Local density of photonic and plasmonic states in ... · Local density of photonic and plasmonic...
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Local density of photonic and plasmonic states in nanoscale systems
Rémi CARMINATI
Institut Langevin, ESPCI ParisTech, CNRS Paris, France
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People involved
Da CAO
Lionel AIGOUY P. GREDIN and M. MORTIER
Valentina KRACHMALNICOFF Yannick DE WILDE Alexandre CAZE Romain PIERRAT
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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+
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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
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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( )
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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)
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Near-field scanning of the electromagnetic environment
ω ≈10 kHzλ ≈100 kmδ ≈ 50 cm
δ
ω ≈ 1015Hzλ ≈ 1 µmδ ≈ 50−100 nm
δ
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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
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Theoretical modelling confirms the observed contrasts
Topography
Fluorescence Intensity
Fluorescence decay rate
Krachmalnicoff et al., Opt. Express 21, 11536 (2013)
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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
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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
)
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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)
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Comparison to numerical simulations
Experiment (effective rates) Theory (effective rates)
Cao et al. , ACS Photonics 2, 189 (2015)
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• Photonic LDOS – Radiative versus non-radiative contributions • Electric and magnetic LDOS
• LDOS fluctuations, localized plasmons and spatial coherence
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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, !)
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Fluorescence SNOM with Eu3+- doped nanocrystal
Lionel Aigouy
Synthesis of rare-earth nanocrystals
P. Gredin and M. Mortier (Chimie ParisTech, Paris)
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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)
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Distance dependence of branching ratios
Aigouy , Cazé, Gredin, Mortier, Carminati, PRL 113, 076101 (2014)
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Theory Model
(radiative LDOS + oscillator strength)
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Branching ratio maps (gold stripe on glass)
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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)
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• 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
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Disordered gold films
Filling fraction 30% 100%
A resonant and broadband material
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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)
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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)
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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
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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)
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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)
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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
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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)
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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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