy resolution of ~0.4 eV.This allows EFTEM imaging close to the zero-loss peak, showing SP modes of Au nanoparticles.Schaffer et al., Micron (2008), DOI:10.1016/j.micron.2008.07.004Low-loss mapping by EFTEM

Monochromated EFTEM Monochromated STEM EELSEELS and EFTEM results

Comparison with Simulation@ 1.08 eV@ 1.85 eV@ 2.29 eV123400 nm75 nmEELS and EFTEM resultsB. Schaffer, U. Hohenester, A. Trgler, and F. HoferPhys. Rev. B 79, 041401(R) (2009)

@ 1.08 eV@ 1.85 eV@ 2.29 eV1231.08 eV1.85 eV2.29 eV(0.80 eV)(1.50 eV)(2.33 eV)400 nm75 nmEELS and EFTEM resultsB. Schaffer, U. Hohenester, A. Trgler, and F. HoferPhys. Rev. B 79, 041401(R) (2009) Comparison with Simulation

EELS and EFTEM resultsComparison with Simulation1.08 eV1.85 eV2.29 eV(0.80 eV)(1.50 eV)(2.33 eV)

SummaryTheoretical descriptionLinard-Wiechert potentialsElectromagnetic Green tensor link to simulation

SimulationDiscretize particle surface boundary element method

ResultsVery nice agreement with EELS & EFTEM measurements Direct observation of surface plasmons with unmatched spatial resolution!

Nanooptics (KFU)Ulrich HohenesterHajreta SofticJrgen WaxeneggerJoachim KrennAlfred LeitnerHarald DitlbacherDaniel KollerAndreas HohenauFranz AusseneggFELMI (TU Graz)Ferdinand Hofer Bernhard SchafferTheoretical Nanoscience (KFU)Thank you for your attention!

Surface plasmons bridge between micrometer and nanometer scales of conventional optics and nanodevices.Binding or converting light to coherent electron charge oscillations, confined to the surface.*STS: scanning tunneling spectroscopy CL: cathodoluminescencePEEM: photo-electron emission microscopyNSOM: near-field scanning optical microscopy

Limited spatial resolution provided by optical far- and near-field techniques, the lack of spatial resolution of these techniques sample volume larger than particles the results are usually averaged over a whole set of particles. *Electron beam with transversal extension in the sub-nm scale, probe for the dielectric environment of a metallic nanoparticle

The electromagnetic field that accompanies a point charge can be regarded as an evanescent source of radiation.This has interesting consequences: fast electrons generate SPPs when passing near a metal surface.

*neglect second term of kappa -> classical solution*(for coupled nanoparticles, EELS turns out to be blind to the hot spots in the gap region between the particles.)

***EELS rate! One major limitation: low-energy region usually masked by tail of ZLP (interacting elastically or losses too small to be measured) -> red and infrared regime, energy resolution: conventionally measured as the width at half intensity (FWHM)

-> only few experimental EELS spectra below 3eV; new interest in EELS below 5 eV by development of electron source monochromators for TEM(-> improves energy-spread of the beam and also the long extending tails of the ZLP are diminished)*STEM-EELS on Ag nanoprism with 78nm long sides and 10 nm thick on mica subscrate (eps=2.3) (synthesized by light-induced aggregation of small Ag NPs). EEL spectra acquired at corner A before and after deconvolution. Simulation with BEM (bulk losses for penetrating trajectories were discribed by using Lindhards dielectric function -> spatial dispersion)*Whole image at one filtered energy, poor energy resolution compared to EELS, but nice amplitude maps*Amplitude maps and spectra**