TitleThree linespossible[Replace the following names and titles with those of the actual contributors: Dorena Paschke, PhD1; David Alexander, PhD2; J eff Hay, RN,BSN, MHA3, and Pilar Pinilla, MD41[Add affiliation for first contributor], 2[Add affiliation for second contributor], 3[Add affiliation for thirdcontributor], 4[Add affiliation for fourth contributor]

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OBJ ECTIVES

ETHODS RESULTS

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Saturation Effects in Plasmon-Exciton Systems: Breakdown of Classical Description of Core-Shell NanoparticlesFelix Stete1,2, Wouter Koopman1, Günter Kewes3, Carsten Henkel1, Oliver Benson3, Matias Bargheer1,41) Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Straße 24-25, 14476 Potsdam2) Humboldt-Universität zu Berlin, School of Analytical Sciences Adlershof, Albert-Einstein-Straße 5-9, 12489 Berlin3) Humboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, 12489 Berlin4) Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Wilhelm-Conrad-Röntgen Campus, BESSY II, Albert-Einstein-Straße 15 12489

www.analytical-sciences.deHumboldt-Universität zu Berlin | School of Analytical Sciences AdlershofAlbert-Einstein-Straße 5-9, 12489 Berlin

Financed by the Excellence Initiative:

The emitters behave like a giant oscillator with a transition dipole moment of µtot = Nµ0 [5].

107 meV

Plasmon maximum position [eV]

Max

imum

pos

ition

[meV

]

1.9

2.0

2.1

2.2

2.3 ∅ = 37 nm

1.95 2.0 2.05 2.10

156 meV

2.0 2.05 2.101.95

∅ = 18 nm

Plasmon maximum position [eV]

Max

imum

pos

ition

[meV

]

1.9

2.0

2.1

2.2

2.3

145 meV

Plasmon maximum position [eV]1.95 2.0 2.05 2.101.90

∅ = 34 nm

Max

imum

pos

ition

[meV

]

1.9

2.0

2.1

2.2

2.3

232 meV

Plasmon maximum position [eV]

∅ = 11 nm

2.05 2.10 2.15

Max

imum

pos

ition

[meV

]

1.9

2.0

2.1

2.2

2.3

Polymer covers with different sizes result in different plasmon resonances. Plotting the polariton resonancens against those of uncoupled plasmons gives the anticrossing [6].

Ω0 from anticrossings

Ω0 can be obtained from the anticrossings as half the distance between upper and lower polariton branch.

Different sizes require different saturation terms. Taking this into account, the spectra can all be modelled with good accuracy for otherwise identical parameters!

There is no set of parameters that can remove the third peak and maintain the correct splitting.

The third peak, caused by shell absorption, has been predicted theoretically [3] but has never been observed in an experiment.

450 500 550 600 650 700 750Wavelength [nm]

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measurementsimulation

which leads to a permittivity of

Plugging this expression for εshell into the Mie-Gans formula for the polarisability:

Assuming the dye to be described as a Lorentz oscillator, the susceptibility reads as

Ω0 causes a saturation and the susceptibility can be expressed by with

In a semiclassical approach, the dye is regarded as two-level system. From the Bloch equation, the susceptibility is derived as [4]

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measurementsimulation

with

With this expression for εshell in the Mie-Gans formula for the polarisability the third peak disappears and the spectrum can be reproduced correctly.

SummaryCore-Shell nanoparticles are a popular example system for strongly coupled plasmon-exciton systems.In theory, their spectra can be described by Mie-Gans theory. However, assuming a classical Lorentz oscillator to represent the dye, the solutions either show a too low Rabi splitting or the emergence of another peak which has not yet been observed in experiments.The correct susceptibility from a semiclassical approach introduces a saturation term which is necessary due to the very high electric fields in the vicinity of plasmonic nanoparticles. Saturation even occurs in the one photon limit indicating single photon nonlinearities and vaccum saturation effects.

450 500 550 600 650 700 750Wavelength [nm]

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Mie-Gans-Solution with Lorentz oscillator as dye

Mie-Gans-Solution with quantum mechanical two-level-system oscillator as dye

Dye coatedgold nanorods measurement

Investigated system

GoldnanoparticlesTDBC

24 hoursgold-TDBCcore-shell

particle

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Polarisability α of a core-shell ellipsoid which is small compared to the wavelength [1]:

Gold nanoparticles are mixed with the J-aggregate forming dye TDBC. The resulting core-shell particles possess new split up eigenfrequencies.

Classical model Semiclassical model

Different saturations for different particle sizes

450 500 550 600 650 700

450 500 550 600 650 700

500 550 600 650 700

500 550 600 650 700

500 550 600 650 700

500 550 600 650 700

500 550 600 650 700

500 550 600 650 700

Wavelength

Wavelength

Wavelength

Wavelength

Wavelength

Wavelength

Wavelength

Wavelength

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∅ = 37 nm

∅ = 37 nm∅ = 34 nm

∅ = 34 nm

∅ = 18 nm

∅ = 18 nm

∅ = 11 nm

∅ = 11 nm

measurementsimulation

Ω0 = 100 meV Ω0 = 85 meV Ω0 = 77 meV Ω0 = 65 meV

Dye shell thickness = 3 nmγ = 47 meVDye resonance at 612 nm

f = 0.11

Discussion

References

We work in the single photon limit, i.e only one excitation at a time is present on one particle. But even in this case the vacuum electric field Evac exceeds that saturation field Esat of the emitter, since

The exciting photon already probes the saturation. This can be understood as vacuum field saturation!

Thus, even at low light intensities, saturation has to be taken into account and single photon non-linearities emerge.

[3] Tomasz J. Antosiewicz et al., ACS Photonics, 1, 454 - 463 (2014)

[1] Craig. F. Bohren and Donald R. Huffmann, Absorption and scattering of light by smallparticles. John Wiley & Sons (2008)

[2] K. Lance Kelly et al., Journal of Physical Chemistry B, 107, 668-677 (2002)

[4] Gilbert Grynberg, Alain Aspect, Claude Fabre, Introduction to quantum optics: from the semi-classical approach to quantized light. Cambridge university press (2010)

[5] Päivi Törmä, William L. Barnes, Reports on Progress in Physics, 78, 013901 (2014)

[6] Felix Stete et al., Journal of Physical Chemistry C, 122, 17976-17982 (2018)

Mie Gans Theory

500 nm

450 500 550 600 650 700 750Wavelength [nm]

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Taking into account scattering losses and depolarisation [2]:

ε: Permittivity L: geometrical factorg: fraction of inner ellipsoid

From the polarisabilty, the cross sections for scattering, absorption and extinction can be obtained as

Particle width: 18 nmParticle length: 33 nm

εmed=1.96Citrate shell: 1 nmεshell=2. 37

With rod dimensions taken from TEM images the spectra of bare gold nanorods can be simulated

ε∞ = 1.7