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


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)


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)


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


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)


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


Tensorial responses

• Vector quantities E P• Linear response

• Second-order response


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


Dispersion and permutation

• Dispersion– response depends on wavelength– resonance enhancement– frequency-dependent susceptibility

• Permutation symmetry


(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


Symmetry issues

• Spatial symmetry– symmetry group of material

• Linear response– isotropic achiral material

– anisotropic material

• Nonlinear response– interdependent tensor components


(2) (2) (2)0ijk ijk lmnC

mirrorplane

no polarization dependence

x

y

mirrorplane

birefringence


Centrosymmetry

• Inversion

• Second-order materials– noncentrosymmetric units– noncentrosymmetric ordering– traditionally polar order

• Surface and thin films– centrosymmetry broken– probes based on SHG and SFG


r r(2) 2 (2) 2: ( ) : P χ E χ E P

E E P P(2) 0χ

D+A¯dipole moment


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


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


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


reflection plane

x

z

y

mpz

x

y

m p

• Improper transformations– reflections, inversion

• Axial vectors– transform opposite to r under

improper transformations


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


Isotropic material

• Third-rank tensors– full rotational symmetry

– permutation symmetry– centrosymmetry

• Fourth-rank tensors– full rotational symmetry– centrosymmetry


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


Surface and bulk contributions

• Surface– electric-dipole and higher-multipole response– behaves as effective electric-dipole response

• Bulk– magnetic and quadrupole response– effective polarization


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


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)


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


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


k1k2

k2trans

k2refl

z

2 ,1 ,1

1~( )cL

k k k

2 '( )bulk P E E


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


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?


controlprobe

QWP


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)


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)


Detailed analysis of BK7

• Surface-bulk interference

surface only

2 22surface bulkA A SA


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


Complete polarization study

• Isotropy

• Detailed polarization measurements– unique expansion coefficients


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


, , ,

, , ,

, , ,

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


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)


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

kauranen erice2012 part1 18072012 - università di roma · xyz yzx zxy xzy yxz zyx 00 0 eee mee eem...

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