Local density of photonic and plasmonic states in nanoscale systems

Rémi CARMINATI

Institut Langevin, ESPCI ParisTech, CNRS Paris, France

People involved

Da CAO

Lionel AIGOUY P. GREDIN and M. MORTIER

Valentina KRACHMALNICOFF Yannick DE WILDE Alexandre CAZE Romain PIERRAT

Spontaneous emission dynamics in nanophotonics

•  Optical antenna (nano-antenna) The environment changes the dynamics of a nanosource

•  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)

N

N+

Outline

•  Photonic LDOS – Radiative versus non-radiative contributions •  Electric and magnetic LDOS

•  LDOS fluctuations, localized plasmons and spatial coherence

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

1

2

3

4

Fluorescence dynamics in structured environments

Drexhage (1970) Chance, Prock, Silbey (1978)

d

I(t) ⇠ exp(�t/⌧) = exp(��t)

Pertubation theory

Local Density of States (LDOS)

€

Γ =πωε 0

pge2ρu r0,ω( )

Spontaneous emission dynamics and LDOS

ΓΓ0

= ρρ0

= change in the LDOS (quantum point of view)

large LDOS small LDOS

PP0

= ρρ0

= change in impedance (classical antenna point of view)

Near-field scanning of the electromagnetic environment

ω ≈10 kHzλ ≈100 kmδ ≈ 50 cm

δ

ω ≈ 1015Hzλ ≈ 1 µmδ ≈ 50−100 nm

δ

First signals

Topography

Fluorescence Intensity

Fluorescence decay rate

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

30 nm

N.  Bardou,  S.  Collin    

Valentina KRACHMALNICOFF Yannick DE WILDE

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

Z Silver  nanopar3cle  Diameter  10  nm  

Carmina3  et  al.,  Opt.  Commun.  261,  368  (2006)  Castanié  et  al.,  Opt.  LeD.  35,  291  (2010)  

€

Γ = ΓR + ΓNR

Photon  emission   Absorp3on  

Γ

ΓR  ΓNR  

Leading  contribu3ons  at  short  distance  

€

ΓR ∝1k z( )3

ΓNR ∝1k z( )6

Reciprocity theorem helps Fluorescence  intensity  (vacuum)  

Cao et al. , ACS Photonics 2, 189 (2015)

Reciprocity  theorem  (confocal  geometry)  

�R⌦

= BIexc

(r0

)

Measured  parameters  

Effec3ve  radia3ve  rate  

Apparent  non-­‐radia3ve  rate  

�R⌦

�̃NR⌦ = �� �R

⌦

Ivac

fluo

= A ⌘0

�abs

Iinc

(r0

)

Fluorescence  intensity  with  antenna  

⌘e↵ =�R

⌦

�

Ifluo

= A ⌘e↵

�abs

Iexc

(r0

)

Characterizing the influence of an optical antenna Intensity Decay rate

Effective radiative rate

Apparent non-radiative rate

Cao et al. , ACS Photonics 2, 189 (2015)

Comparison to numerical simulations

Experiment (effective rates) Theory (effective rates)

Cao et al. , ACS Photonics 2, 189 (2015)

mm

0 0.2 0.4 0.6

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0.2

00.260.280.30.320.340.36

mm

0 0.2 0.4 0.6

1

0.8

0.6

0.4

0.2

00.640.660.680.70.720.74

mm

mm

(a) (b)

(c) (d)

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

0.240.260.280.30.320.34

0 0.2 0.4 0.60

0.2

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0.660.680.70.720.740.76

•  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

Joulain, Carminati, Mulet, Greffet, PRB 68, 245405 (2003)

Equilibrium electromagnetic energy density

(blackbody radiation)

T   U(r, !) = ⇢(r, !)

~!

exp(~!/kBT )� 1

Calculation (fluctuation-dissipation theorem)

Full LDOS

⇢(r, !) =!

⇡c2ImTr[GE(r, r, !) + GH(r, r, !)]

⇢(r, !) = ⇢E(r, !) + ⇢H(r, !)

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

Branching ratio �j

(r) =Ifluo

j

(r)

Ifluo

total

(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

•  LDOS fluctuations, localized plasmons and spatial coherence

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

1

2

3

4

Disordered gold films

Filling fraction 30% 100%

A resonant and broadband material

Disordered gold films

Filling fraction 30% 100%

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

Filling fraction 30% 100%

Awada et al., Phys. Rev. B 85, 045438 (2012)

PEEM EELS

Losquin et al. , Phys. Rev. B 88, 115427 (2013)

LDOS distributions on disordered metals (gold)

λ = 605 nm

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

Statistical distributions of Γ (LDOS)

f = 30% f = 82%

Valentina KRACHMALNICOFF Yannick DE WILDE

LDOS fluctuations reveal spatially localized modes

λ = 605 nm

€

ρ2

ρ 2 −1

Measured LDOS fluctuations

Localized plasmon modes

Qualitative analysis (inverse participation ratio)

RIP =E(r)

4d 2r∫

E(r)2d 2r∫"#$

%&'

2=1ξ 2

≈1S

ρ2

ρ2

€

ξ Mode extent

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

Beyond LDOS

•  Density Of States (DOS)

•  Local Density Of States (LDOS)

•  Cross Density Of States (CDOS)

r’

r

r

⇢(r, !) =P

n |en(r)|2 �(! � !n)

⇢(r, r0, !) =2!

⇡c2Im [Tr G(r, r0, !)]

⇢(r, !) =2!

⇡c2Im [Tr G(r, r, !)]

⇢(r, r0, !) =X

n

Re [en(r) · e⇤n(r0)] �(! � !n)

⇢(!) =1V

X

n

�(! � !n)

CDOS reveals spatial localization of plasmon modes

f=20% f=50%

Topography

LDOS

CDOS

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

r’

r

Alexandre CAZE Romain PIERRAT

Intrinsic spatial coherence length

20 40 60 80 100

50

100

150

200

The width of the CDOS defines the intrinsic spatial coherence length

€

coh

€

coh

Influence of spatially localized modes

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

Conclusion

•  Probing the full LDOS : A step towards a full characterization of an optical antenna

•  LDOS fluctuations reveals spatially localized plasmons CDOS describes intrinsic spatial coherence

Opt. Express 21, 11536 (2013)

PRL 113, 076101 (2014)

ACS Photonics 2, 189 (2015)

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

PRL 105, 183901 (2010)

PRL 110, 063903 (2013)

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

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2

3

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