Kauranen Erice2012 Part1 18072012 - Università di Roma · xyz yzx zxy xzy yxz zyx 00 0 eee mee eem...
Transcript of Kauranen Erice2012 Part1 18072012 - Università di Roma · xyz yzx zxy xzy yxz zyx 00 0 eee mee eem...
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 Nanophotonics Summer School, Erice 18.7.2012 2
Where is Tampere?
TAMPERE
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 3
Optics in Tampere
• Tampere University of Technology– Department of Physics (applied optics, nonlinear optics)– ORC (semiconductors, ultrafast optics, nanostructured materials)– Department of Chemistry (photochemistry)
• Spinoff companies– Coherent (diode lasers)– Modulight (diode lasers)– Liekki (nanoparticle doped optical fibers)– Corelase (fiber lasers for materials processing)– Cavitar (pulsed illumination and visualization)– Oseir (industrial imaging)– Epicrystals (laser sources for projection displays)– Reflekron (customized SESAMs)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 4
Acknowledgments
• Research group– several students and postdocs over several years
• Optoelectronics Research Centre (TUT)
• University of Eastern Finland– Profs. Markku Kuittinen, Yuri Svirko, Jari Turunen
• Other– John Sipe (Toronto), Martin Albers (VTT), ….
• Funding– Academy of Finland– Finnish Funding Agency for Technology and Innovation– Ministry of Education of Finland (Research and Technology
Program on Nanophotonics)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Outline
• Part I: Multipole Effects in Nonlinear Optics– electric-dipole and higher-multipole nonlinearities– surface and bulk effects
• Part II: Second-Order Response of Nanoscale Metals– higher-multipole radiation– local-field effects
• Part III: Present challenges– tailorable nonlinear response– surface vs. bulk origin of metal nonlinearity– towards metamaterials with optimized nonlinear response
Nanophotonics Summer School, Erice 18.7.2012 5
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 6
Optical response of materials
• Optical field
• Linear optics
modified field
oscillating field oscillating polarization
radiation
( ) . .i tE t E e c c
(1) (1)( ) ( ) i tP t E t E e
polarizationP(t)
E(t)opticalfield
modifiedfield
E’(t)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 7
Nonlinear optics
• Material polarization
• Second order
• Third order– third harmonic– original frequency
(2) 2 (2) 2 2( ) ( ) i tP t E t E e
(1) (2) 2 (3) 3( ) ( ) ( ) ( ) ...P t E t E t E t
second-harmonic generation
( ) i tE t E e
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Tensorial responses
• Vector quantities E P• Linear response
• Second-order response
Nanophotonics Summer School, Erice 18.7.2012 8
x
y
z
Ex
Ey
x
y
z
P
E
(2) 2y yxx xP E
(1) (1)i jij
jP E P χ E
(2) (2)
,:i j kijk
j kP E E P χ EE
polarization dependentoptical responses
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Dispersion and permutation
• Dispersion– response depends on wavelength– resonance enhancement– frequency-dependent susceptibility
• Permutation symmetry
Nanophotonics Summer School, Erice 18.7.2012 9
(2) (2)2 21 2 1 21 1( ; , ) ( ; , )k kj ji i
(2) (2)(2 ; , ) (2 ; , )ikj ijk SHG
n
(2)1 2 1 2
1 2 1
1( ; , ) ...( )( )ijk
ca ba
a
b
c
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Symmetry issues
• Spatial symmetry– symmetry group of material
• Linear response– isotropic achiral material
– anisotropic material
• Nonlinear response– interdependent tensor components
Nanophotonics Summer School, Erice 18.7.2012 10
(2) (2) (2)0ijk ijk lmnC
mirrorplane
no polarization dependence
x
y
mirrorplane
birefringence
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Centrosymmetry
• Inversion
• Second-order materials– noncentrosymmetric units– noncentrosymmetric ordering– traditionally polar order
• Surface and thin films– centrosymmetry broken– probes based on SHG and SFG
Nanophotonics Summer School, Erice 18.7.2012 11
r r(2) 2 (2) 2: ( ) : P χ E χ E P
E E P P(2) 0χ
D+A¯dipole moment
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 12
Optical activity
• Chiral objects– lack of reflection symmetry– cannot be superimposed on its mirror
image– occur in two mirror-image forms
(enantiomers)
• Optical activity– optical effects associated with chirality– different response to circular
eigenpolarizations– polarization rotation– circular dichroism– reverse sign between the
enantiomers
chiralmedium
k
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics, Erice 11-17.7.2010 13
Isotropic materials
• Electric-dipole response– effective susceptibility
• Sum-frequency generation– arabinose solution (Rentzepis 1966)– recently reinvestigated
(2) (2)~effxyz xzy
chirality required
second-harmonic forbidden
1 2 1 2( ) ( ) ( )eff P E E
chiralmedium
k
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 14
Multipole interactions
• Hamiltonian
• Linear response
• Second-order response
EQBmE :H
EχM me EχBχEχP :eQemee
EχQ Qe
EEχM :2mee
EEχBEχEEχP eeQeemeee ::2
EEχQ :2Qee
weak
e (m)
m (e)e
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Electric and magnetic quantities
• Proper transformations– rotations
• Polar vectors– transform as r
• Electric quantities– polar vectors– odd under parity– even under time reversal
• Magnetic quantities– axial vectors– even under parity– odd under time reversal
Nanophotonics Summer School, Erice 18.7.2012 15
reflection plane
x
z
y
mpz
x
y
m p
• Improper transformations– reflections, inversion
• Axial vectors– transform opposite to r under
improper transformations
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 16
Multipole symmetries
• Second-harmonic generation
• Magnetic and quadrupole tensors– symmetry properties are different from those of the electric-
dipole tensor
lkjeeQijklkj
eemijkkj
eeeijki EEBEEEP
axial 4th rank
electric-dipole-forbiddeneffects can occur
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Isotropic material
• Third-rank tensors– full rotational symmetry
– permutation symmetry– centrosymmetry
• Fourth-rank tensors– full rotational symmetry– centrosymmetry
Nanophotonics Summer School, Erice 18.7.2012 17
xyz yzx zxy
xzy yxz zyx
0 0
0
eee mee
eem
χ χ
χ
0, 0, 0iijj ijij ijji
iiii iijj ijij ijji
SHG
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Surface and bulk contributions
• Surface– electric-dipole and higher-multipole response– behaves as effective electric-dipole response
• Bulk– magnetic and quadrupole response– effective polarization
Nanophotonics Summer School, Erice 18.7.2012 18
2 :surface surface P χ E E
2 :bulk mee M χ E E 2 :Qeebulk
Q χ E E2 : eeQbulk eem P χ E B χ E E
z
2 2 22 ( / 2 )eff i c P P Q M
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 19
Isotropic material
• Effective bulk polarization
• Bulk parameters
2 ( ) ( ) '( )bulk P E E E E E E
/ 2 ( / 2 )
' 2 ( / )
eeQ Qee Qeexxyy xyyx xyxyeeQ Qee eemxyyx xxyy xyzeeQ Qee eemxyyx xyxy xyz
ic
ic
Progress in Optics 51, 69 (2008)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 20
Isotropic material
• Effective bulk polarization
• Surface– effective electric-dipole tensor
– isotropic surface symmetry
, ,s s dipolar s multipolar χ χ χ
2 ( ) ( ) '( )bulk P E E E E E E
0 Esurface
separable bulk contribution
,s eff szzz zzzχ χ ,s eff s
zxx zxxχ χ ,s eff s
xxz xxzχ χmeasurable components
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Separable bulk contribution
• Effective polarization– two input beams required– coherent growth in the bulk
• Separation (Shen 1980’s – 2000’s)
– different bulk and surface spectra in SFG– different coherence lengths in reflection and transmission– difficult due to dispersion and calibration problems
Nanophotonics Summer School, Erice 18.7.2012 21
k1k2
k2trans
k2refl
z
2 ,1 ,1
1~( )cL
k k k
2 '( )bulk P E E
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 22
Polarization signatures
• s-polarized signals– unique signatures– not sensitive to linear optics
• Isotropic bulk
• Isotropic surface
21 2 1 22
1
sin( )sin
surface surfaceyyz p s s pA A A A A
2 1 2 1 2'( )bulkp s s pA A A A A
PRB 72,033412 (2005)
xy
z
spp
s
A1
A2 s
p
s p
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Experiment: Two-beam SHG
• Control beam– polarization fixed
• Probe beam– polarization varied
• SHG signals– reflected and transmitted
• Samples– poled polymer film surface dominates
– BK7 glass surface-bulk competition?
Nanophotonics Summer School, Erice 18.7.2012 23
controlprobe
QWP
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 24
Results for BK7
angle of quarter-wave plate (deg)-90 -45 0 45 90
SHG
sign
al (a
.u.)
0.2
0.6
1.0
SHG
sign
al (a
.u.)
0.2
0.6
1.0
(a)
(b)
angle of quarter-wave plate (deg)-90 -45 0 45 90
SHG
sign
al (a
.u.)
0.2
0.6
1.0
SHG
sign
al (a
.u.)
0.2
0.6
1.0
(a)
(b)
surface model
surface model
surface model
bulkmodel
poled polymer BK7 surface
PRB 72, 033412 (2005)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 25
Detailed analysis of BK7
• Surface-bulk interference
surface only
2 22surface bulkA A SA
angle of quarter-wave plate (deg)-90 -45 0 45 90
SHG
sign
al (a
.u.)
0.2
0.6
1.0
SHG
sign
al (a
.u.)
0.2
0.6
1.0
(a)
(b)
surface+bulk 0.08S
surface+bulkbulk only
6.54S
0.12 mcL
10 mcL
reflection
transmission
bulk contribution scaleswith coherence length
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
Complete polarization study
• Isotropy
• Detailed polarization measurements– unique expansion coefficients
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solve tensor components
2 , 1 2 1 2s sps p s ssp s pA f A A f A A
2 , 1 2 1 2p ppp p p pss s sA f A A f A A
, , ,( , , , ')s eff s eff s effijk ijk zzz zxx xxzf f
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics
, , ,
, , ,
, , ,
6.4
0.49
1
s eff s dipolar s multipolarzzz zzz zzzs eff s dipolar s multipolarzxx zxx zxxs eff s dipolar s multipolarxxz xxz xxz
χ χ χ
χ χ χ
χ χ χ
Nanophotonics Summer School, Erice 18.7.2012 27
Tensor analysis of BK7 glass
• Effective surface components
• Separable bulk contribution
• Calibration against quartz
' 1.01 Opt. Express 15, 8695 (2007)Opt. Express 16, 8704 (2008)
TAMPERE UNIVERSITY OF TECHNOLOGYDepartment of Physics Nanophotonics Summer School, Erice 18.7.2012 28
Summary
• Material symmetry– strong influence on second-order nonlinear properties– electric-dipole and higher-multipole effects– polarization effects
• Surface and bulk contributions– unambiguous separation by two-beam SHG– magnetic effects important in the bulk of glasses
• Future work– models with various multipoles explicit– materials with enhanced multipolar responses