Kauranen Erice2012 Part2 19072012 · – resonant surface modes exist • Proper approach –...
Transcript of Kauranen Erice2012 Part2 19072012 · – resonant surface modes exist • Proper approach –...
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Nonlinear optics with metals
Martti KauranenDepartment of Physics
Tampere University of Technology
Finland
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Outline
• Part II: Second-Order Response of Nanoscale Metals– higher-multipole radiation– dipole limit in effective response– nanodimers with nanogaps– local-field effects
Nanophotonics Summer School, Erice 19.7.2012 2
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Second-order nonlinear optics
• Second-order polarization
• Vector quantities E P
• Tensorial response
Nanophotonics Summer School, Erice 19.7.2012 3
(2) 2 (2) 2 2( ) ( ) i tP t E t E e
second-harmonic generation
( ) i tE t E e
(2) (2)
,:i j kijk
j kP E E P χ EE
x
y
z
Ex
Ey
(2) 2y yxx xP E
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Symmetry issues
• Spatial symmetry– symmetry operations– interdependent tensor components
• Inversion
• Surfaces and thin films– centrosymmetry broken– probes based on SHG and SFG
Nanophotonics Summer School, Erice 19.7.2012 4
(2) (2) (2)0ijk ijk lmnC
mirrorplane
r r(2) 2 (2) 2: ( ) : P χ E χ E P
E E P P
(2) 0χ
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Multipole interactions
• Hamiltonian
• Second-order response
• Magnetic and quadrupole effects– different symmetry properties
Nanophotonics Summer School, Erice 19.7.2012 5
EQBmE :H
EEχM :2mee
EEχBEχEEχP eeQeemeee ::2
EEχQ :2Qee
weak
e (m)
m (e)e
eem
electric-dipole-forbidden effects can occur
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 6
Multipolar?
• Light-matter interaction Hamiltonian
• Scattering (Heinz, Dadap, Brevet, …)
– dipolar interaction– retardation across particles
• Multipolar structures (Zyss, …)
– octupolar molecules
EQBmE :H
multipolar susceptibilities
Mie-type multipolar radiation patterns
eeeχeemχ
meeχ
eeQχQeeχ
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 7
Metal nanoparticles
• Plasmon resonances– collective oscillations of
conduction electrons
• Resonances depend on– size and shape– mutual ordering and coupling– dielectric environment
• Nanoscale variations
– local fields– ”hot spots”
– material properties– strong gradients
tieEE 0
enhanced nonlinearresponse
multipole effects
localfield
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Second-order response
• Symmetry rule– noncentrosymmetric structures needed
• Normal incidence– avoid coupling with traditional
surface nonlinearity– sample must appear noncentrosymmetric
• Basic shapes– L-shaped nanoparticles– T-shaped nanodimers with a nanogap
• Typical sample dimensions– period 400-500 nm– gold thickness 20 nm
Nanophotonics Summer School, Erice 19.7.2012 8
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 9
Theoretical descriptions
• Traditional susceptibility
• Effective medium approach?– sub-wavelength structure– resonant surface modes exist
• Proper approach– coupling of radiation fields to modes– local material properties– local nonlinear sources
,(2 ) ( ) ( )i ijk j k
j kP E E
nanoscale variations
excitation depends on experimental details
Dadap et al., PRL 83, 4045 (1999)JOSAB 21, 1328 (2004)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 10
Nonlinear response tensor
• Definition [JOptA 8, S278 (2006)]
– macroscopic input-output fields (”scattering matrix”)
• Disadvantage– specific to experiment, not the sample itself
• Advantages– avoids nanoscopic difficulties– directly measurable quantities– all multipoles implicit– electric-dipole selection rules– equivalent to effective-medium susceptibility
,(2 ) ( ) ( )i ijk j k
j kE A E E
y
x
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 11
Tensor analysis
• Fundamental beam [JOptA 8, S278 (2006)]
– QWP modulation of polarization
• Polarized SHG signals
• Fit coefficients
2 2(2 )i i x i y i x yE f E g E h E E
x y xxx yxxf A A
relative complexvalues of Aijk
0 90 180 270 360QWP Angle [degrees]
0
1
2
3
4
SH In
tens
ity [a
rb. u
nits
]
Ex
x
y
Ex
EyQWP
1060 nm170 fs
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 12
Early results
• Linear spectra[JOptA 7, S110 (2005); APL 86, 183109 (2005)]
– axis shifts and dispersion of axes– optical activity
• Second-harmonic response[Opt. Exp. 12, 5418 (2004); 14, 950 (2006)]
– ”forbidden signals”– circular-difference effects– chiral symmetry breaking due to defects– varying levels of equivalent signals
• Nonlinear microscopy of nanodots[New J. Phys. 10,013001 (2008)]
– inhomogeneous tensorial SHG and THG
x yAB
Y
X
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 13
Multipole effects
• Multipole sources– electric dipoles– magnetic dipoles– electric quadrupoles
• Higher multipoles– magnetic dipoles and electric
quadrupoles cannot be separated?– can be separated from electric
dipoles
opposite interferencein transmission and
reflectionB
p
m
E
E
E
E
E
EQ
B
B
B
BB
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Multipole experiment
• Fundamental beam– modulate polarization
with quarter-wave plate– angle of incidence
very small (~1°)
• Second-harmonic signals– s-polarized detection– compare reflected and
transmitted lineshapes
Nanophotonics Summer School, Erice 19.7.2012 14
0 45 90 135 180
0.0
0.5
1.0
QWP Angle [deg.]
SH In
tens
ity
TransmissionReflection
clear differencesobserved
[PRL 98, 167403 (2007)]
p-pol s-polQWP
PMTPMT
s-pol
1060 nm170 fs
2
2 sample
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics CFN Summer School, Bad Herrenalb 29.8.2010 15
Results of tensor analysis
• Symmetric and antisymmetric parts
• Result [PRL 98, 167403 (2007)]
sxxx xxx
s asxyy xyy xyy
s asxxy xxy xxy
A AA A A
A A A
allowed resonant
allowed nonresonant
forbidden (chiral)
transmission reflection |As| |Aas|
xxxxyyxxy
10.66 - 0.58i0.51 - 0.13i
10.37 - 0.67i0.37 - 0.26i
10.810.48
10.150.10
higher multipole amplitude ~20%
assume dipolar
x
y
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 16
Phenomenological model
• Full tensor analysis [Opt. Express 16, 17196 (2008)]
– ”forbidden” signals dominate and have strong multipole part
– chiral symmetry breaking
• Role of surface defects– non-equivalent defects at symmetrically
opposite sites– local dipolar sources retarded along the
direction of observation
/ 2 / 21 2 1 2 2 1(2 ) ( ) / 2ika ikae e ika E p p p p p p
effectivedipole effective
quadrupole
22
z
a
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Effective multipole tensors
• Effective dipolar and magnetic tensors[New J. Phys. 13, 023025 (2011)]
Nanophotonics Summer School, Erice 19.7.2012 17
metal trans. + + +
metal refl. + + -
substrate trans. + - +
substrate refl. + - -
eeexxxA mee
xxyA eyxxmeA
x
y
xy
y y
multipolar components about50% of dipolar components
eee eem meexxx xxx xxy yxxA A A A
0 45 90 135 1800.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
SH
inte
nsity
QWP rotation angle (degrees)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
New samples
• Significantly improved quality[Opt. Express 18, 16601(2010)]
– narrow extinction peaks– high-order resonances observed– stronger SHG signals
• Four equivalent signals– all lineshapes overlap
Nanophotonics Summer School, Erice 19.7.2012 18
effective dipolelimit reached
0 45 90 135 1800.0
0.2
0.4
0.6
0.8
1.0
QWP rotation angle (degrees)
Nor
mal
ized
SH
inte
nsity
path open for tailorablenonlinear metamaterials
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 19
Enhancement in nanogaps
gap-dependent FWM[Danckwerts and Novotny,
PRL 98, 026104 (2007)]
bowtie antenna[Fromm et al.,NanoLett. 4, 957 (2004)]
resonant antenna[Mühlschlegel et al.,
Science 308, 1607 (2005)]
self-similar spheresfor SHG[Li et al., PRB 72,153401 (2005)]
coupled dimers[Atay et al., NanoLett. 4, 1627 (2004)]
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 20
Designer dimers for SHG
• Symmetry rule– noncentrosymmetric structures needed
• Nanodimers [Nano Lett. 7, 1251 (2007)]
– T shape– noncentrosymmetric– vary gap between the bars– resonant with 1060 nm laser
• Expected result– only Y polarization enhanced– smallest gap leads to largest
enhancement
X
Y
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 21
Gap dependence of SHG
• SHG signals allowed by symmetry– pure polarization combinations for
normal incidence
,YXX YYYA A
X
Y
0 10 20 30 40
0
10
20
30
40
50
60
SHG
Inte
nsity
(arb
. uni
ts)
Gap (nm)
YXX YYY
nontrivial gap dependence
small gaplow response
YYY
YXX
1060 nm170 fs
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 22
Calculated local-field distributions
• Fundamental field– plasmon resonance with
the dimer– strong local-field effects– polarization conversion
• Second-harmonic field– off-resonant– weak local-field effects
local field contains new polarization
components Y incident, Y local
2 nm 23 nm
X incident, Y local
2 nm 23 nm
500 nm
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 23
Origin of SHG
• Local-field distribution– hot spots near the boundary of the dimer
• Surface nonlinearity– dominated by local component– integrate response around dimer perimeter
• Gap region– formally noncentrosymmetric– responses from top and
bottom tend to cancel nn X
Y
nnn
nnn
n
nnn
nnn
n
nnn
parts with opposite normal tend to cancel
asymmetric field distribution required
[Nano Lett. 7, 1251 (2007)]
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 19.7.2012 24
Chiral symmetry breaking
• Slanted bar orientations– reflection symmetry broken
• Circular-difference response
samples are chiral
reflection plane
2 LHC RHC
LHC RHC
I ICDRI I
0 45 90 135 180
0,0
0,2
0,4
0,6
0,8
1,0
Nor
mal
ized
SH
G In
tens
ity
QWP Angle0 10 20 30 40
0
20
40
60
80
100
120
CD
Res
pons
e (%
)Gap (nm)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
0 10 20 30 400
20
40
60
80
100
120C
D R
espo
nse
(%)
Gap (nm)
Nanophotonics Summer School, Erice 19.7.2012 25
Local-field calculations
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Part II: Conclusions
• Multipole effects– higher multipoles arise from surface defects
• Dipole limit reached– improved sample quality– multipole effects suppressed– prerequisite for nonlinear metamaterials
• Nanodimers– complicated gap dependence of SHG– symmetry and polarization of local fields
Nanophotonics Summer School, Erice 19.7.2012 26
22
0 45 90 135 1800.0
0.2
0.4
0.6
0.8
1.0 M-T M-R S-T S-R
Nor
mal
ized
SH
inte
nsity
QWP rotation angle (degrees)