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Class 1
Introduction to Nonlinear Optics
Prof. Cleber R. Mendonca
http://www.fotonica.ifsc.usp.br
f f thi t tifor a copy of this presentation
www fotonica ifsc usp brwww.fotonica.ifsc.usp.br
presentations
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
high light intensity
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
high light intensity
Erad.~ Einter.
anharmonic oscillator
anharmonic term
Nonlinear optics
anharmonic oscillator
ener
gypo
tent
ial
charge displacement
P
nonlinear polarization response
E...EEEP )()()( +χ+χ+χ= 33221
Nonlinear optics
high light intensity
Erad.~ Einter.
anharmonic oscillator
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
Prof. Cleber R. Mendonca
http://www.fotonica.ifsc.usp.br
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
Two-photon absorption
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
Prof. Cleber R. Mendonca
http://www.fotonica.ifsc.usp.br
Sculpturing with light: micro/nanofabrication i lt h t lusing ultrashort pulses
laser microfabrication
focus laser beam on material’s surface
laser microfabrication
laser microfabrication
laser microfabrication
surface microstructuring
laser microfabrication
examples of fabricated surfaces
20 μm
40 μm
fs-laser microfabrication
photon energy < bandgap
nonlinear interaction
fs-laser microfabrication
nonlinear interaction
Egap
Ef = hν
fs-laser microfabrication
nonlinear interaction
Egap
Ef = hν
multiphoton absorptionp p
fs-laser microfabrication
focus laser beam inside material
fs-laser microfabrication
curved waveguides inside glass
fs-laser microfabrication
3D waveguides in PMMA
cross-section view
Optics Express, 16, 200-205 (2008) Applied Surface Science, 254, 1135–1139 (2007)
fs-laser microfabrication
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
Two-photon absorption
)( 3χThird order processes
2ω ω
ω
ance
abso
rba
Iβαα += 0 wavelength0 wavelength
Two-photon absorption
Nonlinear interaction provides spatial confinement of the excitation
fs-microfabrication
0αα = Iβαα += 0
Two-photon absorption
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)
Two-photon polymerization
After the fabrication, the sample isimmersed in ethanol to wash away anyunsolidified resin and then dried
Two-photon polymerization
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
Microstructures containing MEH-PPV
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)
Microstructures containing MEH-PPV
d - Emission of the microstructure (black line) and of a film with the same composition (redline)
Microstructures containing MEH-PPV
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)
Microstructures containing MEH-PPV
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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