Introduction to Nonlinear Optics - Portal IFSCfotonica/presentations/talks/2010/ta... · 2013-03-26 · f f thi t tifor a copy of this presentation ... Introduction to nonlinear optics

Class 1

Introduction to Nonlinear Optics

Prof. Cleber R. Mendonca

http://www.fotonica.ifsc.usp.br

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Outline

Linear optics

Introduction to nonlinear opticsp

Second order nonlinearities

Third order nonlinearitiesThird order nonlinearities

Two-photon absorption

Conclusions

Linear optics vs Nonlinear optics

Optics is a branch of physics that describes the behavior and properties of light and the interaction of light with matter Explains optical phenomenaand the interaction of light with matter. Explains optical phenomena.

Nonlinear OpticsTh b h f ti th t d ib ti l h th t hThe branch of optics that describes optical phenomena that occur when very intense light is used

Linear optics

Maxwell equations

ρ: charge densityρ: charge densityJ: current density

P: electric polarizationM: magnetization

Linear optics

P e M: response of the media to the applied field

Electric Polarization

pp

Linear optics

Maxwell equations can be combined, leading to a equation describing the electromagnetism

Constitutive relationshipsConstitutive relationships

EPrr

rrχ=

response of the media

EJ

HM mrr

σ

χ

=

=p

to the applied field

Linear optics

wave equation ( )0;0 == Jr

ρ( );ρ

left rightleft

Matter light interactionLight propagation in vacuum

right

Matter-light interactionLight propagation in vacuum

Linear optics

Erad.<< Einter.

harmonic oscillatorharmonic oscillator

electron on a spring

kme

k=0ω

oscillation frequency

k em0ω

Linear optics

electron on a spring

equation of motion

Linear optics

harmonic oscillator

Steady state: electron oscillates at driving frequency

Linear optics

Oscillating dipole

Polarization oscillator

N 2 /( ) E

imNetP

ωγωω −−=

20

20

2 /)(

EP χ=linear response

( )

EP χ=

Linear optics

by comparison

( )χi

mNe=

22

2 /~( ) ωγωω i−− 2

020 which is a complex number

then

where and are the real and imaginary parts of the complex index of refraction

refraction absorption

Linear optics

Linear optical process

absorption refractionabsorption

α0 does not depend on light intensity n0 does not depend on light intensity

refraction

absorption of 10 % index of refraction 1.3

Nonlinear optics

high light intensity

Erad Einter


Erad.~ Einter.

How high should be the light intensity ?

Nonlinear optics

Inter-atomic electric field cw laser

P = 20 Wwo = 20 μm 2

0

2wPI

π=

I = 3 × 1010 W/m2

e = 1.6 × 10-19 Cr ~ 4 År 4 Å

E ~ 1 × 1010 V/m Eo= 4 × 106 V/m

Nonlinear optics

Inter-atomic electric field pulsed laserInter atomic electric field pulsed laser

I 10 GW/cm2I = 10 GW/cm2 = 10 × 1013 W/m2

E ~ 1 × 1010 V/m

E 1 108 V/Eo= 1 × 108 V/m

Nonlinear optics


Erad.~ Einter.

anharmonic oscillator

anharmonic term

Nonlinear optics


ener

gypo

tent

ial

charge displacement

P

nonlinear polarization response

E...EEEP )()()( +χ+χ+χ= 33221

Nonlinear optics


Erad.~ Einter.


nonlinear polarization response

...EEEP )()()( +χ+χ+χ= 33221

Nonlinear optics

wave equation ( )0;0 == Jr

ρ

left right

Matter-light interactionLight propagation in vacuum

Nonlinear optics

li i f th l i tinonlinear expansion of the polarization

)3()2()1(rrr

Mrrrr

...EEEEE:E.P )3()2()1( +++= Mχχχ

linear SHG THGK ff tprocesses Kerr effect

Nonlinear optics

nonlinear expansion of the polarization

Nonlinear Optics

Second order processes )2(χ

ω11

χ(2)ω2

ω1+ω2χ2 ω1−ω2

– If ω1= ω 2If ω1 ω 2

– second harmonic generation: 2 ω0– optical retificatio: 0

Nonlinear Optics

Second order processes )( 2χ

Second Harmonic GenerationSecond Harmonic Generation

2ω 2ω

λ = 1064nm λ = 532nm

Second Harmonic Generation

)( 2χχ

1- higher energy light

2- transparent material2 transparent material

Second Harmonic Generation

)( 2χ

Phase Matching

( ) ( )2( ) ( )ωω 2vv =

Nonlinear Optics

in medium with inversion symmetryy y

and consequentlyq y

Nonlinear Optics

Third order processes )3(χ

ω1ω1+ω2+ω3

χ(3)ω2 ω1−ω2−ω3

ω1−ω2+ω3ω3

– If ω1= ω 2= ω 3If ω1 ω 2 ω 3

– Third harmonic generation: 3 ω– Self phase modulation: ω

Third Harmonic Generation χ(3)

ω 3ω

ω

Nonlinear media

Nonlinear Optics

Third order processes 02 =)(χ )3(χ

Nonlinear polarizationp

Third order polarizationThird order polarization

Nonlinear Optics

consequently

and

Kerr media

Innn 20 +=

Nonlinear Optics

)( 3χThird order processes

)(n 32 χ≈

K di

n2 χ≈

Kerr media:

Innn 20 += Innn 20 +

Index of refraction depends on the light intensity

Self phase modulation

χ( )2 0=Kerr media: centre symmetric:

Innn 20 += 33 EP )(NL χ=

n2>0 Material behaves as a convergent lensx d

f

2

f

Sample

y z

Sample

Optical switching

ti 10 15response time: 10-15 s

1×10-9 1×10-15

1GHz → 1 THz

response time

1 million times faster

Nonlinear optics

2ω

Nonlinearω ?

2ω

Nonlinear material ω ?

3ω

• Intense light induced nonlinear response Self actionin the material• Material change the light in a nonlinear

way

Self action effect

way

Nonlinear Optics

χ(3) is a complex quantity

Third order processes: χ(3)

Refractive process: Absorptive process:Refractive process:

Innn 20 +=

Absorptive process:

Iβαα += 020 β0

• self-phase modulation• lens-like effect

• nonlinear absorption• two-photon absorptionp p

Two-photon absorption (2PA) process

Phenomenon does not described for the Classical Physics and does not observed until the development of the Laser.

1-photon absorption(Linear)

2-photon absorption(Nonlinear)

Theoretical model: Maria Göppert-Mayer, 1931

Two photons from an intense laser light beam are simultaneously absorbedp g yin the same “quantum act”, leading the molecule to some excited state withenergy equivalent to the absorbed two photons.

two-photon absorption

Iβαα += 0

2ω ω Abs

Iβαα +0

ωω

λ

Applications:optical limiting

fl ifluorescence microscopy

microfabrication

two-photon fluorescence

ω

light emissionfl

Iβαα += 0

ωfluorescence

localization of the excitation with 2PA

dilute solution of fluorescent dye

2PA

1PA1PA

spatial confinement of excitation

R di d i t it f f d b

excitation profile along zRadius, area and intensity of focused beam

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

00 1

zz)z( ωω

⎠⎝ 0

2

0

20

2 1 ⎟⎟⎠

⎞⎜⎜⎝

⎛+==

zz)z(A πωπω0 ⎠⎝

220 1

11

⎟⎟⎞

⎜⎜⎛

+

=∝=zAAt

E)z(I

πω0

0 1 ⎟⎟⎠

⎜⎜⎝

+z

πω

Normalized excitation rates(ignoring beam atten ation)(ignoring beam attenuation)

2

10

−

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

z)(I)z(I

one photon00 ⎟

⎠⎜⎝ z)(I

4

1−

⎟⎞

⎜⎛ z)z(I

p

two photon

0

10 ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

zz

)(I)z(I

Class 2

St d i ti l li itiStudying optical nonlinearities



Investigating nonlinear optical materials

Very intense light: femtosecond pulses

Ti:Sapphire lasers

100 fs 50 fs 20 fs 1 fs = 10-15 s

1 fs 1s

Laser intensities ~ 100 GW/cm2

1 x 1011W/cm2

Laser pointer: 1 mW/cm2 (1 x10-3 W/ cm2)

Organic materials• Flexibility to tune the nonlinear optical response by manipulating the molecular structure

• π-conjugated structures

σσ

C CC C Conjugation: alternation of single and doubles bonds

π

C CC C j g gbetween carbon atoms

Conjugation π-conjugation

σ bond: forms a strong chemical bond; localized

π bond: weaker bond; out of the C atoms axis

“Free electrons” that are easier to move under an applied electric filed

π bond in conjugated system: delocalized electrons

high optical nonlinearities

χ(3)

Research

• Understanding the physical principles behind two-photon absorption

• Understanding the relationship between molecular structure and two-photon absorption

• Developing molecules with high optical nonlinearities that can be p g g pused for application

Z-scan

closed aperture Z-scan

Iz<0z<0 Innn 20 +=

z>0

1 04ttace

z>0

1.04ance

1.00

1.04

zed

Tran

smi

1.00

1.04

aliz

ed tr

ansm

itta

InT 2∝Δ

Z-10 -5 0 5 10

0.96

Nor

mal

i

Z-10 -5 0 5 10

0.96

norm

a

Nonlinear refraction

AminoacidsC

-COO C-COO

1.2

e

C

C2CH

CH

COO

C

C2CH

CH

COO

1.0

1.1

mitâ

ncia

trans

mitt

ance C 2CH

H C 2CHH

L-Proline

0.9

Tran

smno

rmal

ized

t

⎟⎞

⎜⎛ΔΦΔ LIT 240604060 π

-5 0 50.8

Z (mm)

⎟⎠⎞

⎜⎝⎛=ΔΦ=Δ LIn..Tpv 020 40604060

λπ

150 fs 100 GW/cm2)(n 3

2 χ∝775 nm 2 χ

Nonlinear refraction

L-Proline

C

C2CH

-COO

C

C2CH

-COO

CC 2CH

HC

C 2CHH

Z-scan (nonlinear absorption)

open aperture Z-scan

z<0z<0

I)I( 0 βαα +=

IT β∝Δz>0

1.04

mitt

ace

z>0

1.04

mitt

ance

IT βΔ

( )[ ]0 m

0.96

1.00

aliz

ed T

rans

0.96

1.00

rmal

ized

tran

sm ( )[ ]( )∑

∞

= +

−=

02/3

0

10,

)(m

m

mzq

zT

Z-10 -5 0 5 10N

orm

Z-10 -5 0 5 10

nor

( )20

200 1 z/z/LI)t,z(q += β

two-photon absorption cross-section

A pair of photon incident on a molecule

For two-photon absorption to occur, a pair of photons must be incident within a cross sectional area and within the lifetime of the virtual sate, τ ∼ 10-15 s

Nonlinear spectrum

Iβnonlinear absorption

intense laser (ultra short pulses)Iβαα += 0intense laser (ultra short pulses)

discrete λ s

δ(λ) n2(λ)

nonlinear spectrum ???nonlinear refraction

( ) 2( )

p

Innn 20 +=

Nonlinear absorption spectrum

Optical parametric amplifier

460 - 2600 nm120 f≈ 120 fs

20-60 μJ


1.00

ttanc

e

DR13

0.95700 nm750 nm860 nm930 nmze

d Tr

ansm

it

N

NO2NN

CH2CH3

CH2CH2OH

Cl0.90

930 nm1010 nm

Nor

mal

iz Cl

( )[ ]( )∑

∞

= +

−=

02/3

0

10,

)(m

m

mzq

zT-0.5 0.0 0.5

0.85

Z / cm ( )

Iβαα + Iβαα += 0 β: two-photon absorption coefficient

Azoaromatic samples

N NAZO

N N NH2H2N DIAMINO

N NH2N

N N NO2H2N

p-AMINO

DO3

N N NO2N

Cl

DR19ClH2CHO H2C

H2CHO H2C

H2CHO H2C

N N NO2N

N N NO2N

ClDR19

DR13

H2CHO H2C

H2CHO H2C

H3C H2C

N N NO2N DR13

DR1

H2CHO H2CN N NO2N

H3C H2C

PsuedostilbenosA b

0 3

0.6

0.9DO3

300

600

0.9PAMINO

600

Aminoazobenzenos

0.6

0.0

0.3

DR1

400

0

0.3

0.6

M)

banc

e

300

0.90.0

0.3

600DR19

0

200

0 3

0.6

0.0

DIAMINO δ(G

M

300

600Abs

orb 0

0.0

0.3

0.6

0.6

0

300

DR13

400 600 800 10000.0

0.3

λ (nm)

0

300

0 0

0.3

Abs

orba

nce

0

300

600

DR13δ

(GM

)λ (nm)

( ) ⎥⎤

⎢⎡2 AAν

0.3

0.6

0.0

DR19-Cl

300

600

0 ( )( ) ( ) ( ) ⎥

⎥⎦⎢

⎢⎣ +−

++−+−

∝2

0f2

0f

22

0f2

0f

120i

20i 2211

2A

2A

ΓννΓννΓννννδ

400 600 800 10000.0

λ (nm)

0

Planarity of the π-bridge

Thermally induced torsion in the molecular structure

Molecular design strategy

• Increasing the molecular conjugation

• Adding charged groups to the molecule

• Keep molecular planarityKeep molecular planarity

Increasing the conjugation

π-bridge

I i h i l li iπ-bridge Increase in the optical nonlinearity

Increasing the conjugationπ-bridge

Increasing the π-conjugation

π-bridge

Donor and acceptor groups

electron donor electron acceptor

e- e-

b idπ-bridge

R+R

R-

Incorporating electron donor and acceptor groups in a predictable way leads to an enhancement of the optical nonlinearityto an enhancement of the optical nonlinearity

Planarity of the π-bridge

Perylene compounds are very planar molecules, which explains its high optical nonlinearities

Class 3

A li ti f li tiApplications of nonlinear optics



Sculpturing with light: micro/nanofabrication i lt h t lusing ultrashort pulses

laser microfabrication

focus laser beam on material’s surface




surface microstructuring


examples of fabricated surfaces

20 μm

40 μm

fs-laser microfabrication

photon energy < bandgap

nonlinear interaction



Egap

Ef = hν



Egap

Ef = hν

multiphoton absorptionp p


focus laser beam inside material


curved waveguides inside glass


3D waveguides in PMMA

cross-section view

Optics Express, 16, 200-205 (2008) Applied Surface Science, 254, 1135–1139 (2007)


Novel concept:

build a microstructure using fs-laser and nonlinear optical processes

two-photon polymerization

photonic crystal – J. W. Perry

20 µmµ

two-photon polymerization

applicationsapplications

• i h i• micromechanics

• waveguideswaveguides

• microfluidics

• biology

• optical devices

Outline

• two-photon polymerization microfabricationp p y

• microstructures containing MEH-PPV

• waveguiding the MEH-PPV emission

• other studies

• summarysummary


)( 3χThird order processes

2ω ω

ω

ance

abso

rba

Iβαα += 0 wavelength0 wavelength


Nonlinear interaction provides spatial confinement of the excitation

fs-microfabrication

0αα = Iβαα += 0


spatial confinement of excitation

Two-photon polymerization

Monomer + Photoinitiator → Polymer

light

Photoinitiator is excited by two-photon absorption

22 IR PA ∝

The polymerization is confinedto the focal volume.

High spatial resolution

Two-photon polymerization setup

Laser Ti:sapphire laser oscillator

Scanningi

• 130 fs• 800 nm

y

BeamExpansion

Mirror • 76 MHz• 20 mW

x

CCDcamera

resinspacer

glass (150 micron)

glass (150 micron)ObjectiveObjective

Illumination

40 x0.65 NA

z

Illumination

Resin preparation

M A M B

Monomers

Monomer A Monomer B

reduces the shrinkage upon polymerization gives hardness to the polymeric structure

Ph t i iti tPhotoinitiator

Lucirin TPO-L

Appl. Phys. A, 90, 633–636 (2008)


After the fabrication, the sample isimmersed in ethanol to wash away anyunsolidified resin and then dried


Microstructures fabricated by two-photon polymerization

50 μm50 μm50 μm

20 µm 20 μm20 μm20 μm20 µm

Microstructures containing active compounds

monomer monomer

Optical active dye Active Polymer

Microstructures containing MEH-PPV

MEH-PPVMEH PPV

FluorescenceElectro

LuminescentConductive


MEH-PPV: up to 1% by weightlaser power 40 mW

a - Scanning electron microscopy

b,c - Fluorescence microscopy of the microstructure with the excitation OFF (b) and ON (c)


d - Emission of the microstructure (black line) and of a film with the same composition (redline)


Fluorescent confocal microscopy images in planesseparated by 16 μm in the pyramidal microstructureseparated by 16 μm in the pyramidal microstructure.

Appl. Phys. Lett 95, 113309 (2009)


waveguiding of the microstructure fabricated onporous silica substrate (n= 1 185)porous silica substrate (n 1.185)

Applications: micro-laser; fluorescent microstructures; conductive microstructures

Other studies

• 3D cell migration studies in micro-scaffolds SEM of the scaffolds

110 µm pore size

52 µm pore size

Top viewp

110, 52, 25, 12 µm pore sizepore size

Side view

25, 52 µm pore size

Other studies

• 3D cell migration studies in micro-scaffolds

Advanced Materials, 20, 4494-4498 (2008)

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Introduction to Nonlinear Optics - Portal IFSCfotonica/presentations/talks/2010/ta... · 2013-03-26 · f f thi t tifor a copy of this presentation ... Introduction to nonlinear optics