Local density of photonic and plasmonic states in ... · Local density of photonic and plasmonic...
Transcript of Local density of photonic and plasmonic states in ... · Local density of photonic and plasmonic...
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
1
0.8
0.6
0.4
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
0.4
0.6
0.8
1
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
1
2
3
4