OUTLINE:ONO2000Tutorial

INTRODUCTION --The phenomena of optical nonlinearity --Voltage dependent index of index of refraction --Simple Devices

CHROMOPHORES --Optimizing hyperpolarizability -- Auxiliary Properties

MATERIALS --Optimizing electro-optic activity --Theory and optimized design of chromophores --Optical Loss --Lattice Hardening

PROCESSING --Fabrication of buried channel wavguides --Tapered and vertical transitions --Fabrication of 3-D integrated circuits

DEVICES AND PERFORMANCE --Prototype devices and performance evaluation --Advanced devices (e.g., phased array radar)

FUTURE PROGNOSISREFERENCES

A molecular medium, such as an organic crystal or a solid polymer, is generally nonconductingand nonmagnetic. The electron motions are restricted within atomic or molecular orbitals. Theinteraction of light with such media causes a cha rge displacement within the molecularframework, resulting in an induced dipole moment or molecular polarization p. When light fieldis weak, p is linear to the electric field of the light:

p = α.Ewhere α i s the linear polarizabilit y of the molecule. The bul k polarization P i s expres sed as

P = χ(1).Ewhere χ(1) is the linea r susceptibility o f the material. χ(1) is a second-r anktenso r because it relatesall components of P vector t oall components of E vecto :r

Px

Py

Pz

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

= χ 11 χ 12 χ 13

χ 21 χ 22 χ 23

χ 31 χ 32 χ 33

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

Ex

Ey

Ez

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

When a medium is subject to an intense electric field, the medium’s response, thenonlinear polarization, can be exp ressed in a po wer series of the field strength, assuming thepolarization of the medium is weak compared with the binding force between the electrons andthe nuclei:

p = αE + βEE + γEEE + …

P = χ (1)E + χ (2)EE + χ (3)EEE + …

where β (a third-rank tensor) and γ are the first and the second hyperpolarizabilities respectively,

χ (2) and χ (3) are the second and the third order susceptibilities respectively. χ (2) is a third-rank

tensor which can be expressed by a 3×6 matrix using the contracted indices notation.

INTRODUCTION: Linear andNonlinear Polarization

ONO2000Tutorial

INTRODUCTION: TensorProperties of χ(2)

χ(2) relates the polarization P to the square of the field strength E:

Px

( 2 )

Py

( 2 )

Pz

( 2 )

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

=

χxxx

( 2 )

χxyy

( 2 )

χxzz

( 2 )

χyxx

( 2 )

χyyy

( 2 )

χyzz

( 2 )

χzxx

( 2 )

χzyy

( 2 )

χzzz

( 2 )

χxyz

( 2 )

χxxz

( 2 )

χxxy

( 2 )

χyyz

( 2 )

χyxz

( 2 )

χyxy

( 2 )

χzyz

( 2 )

χzxz

( 2 )

χzxy

( 2 )

⎞

⎠

⎟

⎟

⎟

⎛

⎝

⎜

⎜

⎜

E

x2

E

y2

E

z2

2 Ey

Ez

2 Ex

Ez

2 Ex

Ey

⎛

⎝

⎜

⎜

⎜

⎜

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

⎟

⎟

⎟

⎟

From tensor properties, a non-zero χ (2) requires a noncentrosymmetric medium. For a poled

NLO polymer with the poling field direction along the z direction, it has a ∞-fold rotational

symmetry. Therefore the material has a C ∞v symmetry which stipulates that only 3 of the 18

tensor elements can be non-zero. The χ (2) tensor becomes

χ (2) = 0 0 0

0 0 0

χ

31

( 2 )

χ

31

( 2 )

χ

33

( 2 )

0 χ

15

( 2 )

0

χ

15

( 2 )

0 0

0 0 0

⎞

⎠

⎟

⎟

⎟

⎛

⎝

⎜

⎜

⎜

In the case when all frequencies of all electric fields involved in the second order process are

much lower than the resonance absorption frequency of the material (chromophore), Kleinman

symmetry holds and the independent tensor elements are reduced to only two:

χ (2) = 0 0 0

0 0 0

χ

31

( 2 )

χ

31

( 2 )

χ

33

( 2 )

0 χ

31

( 2 )

0

χ

31

( 2 )

0 0

0 0 0

⎞

⎠

⎟

⎟

⎟

⎛

⎝

⎜

⎜

⎜

ONO2000Tutorial

INTRODUCTION: FrequencyDependence of Polarization

ONO2000Tutorial

P = χ

( 1 )

E

0

cos( ω t − kz ) + χ

( 2 )

E

0

2

cos

2

( ω t − kz ) + χ

( 3 )

E

0

3

cos

3

( ω t − kz )

= χ

( 1 )

E

0

cos( ω t − kz ) +

1

2

χ

( 2 )

E

0

2

1 + cos( 2 ω t − 2 kz )[ ] +

χ

( 3 )

E

0

3 3

4

cos( ω t − kz ) +

1

4

cos( 3 ω t − kz )[ ]

=

1

2

χ

( 2 )

E

0

2

+ ( χ

( 1 )

E

0

+

3

4

χ

( 3 )

E

0

3

) cos( ω t − kz ) +

1

2

χ

( 2 )

E

0

2

cos( 2 ω t − 2 kz ) +

1

4

χ

( 3 )

E

0

3

cos( 3 ω t − kz )

For a sinusoidal field,

E(z,t) = E0cos(t-kz)

the polarization becomes:

INTRODUCTION: FrequencyDependence of Index of Refraction

ONO2000Tutorial

When a light beam travels through the nonlinear optic mediummodulated by a dc (or low frequency) field, E(0), the total field(E) to which the medium is exposed is

E = E(0) + E() = E(0) + E0cos( -t k )zSubstituting int othe expressio n fo r polarizatio n an dignoringhigher order terms,

P = χ(1)[E(0) + E0cos(w -t k )]z + χ(2)[ E(0) + E0cos( -t k )]z 2 +χ(3)[E(0) + E0cos( -t k )]z 3

Expandin gan dcollectin gterm s describin goscillatin g a t ,

P() = [() ()( ()( ()]χχ χ χ1220)330)343+ + +EEE2E E030 0 E0cos( -t k )z =χeff E0cos( -t k )z

The effective inde x fo r the fundamenta l light.

n2() = 1 + 4πχeff = 1 +

4π[ () () ]() () () ()χχ χ χ1 2 3 3432 03 0+ + +EE EE E2 030 0 =

n

0

2

( ω ) + 8 π χ

( 2 )

E (0) + 12 π χ

(3)

E

2

(0) + 3 π χ

(3)

E

0

2

where n0 is linear refractive index, the second term defines thelinear electro-optic effect or Pockels effect, the third term and

the fourth term correspond to the quadratic EO effect and theoptic Kerr effect respectively.

INTRODUCTION: The Electro-Optic Coefficient

ONO2000Tutorial

When the applied electric field is not very strong and thelight beam is not very intense, both the quadratic EO andoptic Kerr effect can be omitted:

n2() = nw02 82() ()+πχE(0)The change in refractive index due to the linear EO effectis common ly defin edas

Δ

1

n

2

⎛

⎝

⎞

⎠

= rE ( 0 )

where r is t he electro-optic coefficient. The left side ofthe equation may be expanded as

Δ

1

n

2

⎛

⎝

⎞

⎠

=

1

n

0

2

−

1

n

2

=

n

2

− n

0

2

n

0

2

n

2

≈

n

2

− n

0

2

n

4

The relationship between r and χ (2) is:r n=−824πχ()

Combining the above equations, the relationship betweenrefractive index change and the applied dc f ield strengthbecomes:

n

2

− n

0

2

n

4

=

( n + n

0

)( n − n

0

)

n

4

≈

2 n ( n − n

0

)

n

4

=

2 Δ n

n

3

= rE ( 0 )

Δ n =

1

2

n

3

rE ( 0 )

INTRODUCTION: UsefulRelationships

ONO2000Tutorial

φ = 2 π Δ n

L

λ

= n

3

r

EL

λ

π

Relationship of phase shift to EO coefficient and applied field

Relationship of Vπ voltage to EO coefficient

V

π

=

λ d

n

3

rL

where λ is the free-space wavelength, d is the thickness of thewaveguide core and cladding, L is the length of the electrode.Applied electric field is now denoted by V rather than E.

Voltage Length Product

Δ f ⋅ L =

c

4 ε

r

− n

Figure of Merit

FOM =n3

εr

where is the dielectric constant

INTRODUCTION: Comparison ofOrganic and Inorganic Materials

ONO2000Tutorial

Property Gallium Arsenide Lithium Niobate EO PolymersEO Coefficient 1.5 31 >70(pm/V at 1.3 μ )m

Dielectric 10-12 28 2.5-4Constant, Refractive 3.5 2.2 1.6-1.7Index, nBandwidth- > 100 10 > 100Length ProductGHz-cmVoltage-Length 1-5 5 1-2Product, -V cmFigure o f Merit 6 10 100Optical Loss 2 0.2 0.7-1.1d /B c mat 1.3 μm

Thermal 80 90 80-125Stability, °CMaximum 30 250 250Pptical PowermW

INTRODUCTION: Comparison ofOrganic and Inorganic Materials

ONO2000Tutorial

Stability will vary depending how the final polymeric EOmaterial is prepared.

Circles denote an IBM polymer with the DANS chromophorecovalent attached by one end to PMMA. DEC refers to adouble end crosslinked chromophore prepared by Dalton, et al.

Trace 1, guest/host composite; Traces 2-4, chromophores inhardened polymers. Trace 3 corresponds to DEC shownbelow. Trace 5 corresponds to sol-gel glass.

INTRODUCTION: Simple DeviceConfigurations

ONO2000Tutorial

Mach Zehnder Modulator

Birefringent Modulator

Directional Coupler

INTRODUCTION: MachZehnder Modulator and SimpleDevice Performance Comparison

ONO2000Tutorial

V(t) = Vosin( ) + t VB

IDC ( )in IAC ( )out

I1

L I2

IAC ( ) = out I1 + I2 +2(I1I2)1/2 (sinρVosin( ))t

ρ = 2πr33n3LV o / Tλ

- Strip Line Top Electrode

Comparison of key features of simple devicesMach Zehnder Birefringent

DirectionalInterferometer Modulator Coupler

reff r33 r33-r13 r33

Vπ VπMZ 1.5 VπMZ 1.73 VπMZ

Mod. PMZ 2.75 PMZ 3 PMZ Power

CHROMOPHORES: Charge-Transfer (Dipolar Chromophores)

ONO2000Tutorial

S

*

*

*

•

•

S

•

R R

S *•

R R

R'

N

•

HO

HO

N

•

HO

N

•

HO

N

•

HO

HO

S

S

•

HO

*

N

O

O

OH

*

N

N

CF3

O

OH

*

N

N

CF3

O

m

OH

n

CN

*CN

n

Ar

Ar

N

*

OH

O

O

Ar

=

,

n

Ar

N

*

OH

O

O

BridgesDonors

R = H, butyl, hexyl

R' = H, perfluoroalkyl

n = 1,2

m = 0,1

Acceptors

Ar

n

With the exception of octupolar chromophores (which we willnot discuss) electro-optic chromophores are dipolar charge-transfer molecules consisting of donor, bridge, and acceptor

segments. They are by nature modular materials (see below).

CHROMOPHORES: OptimizingChromophore Hyperpolarizability

ONO2000Tutorial

β ( − 2 ω ; ω , ω ) ≅

3 e

2

2 h m

ω

eg

f Δ μ

( ω

eg

2

− ω

2

)( ω

eg

2

− 4 ω

2

)

The two level model has provided useful guidancein optimizing molecular hyperpolarizability, β.

N

alkyl

alkyl

N

aryl

aryl

S

N

aryl

aryl

S

N

alkyl

alkyl β 0

BLA parameter

where eg is the frequency of the optical transition, f is theoscillator strength, Δμ is the difference between the groundand excited state dipole moments.

Through this relationship, β can be related tomaterial properties such as bond length alternation,BLA, and to donor and acceptor strength.

CHROMOPHORES: Variation ofμβ with Molecular Structure

ONO2000Tutorial

Structure μβ (10-48 esu) Structure μβ (10-48 esu)

580

926

2000

3300

4000

6100

9800

>10000

>10000

>10000

N

N

M e

2

N

N O

2

N

SA c O

N

OO

P h

N

S

C N

C N

C F

2

( C F

2

)

5

C F

3

A c O

A c O

N

O

O

P h

N

APTEI

FCN

ISX

N

O H

H O

N

O

P h

O

A P I I

D R

N

S

A c O

A c O

C N

C N

C N

C N

N

S

C N

N C

C N

N

S

C N

N C

C N

B u

2

NS

S O

2

C N

N C

NS

B u B u

A c O

A c O

O

N C C N

N C

TCI

SDS

F T C

The simple two level model and structure/function insightgained from the model has permitted a dramatic improvement inmolecular hyperpolarizability (see below). In the limit of non-interacting chromophores, electro-optic activity (induced by electric field poling) scales as Nμβ (where N is number density and μ is dipole moment); thus, we list μβ instead of β. Inthe 1990s, an improvement of a factor of 40 was achieved.

CHROMOPHORES: AuxiliaryProperties--Thermal Stability

ONO2000Tutorial

1.0

0.8

0.6

0.4

0.2

0.0

Weight Loss

7006005004003002001000

Temperature(o

C)

S

N

OO

CN

CN CN

CN

O O

O Oy

zx

N

OAc

OAcS

CN CN

CN CN

Thermal Gravemetric Analysis of Chromophore and Polymer

N

S

N C

C N

C N

N

S

N C

C N

C N

N

C N

C N

N

S

S

N

C N

N C

N

C N

N C

B u

B u

N

C N

N C

E t

N

C N

C N

N

S

S

N

C N

N C

Td

(

o

C)

274

296

325

μβ1.9m m

(10

-48

esu)

6200

2700

2500

313 1720

268 2520

322 1211

354 1300

367 2570

Td

(

o

C)μβ

1.9m m

(10

-48

esu)

* Zhang and Jen et al . Proc. SPIE 3006 , 372 (1997).* Ermer et al. Chem Mater. 9, 1498 (1997).

Thermal stability depends on host matrix (see below) andatmosphere (packaging). Typically defined as temperature atwhich EO activity is first observed to decrease.

CHROMOPHORES: AuxiliaryProperties--Thermal Stability

ONO2000Tutorial

N S

SO

CN

CNCN608 nm in chloroform

556 nm in dioxane

M.P:

Td:

UV-vis:

M.W.: 717.06 for C44H52N4OS2

412 oC (by TGA, 4oC/min)

187 oC

1. Thermal and optical properties

2. Synthetic scheme

S

S

Br2 S

SBrBr

Br

BrZn

CH3COOH

S

S

Br

Br

S

S

C6H13

C6H13HexylMgBr

Ni(dppp)Cl2

1. t-BuLi2. CuI 3. ICH2PO(OEt)2

S

S

C6H13

C6H13

CH2PO(OEt)2NBSS

S

C6H13

C6H13

CH2PO(OEt)2Br

N CHO

t-BuOK

N S

S

C6H13

C6H13

Br1. n-BuLi

2. DMF

N S

S

C6H13

C6H13

CHO

OCN

CNCN

Chromophore

Good thermal stability and molecular hyperpolarizability arenot mutually exclusive (see example below)

CHROMOPHORES: AuxiliaryProperties--Purity

ONO2000Tutorial

3x10-12

2

1

0

Conductivity (1/

Ω. )m

1201008060(Temperatureo )C

30 % - /wt doped APT BDMI PMMA

Pristine PMMA

( . .)SHG signal a u

1601208040 (Temperatureo )C

Ionic impurities can lead to ionic conductivity duringelectric field poling. This can reduce the field felt bychromophores and poling efficiency.

CHROMOPHORES: SummaryONO2000Tutorial

Chromophore Requirements:

•Large hyperpolarizability and large dipole moment

•No absorption at operating wavelength

•Stability --Thermal --Chemical & Electrochemical --Photochemical

•Solubility in spin casting solvents

•Compatibility with polymer hosts (particularly for guest/host materials)

•Low volatility (particularly if used for guest/host materials with high Tg polymer)

CHROMOPHORES: DipoleMoments

ONO2000Tutorial

N

R

R

S O

NC

CNNC

N

R

R

O CN

CNCN

N

R

R

O CN

CNCN

N

R

R

S

OO N

O

O

NN

R

R

ISX

FTC

CLD

GLD

R'R'

JH

R=H

8.6021

10.2698

12.1898

13.4668

13.8811

Dipole Moment (μ), Debye=R OTBDMS

______

______

13.1512

15.5491

15.8711

Chromophore dipole moments will be very useful for understanding the translation of microscopic optical non-linearity to macroscopic electro-optic activity. Below weshow dipole moments calculated for representative EOchromophores using SpartanTM

MATERIAL ISSUES: TranslatingMolecular Optical Nonlinearity toMacroscopic Electro-Optic Activity

ONO2000Tutorial

.

1 . 0

0 . 8

0 . 6

0 . 4

0 . 2

0 . 0

4 03 02 01 00

Chromophore loading wt%

T C I μ β = 6 0 0 0 x 1 0- 4 8

e s u

I S X μ β = 2 2 0 0 x 1 0- 4 8

e s u

D R 1 9 μ β = 5 5 0 x 1 0- 4 8

e s u

NN

Me2NNO2

N

SAcON

OO

Ph

N

SCN

CN

CF2(CF2)5CF3

AcO

AcO

N O

O

Ph

N

APTEI

FCN

ISX

N

OH

HONO

Ph

O

APII

DRN

SAcO

AcO

CN

CN

CN

CN

NS

CN

NC

CN

N

S

CN

NC

CN

Bu2N S SO2

CN

NC

N S

Bu Bu

AcO

AcO

O

NC CNNC

TCI

SDS

FTC

EO coefficient is not a simple linear function of chromophoreloading. Curves exhibit a maximum. Why?

MATERIALS ISSUES: OptimizingMaterial Electro-Optic Activity--Dependence on Chromophore Shape

ONO2000Tutorial

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Number Density (10^19/cc)

O

NC

CN

NC

N

CLD-72C33H36N4O

Mol. Wt.: 504.67705 nm in chloroform

O

NC

CN

NC

N

CLD-56C28H28N4O

Mol. Wt.: 436.55688 nm in chloroform

Data are shown for two different structures of the samechromophore: With isophorone groups (circles) and without isophorone protection of the polyene bridge (diamonds)

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Variationwith Chromophore Structure

ONO2000Tutorial

0 10 20 30 400

50

100

150

200

Number Density (10^19/cm^3)

1

1

r33pm/V

Electro-optic coefficients for 4 different chromophores (FTC,squares; CLD,diamonds; GLD, circles; and CWC, crosses) are shown as a function of chromophore number density inPMMA. The dipole moments for these chromophores wereshown in a previous overhead.

MATERIAL ISSUES: OptimizingElectro-Optic Activity: Theory--Equilibrium Statistical Mechanics

ONO2000Tutorial

cosn θ( ) =

cosn θ( )exp−UkT{ }dcosθ

cosθ( )=−1

1

∫

exp−UkT{ }dcosθ

cosθ( )=−1

1

∫

Electro-optic activity can be calculated according to

r33 = 2NβF()<cos3>/n4 The order parameter is

where U = U1 + U2 is the potential energy describing the interaction of chromophores with the poling field (U1) and with each. For non-interacting chromophores, U = -μFcos where F is the poling field felt by the chromophore. For this

case, <cosn> is ()()fLnn=θcosLn is the nth order Langevin function and f = |μF/kT|

Consider chromophores interacting through a mean distance, r, which is related to number density by N = r-3. Let us follow Piekara and write the effective field at a given chromophore from surrounding chromophores as U2 = -Wcos(2). The position w.r.t. the poling field is defined by Euler angles, Ω1 = {1,1} and the angles. orΩ1 =Ω⊕ Ω2 ()()()()()()2221 cossinsincoscoscos φφθθθθθ −+=

MATERIAL ISSUES: OptimizingElectro-Optic Activity: Theory--Equilibrium Statistical Mechanics

ONO2000Tutorial

cos

n

( ) =

1

4 πφ = 0

2 π

∫

φ = 0

2 π

∫cos

n

1

( ) ⋅ exp− U

kT{ }

d cos 2

d φ2

cos ( ) = − 1

1

∫

φ = 0

2 π

∫exp

− U

kT{ }

d cos 2

d φ2

cos ( ) = − 1

1

∫

d cos d

cos ( ) = − 1

1

∫

Averaging is done over the two variables Ω and Ω2. Explicitly,

The total potential is taken as -fcos() -Wcos(2). In thehigh temperature approximation, exp(-U1/kT) = 1-fcos(1).

cosn θ( ) =cosn θ1( )

2−f cosn+1 θ1( )

2

1−f cosθ1( ) 2

cosn θ( ) = cosn θ1( )2−f cosn+1 θ1( )

2− cos1 θ1( )

2cosn θ1( )

2{ }

These integrals can be done analytically with the result

cosn θ( ) =Ln f( ) 1−L12 W

kT( ){ }

MATERIAL ISSUES: OptimizingElectro-Optic Activity

ONO2000Tutorial

Equilibrium statistical mechanical calculations are easilymodified to take into account nuclear repulsive effects (bysimply adjusting the integration limits). Below we show simulation data for a typical chromophore separating nuclear(shape) and intermolecular electronic effects.

O

NC

CN

NC

N

O

OMe

Me

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory

ONO2000Tutorial

(Independent particle model)

Critical Conclusion: Chromophore shape is veryimportant. Need to try to make chromophores morespherical.

Comparison of Theory andExperiment for FTC

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory &Practice

ONO2000Tutorial

S

O

CN

CN

CN

O

SO

N

O

O

F

F

FF

F

F

F

FF

F

O

O

O

F

F

FF

F

F

F

FF

F

O

An example of modification of chromophore shape(CWC) to improve electro-optic activity is shown.

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Monte Carlo Methods

ONO2000Tutorial

Initially: No applied poling field, no intermolecular interactionsSteps 1-400: Poling field on, no interactionsSteps 400-800: Poling field and full interactions

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Monte Carlo Methods--ChromophoreDistributions with Increasing Interactions

ONO2000Tutorial

Chromophore distributions are shown as a function of increasingchromophore concentration for concentrations of 1 x 1017/cc, 5 x 1020/cc, and 1.5 x 1021/cc.

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Monte Carlo Methods

ONO2000Tutorial

Variation of calculated electro-optic activity with numberdensity is shown for different values of chromophore dipolemoment.

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Comparison of Methods

ONO2000Tutorial

Comparison of Monte Carlo and equilibriumstatistical mechanical (smooth and dashed lines)

methods. Methods is shown below. Both methods predict same functional dependence on number density.

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Monte Carlo Methods

ONO2000Tutorial

The effect of chromophore shape on electro-optic activity is shown.

MATERIAL ISSUES: OptimizingElectro-Optic Activity--Theory:Phase Separation

ONO2000Tutorial

Theory can also be used to identify the conditionswhere phase separation (chromophore aggregation)occur. Phase separation will depend on appliedelectric field, chromophore concentration, and hostdielectric constant. Curves 1-5 correspond to phaseboundary lines for host dielectric constants of 2,3,5,7, and 10. To the left is the homogeneous phase.