Plasmonics : Tailoring the at the nanoscale

Rémi CARMINATI

Institut Langevin, ESPCI Paris, CNRS Paris, France People involved

Valentina Yannick DE WILDE Romain PIERRAT Lionel AIGOUY KRACHMALNICOFF

Dorian BOUCHET Da CAO Alexandre CAZE (PhD student) (former PhD student) (former PhD student)

Outline

• Surface : A (biased) introduction

• Spontaneous emission, local density of states and antennas

MDOS(centre,r) ; 1 film ; taille laterale 340 nm ; f=50% ; = 780 nm

4

3 2 • Spatial coherence and cross density of states 1

• Energy transfer (a simple example)

• Surface plasmons : A (biased) introduction

• Spontaneous emission, local density of states and antennas

• Spatial coherence and cross density of states

• Energy transfer (a simple example) Surface electromagnetic modes

z E exp(iKx + iq z)exp( i!t) 1 x E exp(iKx iq z)exp( i!t) ε(ω) 2

Reflection factor (TM polarization) ! ✏(!) ✏(!) q1 q2 K(!)= Re [✏(!)] < 1 r = c ✏(!)+1 ✏(!) q1 + q2 s

Pole in the reflection factor Evanescent wave

2 2 K(!) > !/c [✏(!) q1] = q2 | | (note: also a zero – Brewster) Surface

K Drude model !2 !2 ✏(!)=1 p 1 p (! ) !2 + i! ' !2 ε(ω) ! ✏(!) ! !2 !2 K(!)= = p c ✏(!)+1 c 2!2 !2 s s p

ω = c K ω

ω = ω p 2

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K Microscopic picture

Collective oscillation Bulk plasmon of conduction Acoustic mode in an

2 2 ne Surface plasmon !p = Coupling between plasmon and m ✏0 electromagnetic field at the surface E

ω = c K ω K ω = ω p 2

plasmon € metal ε(ω) polariton

K Early plasmonics : Total coherent absorption of light Theory Measurement

M.C. Hutley and D. Maystre, Opt. Commun. 19, 431 (1976) Direct observation of SPP by near-field optical microscopy

Surface profile

Near-field optical image

Bozhevolnyi et al., Phys. Rev. Lett. 78, 2823 (1997) Local excitation and scattering of SPP

Gold film, 60 nm λ = 514 nm

Courtesy of A. Bouhelier

Hecht et al., PRL 77, 1889 (1996) Surface plasmons in nanoparticles

E

• Damped harmonic oscillator (dipole)

• Quasi-static polarizability (sphere)

✏(!) 1 ↵ (!)=4⇡R3 0 ✏(!)+2

• Resonance

• Confinement below λ (quasi-static regime) Absorption spectrum

E

Absorption spectrum of spherical gold particles (30 nm)

www.nanocomposix.eu Subwavelength resonators

LOW FREQUENCIES

RLC circuit Two-level Plasmonic nanoparticle Middle-age plasmonic engineering

Blue : cobalt, nickel

Green : iron oxyde, chrome

Sainte Chapelle (Paris) Red : gold

Yellow : silver, cadmium Features of surface plasmons (plasmonics)

• Coupling between light and confined excitations on surfaces

Sub-λ devices (integrated ) Evanescent-wave microscopy Surface enhanced

• Resonators with small mode volume Q 10 100 ⇠ Enhanced light-matter interaction (sources, absorbers) ! 2⇡.1015 Hz Labels (biomedical) ⇠ 3 V mode ⌧ • Sensitivity to surface contamination

Sensing applications

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• Surface plasmons : A (biased) introduction

• Spontaneous emission, local density of states and antennas

• Spatial coherence and cross density of states

• Energy transfer (a simple example) Spontaneous emission dynamics

I(t) exp( t) ⇠

e 2 2 Pertubation theory 2 p Im#u G r ,r , u% ω Γ = µ0 ω ge ⋅ 0 0 ω ! $ ( ) & g Wiley and Sipe, Phys. Rev. A 30, 1185 (1984)

π ω 2 Often written as Γ = p ρ r ,ω (Fermi's golden rule) ge u ( 0 ) ε0!

Local Density of States (LDOS) DOS and LDOS

1 • Density Of States (DOS) ⇢(!)= (! !n) V n X

⇢(r, !)= e (r) 2 (! ! ) • Local Density Of States (LDOS) n | n | n 2P! ⇢(r, !)= Im [TrG(r, r, !)] ⇡c2

r

Meaning of the LDOS

Γ ρ = = change in the LDOS Γ0 ρ0

large LDOS small LDOS Surface plasmons increase the LDOS

⇢0 Im[✏(!)] d ⇢(z,!) 3 3 2 ⇠ k0 z ✏(!)+1 Al | |

!2 ⇢ (!)= 0 ⇡2 c3

Joulain, Carminati, Mulet, Greffet, PRB 68, 245405 (2003) Radiative and non-radiative contributions

Silver nanoparcle Diameter 10 nm

ρ = ρR + ρNR

Photon emission Absorpon

Carmina et al., Opt. Commun. 261, 368 (2006) Castanié et al., Opt. Le. 35, 291 (2010) Nanoscale controlled experiments on single emitters

+ N 0.2

N 0.1 0 1 2 5 10 50 100 200 0.2

+ N

N 0.1 0 1 5 10 50 100 200

0.2 0.1 + N

N 0 1 5 10 50 100 200

Probability 0.2

+ N 0.1

N 0 1 5 10 50 100 200

0.2

+ N N 0.1 0 1 5 10 50 100 200 Γ/Γ0

S. Kühn et al., PRL 97, 017402 (2006) M. Busson, S. Bidault, Nature Comm. 3, 962 (2012) Fluorescence SNOM to characterize optical antennas

Topography Valentina Yannick DE WILDE KRACHMALNICOFF

Fluorescence Intensity

30 nm

Fluorescence decay rate

Krachmalnicoff et al., Opt. Express 21, 11536 (2013) Reciprocity theorem helps

Fluorescence intensity with antenna

Ifluo = A ⌘e↵ abs Iexc(r0)

R ⌘ = ⌦ e↵

Reciprocity theorem (confocal geometry)

R I (r ) ⌦ ⇠ exc 0 Measured parameters

R ⌦ Effecve radiave rate ˜NR = R Apparent non-radiave rate ⌦ ⌦

Cao et al., ACS Photonics 2, 189 (2015) Characterizing the influence of an optical antenna

Intensity Decay rate

Effective Apparent non- radiative rate radiative rate

Cao et al., ACS Photonics 2, 189 (2015) Theory supports the analysis

(a) 1 (b) 1 0.36 0.74 0.8 0.8 0.34 0.72 Experiment 0.6 0.32 0.6 0.7 (effective rates) m m m m 0.4 0.3 0.4 0.68 0.28 0.66 0.2 0.2 0.26 0.64 0 0 0 0.2 0.4 0.6 0 0.2 0.4 0.6

(c)1 (d) 1 0.34 0.76 0.8 0.8 0.32 0.74 Theory 0.6 (effective rates) 0.3 0.6 0.72 m m m 0.28 m 0.4 0.4 0.7 0.26 0.68 0.2 0.2 0.24 0.66

0 0 0 0.2 0.4 0.6 0 0.2 0.4 0.6

Cao et al., ACS Photonics 2, 189 (2015) The full LDOS contains a magnetic contribution

Equilibrium (blackbody) energy density

T

~! U(r, !)=⇢(r, !) exp(~!/kBT ) 1

Full LDOS

⇢(r, !)=⇢E(r, !)+⇢H (r, !)

Joulain, Carminati, Mulet, Greffet, PRB 68, 245405 (2003) Electric and magnetic contributions close to a metal surface

d=10 nm Al

Joulain, Carminati, Mulet, Greffet, PRB 68, 245405 (2003) Fluorescence SNOM with electric and magnetic dipole transitions

Lionel Aigouy (CNRS, ESPCI, Paris) Fluorescence spectra in the near field of a gold mirror

fluo Ij (r) Branching ratio j(r)= fluo Itotal(r) Branching ratio maps (gold stripe on )

Aigouy, Cazé, Gredin, Mortier, Carminati, PRL 113, 076101 (2014) Distance dependence of branching ratios

Aigouy, Cazé, Gredin, Mortier, Carminati, PRL 113, 076101 (2014) [method: S. Karaveli and R. Zia, PRL 106, 193004 (2011) – no scanning probe] Quantifying electric and magnetic LDOS

Theoretical analysis allows to deduce the relative LDOS from the branching ratio [see T.H. Taminiau, S. Karaveli, N.F van Hulst and R. Zia Nature Comm. 3, 979 (2012)]

Aigouy, Cazé, Gredin, Mortier, Carminati, PRL 113, 076101 (2014)

• Surface plasmons : A (biased) introduction

• Spontaneous emission, local density of states and antennas

MDOS(centre,r) ; 1 film ; taille laterale 340 nm ; f=50% ; = 780 nm

4

3 2 • Spatial coherence and cross density of states 1

• Energy transfer (a simple example) A complex plasmonic sample

gold

glass

150 nm The colors of gold

30% 100% Filling fraction

A resonant and broadband material Near fields

30% 100% Filling fraction

SNOM PEEM EELS λ = 720 nm

Grésillon et al., PRL(1999) Losquin et al. , PRB (2013) PRB (2001) Awada et al., PRB (2012) LDOS fluctuations reveal localized plasmon modes

Measured LDOS fluctuations

Localized ρ 2 plasmons 2 −1 λ = 605 nm ρ

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Γ ρ = = change in the LDOS Γ0 ρ0

Krachmalnicoff, Castanié, De Wilde, Carminati, Phys. Rev. Lett. 105, 183901 (2010) Spatial coherence

Classical coherence is a mesure of field-field correlations

E (r, !)E⇤(r0, !) h j k i Average over source or medium fluctuations Equilibrium (blackbody) radiation

T

Electromagnetic energy density Spatial coherence ~! U(r, !)=⇢(r, !) Ej(r, !)Ej⇤(r0, !) ImGjj(r, r0, !) exp(~!/kBT ) 1 h i/

LDOS ImGjj(r, r, !) Vacuum : ⇠ E (r, !)E⇤(r0, !) sinc(k r r0 ) h j j i/ 0| | Vacuum : LDOS = !2/(⇡2c3) / 2 spatial coherence length Planck’s spectrum

Landau, Lifshitz, Pitaevskii, Statistical Physics (Pergamon, Oxford, 1980) Rytov, Kravtsov and Tatarskii, Principles of Statistical Radiophysics (Springer, Berlin, 1989) Beyond LDOS

1 • Density Of States (DOS) ⇢(!)= (! !n) V n X

⇢(r, !)= e (r) 2 (! ! ) • Local Density Of States (LDOS) n | n | n 2P! ⇢(r, !)= Im [TrG(r, r, !)] ⇡c2

r

• Cross Density Of States (CDOS) ⇢(r, r0, !)= Re [e (r) e⇤ (r0)] (! ! ) n · n n n r’ X 2! ⇢(r, r , !)= Im [TrG(r, r0, !)] 0 ⇡c2

r Cazé, Pierrat, Carminati, Phys. Rev. Lett. 110, 063903 (2013) CDOS describes plasmon localization

f=20% f=50%

Topography

LDOS fluctuations

ρ 2 2 −1 ρ LDOS

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CDOS r r’

Cazé, Pierrat, Carminati, Phys. Rev. Lett. 110, 063903 (2013) Theory confirms the localization of plasmons by disorder

The intrinsic spatial coherence length measures the extent of eigenmodes

200  coh  coh 150

100 € € 50 20 40 60 80 100

Cazé, Pierrat, Carminati, Phys. Rev. Lett. 110, 063903 (2013)

• Surface plasmons : A (biased) introduction

• Spontaneous emission, local density of states and antennas

MDOS(centre,r) ; 1 film ; taille laterale 340 nm ; f=50% ; = 780 nm

4

3 2 • Spatial coherence and cross density of states 1

• Energy transfer (a simple example) Molecular Energy Transfer

Fluorescence Resonance Long-range energy transfer Energy Transfer (FRET) using surface plasmons

Donor Acceptor

silver or gold

FRET rate (Förster, 1948)

R 6 DA = 0 R 0 ✓ ◆ Sketch of the experiment

50 nm The donor excites a surface plasmon

d

d = 5 µm

d = 0

Bouchet, Cao, Carminati, De Wilde, Krachmalnicoff, PRL 116, 037401 (2016) Energy transfer through the surface plasmon

Surface plasmon Distance dependence d of acceptor fluorescence Acceptor fluorescence

` =5.4 0.9 µm et ± ET measured up to 7 µm

Bouchet, Cao, Carminati, De Wilde, Krachmalnicoff, PRL 116, 037401 (2016) Conclusion

+ N

• Plasmonics offers degrees of freedom N to control the LDOS at the nanoscale

• Probing the full LDOS Towards a full characterization of an optical antenna

MDOS(centre,r) ; 1 film ; taille laterale 340 nm ; f=50% ; = 780 nm

• Intrinsic spatial coherence and CDOS 4

3 2 1

• Long-range plasmon-assisted molecular energy transfer

Opt. Express 21, 11536 (2013) ACS Photonics 2, 189 (2015) PRL 110, 063903 (2013) PRL 116, 037401 (2016) PRL 113, 076101 (2014) Review article: Surf. Sci. Reports 70, 1 (2015)