Local Density of Photonic and Plasmonic States in Nanoscale Systems

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Local density of photonic and plasmonic states in nanoscale systems

Rémi CARMINATI

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

Valentina KRACHMALNICOFF Yannick DE WILDE Romain PIERRAT Da CAO Alexandre CAZE

Lionel AIGOUY P. GREDIN and M. MORTIER Spontaneous emission dynamics in nanophotonics

• Optical antenna (nano-antenna)

+ N The environment changes the dynamics of a nanosource N

• Probing photonic modes in complex media from the inside

Spontaneous emission by nanosources immersed in the medium probes the photonic modes

Central concept : photonic local density of states (LDOS)

Outline

• Photonic LDOS – Radiative versus non-radiative contributions

• Electric and magnetic LDOS

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

2 • LDOS fluctuations, localized plasmons and spatial coherence

Fluorescence dynamics in structured environments

I(t) exp( t/⌧)=exp( t) ⇠

Pertubation theory

πω 2 Γ = pge ρu (r0,ω) d ε 0 Local Density of States (LDOS)

€ Drexhage (1970) Chance, Prock, Silbey (1978) Spontaneous emission dynamics and LDOS

Γ ρ = = change in the LDOS (q uantum point of view) Γ0 ρ0

P ρ = = change in impedance (classical antenna point of view) P0 ρ0

large LDOS small LDOS Near-field scanning of the electromagnetic environment

δ ω ≈ 10 kHz ω ≈ 1015Hz λ ≈ 100 km λ ≈ 1 µm δ ≈ 50 cm δ ≈ 50 −100 nm First signals

Valentina Topography KRACHMALNICOFF Yannick DE WILDE

Fluorescence Intensity

30 nm

Fluorescence N. Bardou, S. Collin decay rate

Krachmalnicoff et al., Opt. Express 21, 11536 (2013) Theoretical modelling confirms the observed contrasts

Topography

Fluorescence Intensity

Fluorescence decay rate

Krachmalnicoff et al., Opt. Express 21, 11536 (2013) Radiative and non-radiative contributions

Silver nanoparcle Γ = ΓR + ΓNR Z Diameter 10 nm Photon emission Absorpon

€ Leading contribuons Γ at short distance 1 ΓR ∝ (k z)3 ΓNR 1 ΓNR ∝ 6 ΓR (k z)

Carmina et al., Opt. Commun. 261, 368 (2006) Castanié et al., Opt. Le. 35, 291 (2010)

€ Reciprocity theorem helps

Fluorescence intensity (vacuum) vac Iﬂuo = A ⌘0 abs Iinc(r0)

Fluorescence intensity with antenna

Iﬂuo = A ⌘e↵ abs Iexc(r0)

R ⌘ = ⌦ e↵

Reciprocity theorem (confocal geometry)

R ⌦ = BIexc(r0)

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) Comparison to numerical simulations

(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 (efective 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 (efective 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) • Photonic LDOS – Radiative versus non-radiative contributions

• Electric and magnetic LDOS

• LDOS fluctuations, localized plasmons and spatial coherence The full LDOS contains a magnetic contribution

Equilibrium electromagnetic energy density (blackbody radiation) ~! T U(r, !)=⇢(r, !) exp(~!/kBT ) 1

Calculation (fluctuation-dissipation theorem)

! ⇢(r, !)= ImTr[GE(r, r, !)+GH (r, r, !)] ⇡c2

Full LDOS

⇢(r, !)=⇢E(r, !)+⇢H (r, !)

Joulain, Carminati, Mulet, Greffet, PRB 68, 245405 (2003) Fluorescence SNOM with Eu3+- doped nanocrystal

Lionel Aigouy

Synthesis of rare-earth nanocrystals P. Gredin and M. Mortier (Chimie ParisTech, Paris) Electric and magnetic dipole transitions

Fluorescence spectra in the near field of a gold mirror

fluo Ij (r) Branching ratio j(r)= fluo Itotal(r)

Methods initially used in S. Karaveli and R. Zia, PRL 106, 193004 (2011) (no scanning probe) Distance dependence of branching ratios

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

(radiative LDOS + oscillator strength) Branching ratio maps (gold stripe on glass) Quantifying relative electric and magnetic LDOS

Proposal of the method 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) • Photonic LDOS – Radiative versus non-radiative contributions

• Electric and magnetic LDOS

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

2 • LDOS fluctuations, localized plasmons and spatial coherence

Disordered gold films

30% 100% Filling fraction

A resonant and broadband material Disordered gold films

30% 100% Filling fraction

Near-field intensity (SNOM)

λ = 720 nm

Grésillon et al., Phys. Rev. Lett. 85, 4520 (1999) Phys. Rev. B 64, 165403 (2001) Disordered gold films

30% 100% Filling fraction

PEEM EELS

Awada et al., Phys. Rev. B 85, 045438 (2012) Losquin et al. , Phys. Rev. B 88, 115427 (2013) LDOS distributions on disordered metals (gold)

Valentina KRACHMALNICOFF Yannick DE WILDE Statistical distributions of Γ (LDOS)

f = 30%

λ = 605 nm

f = 82%

Krachmalnicoff, Castanié, De Wilde, Carminati, PRL 105, 183901 (2010) LDOS fluctuations reveal spatially localized modes

Measured LDOS fluctuations

Localized ρ 2 plasmon 2 −1 modes ρ

λ = 605 nm

€

4 2 2 E(r) d r 1 1 ρ R ∫ ξ Mode Qualitative analysis IP = 2 = 2 ≈ 2 2 " 2 % ξ S extent (inverse participation ratio) E(r) d r ρ #$ ∫ &'

€ Krachmalnicoff, Castanié, De Wilde, Carminati, PRL 105, 183901 (2010) 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

• 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 CDOS reveals spatial localization of plasmon modes

f=20% f=50%

Romain PIERRAT Topography Alexandre CAZE

LDOS

CDOS r r’

Cazé, Pierrat, Carminati, PRL 110, 063903 (2013) Intrinsic spatial coherence length

The width of the CDOS defines Influence of spatially the intrinsic spatial coherence length localized modes

200

150  coh  coh 100

€ € 50 20 40 60 80 100

Cazé, Pierrat, Carminati, PRL 110, 063903 (2013) Conclusion

• Probing the full LDOS : A step towards a full characterization of an optical antenna Opt. Express 21, 11536 (2013)

PRL 113, 076101 (2014)

ACS Photonics 2, 189 (2015)

• LDOS fluctuations reveals spatially localized plasmons

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

4 CDOS describes intrinsic spatial coherence 3

2 1 PRL 105, 183901 (2010)

PRL 110, 063903 (2013)

For an overview : R. Carminati et al. , Surf. Sci. Rep. 70, 1 (2015)