Electro-Optics: The Phenomena

• An electro-optic material (device) permits electrical and optical signals to “talk” to each other through an “easily perturbed” electron distribution of a material. A low frequency (DC to 200 GHz) electric field (e.g., a television [analog] or computer [digital] signal) is used to perturb the electron distribution (e.g., -electrons of an organic chromophore) and that perturbation alters the speed of light passing through the material as the electric field component of light (photons) interacts with the perturbed charge distribution.

• Because the speed of light is altered by the application of a “control” voltage, electro-optic materials can be described as materials with a voltage-controlled index of refraction.

Index of refraction = speed of light in vacuum/speed of light in material

Electro-Optic Devices: The on-ramps & interchanges of the information superhighway

• By slowing light down in one arm of the Mach Zehnder device shown below, the interference of light beams at the output can be controlled. Electrical information appears as an amplitude modulation on the optical transmission. This works equally well for analog or digital data. Electro-optic coefficient is the material parameter that defines how large an effect is observed for a given applied voltage

Light InModulatedLight Out

DC bias electrodeground electrode

Substrate

RF electrode

V = d/(2n3r33L)

= optical wavelengthn = index of refractionr33 = electro-optic coefficientL = interaction length= modal overlap integrald = electrode gap

The Mach Zehnder Interferometer

V is the voltage required to achieve signal transduction

Electro-Optic Behavior Depends on Orbital

Type and Position

Pi-electrons are more easily perturbed (displaced) than sigma-electrons

Example of common NLO chromophore design

SN

S

O

NCNC

CNElectronDonor

-conjugated bridge

ElectronAcceptor

PAS 38, a classical linear charge-transfer chromophoreshows typical chromophore design; an electron donor and acceptorpair separated by a -conjugated bridge

Example of an E-O Chromophore: A Charge Transfer (Dipolar) Molecule

NC

CC

C

C

C

CO

H

H

H

H

H

H

HH

H

H

H

NC

CC

C

C

C

CO

H

H

H

H

H

H

HH

H

H

H

The charged separated form will have a larger dipole moment and thus a stronger interaction with an applied electric field

Charge displacement can occur over estended distances using materials with extended -conjugation

pi ijE j ijkEkE l ijklE jE kE l ...

NONLINEAR OPTICAL EFFECTS: Microscopic and Macroscopic Polarization—Power Series Expansion

is the first nonlinear term, known as molecular first hyperpolarizability

For a symmetric molecule even order terms, and higher, are zero.

(2)represents material first nonlinear susceptibility

Oscillators (chromophores) must be aligned acentrically withinthe material to realize a nonzero (2)

Pi ijE j 2 ijkEkE j 3

ijklE jE kE l ...

r33 2 2 zzz /(nz )

4

)(cos3)2( constN zzzzzz

Loading Parameter = N<cos3> = (r33/)(constant)

r33 = N<cos3>(constant)

r33 = electro-optic coefficientN = chromophore number density (molecules/cc) = molecular first hyperpolarizabilityN<cos3> = acentric order parameter*The constant depends on the dielectric properties of the material lattice

The coefficient of the second term in the power series expansion of material Polarization in terms of applied electric fields, (2), is given by

Optimization of Electro-Optic Activity

Macroscopic LevelElectro-optic activity requires noncentrosymmetric

chromophore symmetry, i.e., <cos3> must be large Requires optimization of N<cos3>

*Statistical mechanics is the key

Molecular LevelRequires optimization of

*Quantum mechanics is the key

Let us first focus on the optimization of N<cos3>, then we will consider the optimization of .

Bottom electrode

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

O

NC

CN

NC

CF3

N

TBDMSO

OTBDMS

Top electrodeE

Field

A DC poling field is applied across the chromophore / host matrix.

Ideal case (no intermolecular interactions) : < cos3 θ> = E / 5kT

Use Electric Field Poling to Induce Noncentrosymmetric Order

Translating Microscopic to Macroscopic Electro-Optic Activity

L = Langevin Function; W = Intermolecular Electrostatic Potential; k = Boltzmann constant; Ep is applied poling field; F is poling field felt by chromophore

NONCENTROSYMMETRIC SYMMETRY REQUIRED FOR ELECTRO-OPTIC ACTIVITY

r33 = N<cos3>(constant)

Statistical mechanical calculations permit understanding the role that chromophore shape has on macroscopic electro-

optic activity

Statistical mechanical calculations permit understanding the role that chromophore shape has on macroscopic electro-

optic activity

E x p e r i m e n t — S o l i dD i a m o n d s

2m a x 2 2

0 . 4 8 0 . 2 8 4 . 8 k T k T

N f

E O A c t i v i t y D e p e n d sO n S h a p e !

inAPC

EO Activity vs. Concentration: Theory & Experiment

CLD

Chromophore Shape Determines EO Activity

Region of Enhanced Order

Loading Parameter = N<cos3> r33/(constant)

2

1

With a 2-1 aspect-ratio dipolar head-tail interactions are becoming predominant over side-side interactions

N

S

O

O OR

OR

S

O

ORO

RO

O

NC

CN

NC

Undesired Centrosymmetric Order Desired Noncentrosymmetric (EO active) Oder

Towards improved loading: discotic chromophores

Progress In Discotic Chromophores

S

OO

BuBu

S

OO

BuBu

O

N

NC

CNNC

S

OO

OMe

Me

S

OO

OMe

Me

O

N

NC

CNNC

OLD-1 OLD-2

S

S O

N

NC

CNNC

OLD-3

S

OO

OMe

Me

S

OO

OMe

Me

O

N

NC

CNNC

F3C

OLD-4

Wt % 20% 30%

OLD-1 3.0 ---

OLD-2 2.0 3.6

OLD-3 1.0 ---

OLD-4 4.0 ---

Relative r33 values for a series of modified bi(ProDOT) core in bridges.

The more disc shaped, the more the dipole-dipole interaction are reduced. Prediction: OLD-4 can go to higher loading and still get improved electro-optic conversion. The wt% loading is based on core chromophore weight only.

Blends of Organic Molecular Glass Materials

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100

Poling field (V/um)

HD/FD-AJC(23%)

AJC-AJC(75%)AJC-AJC (50%) HD/FD-AJC(75%)

HD/FD-AJC(50%)

r 33

(pm

/V)

NO

SiO

Si

O

CF3NC

NC

CN

S

NO

SiO

Si

O

CF2CF2CF3NC

NC

CN

S

AJC146 AJC168

N

S

O

NC

NC

CN

CF3

O

OO

O

F

F

F

F

F

F

F

F

F

F

O

O

O

O

HD/FD

Multi-Chromophore-Containing Dendrimers Require the Use of Psuedo-Atomistic Monte Carlo Calculations to Simulate

Poling-Induced Noncentrosymmetric Order

Simulation requires consideration ofIntermolecular electronic (e.g., dipole-dipole) interactionsIntermolecular nuclear repulsive (steric) interactionsPotential functions associate with rotation about covalent bondsVan der Waals interactions

It is critical to reduce computation time by making logical approximationsTreat pi-electron segments within the United Atom Approximation (Pi bonds prevent rotation and segments are thus rigid)Treat sigma-electron segments atomistically using correct bond rotation potentials

Examples of Monte Carlo SimulationsConsideration of Various Modes of Attachment of Chromphore

O O

OOO

OO

OO

SN O

CNNC

NC

S

N

O

NCCN

CNS

N

ONC

NC

NC

O O

OO O

OO

O

O

S

N

O CN

CNCN

S

N

O

NCCN

CN

S

N

O

CNNC

NC

Side-onD2.PAS.31

IV

End-onAALD-1104

V

• Chromophores are the prolate ellipsoids. Solvent is assumed.

D2.pas.41 VIII MC modeling in static DC field (Simulation of Results for Side-On Attachment Dendrimer)

Low Density

2% loading

cos 0.16

Simmulations performed by Harry Rommel and Bruce Robinson.

PAS Side-On Dendrite: High Density

<cos3> greater than 0.3

Discussion of Results

Results are complicated as might be expected when multiple forces influence resultsVan der Waals interactions are clearly important in defining the order achieved in the preceding two figuresThus, results are not as simple as for the case of single chromophore dendrimers where the competition of electronic and nuclear intermolecular interactions dominateCovalent bond potentials do prevent dipole-dipole interactions from diving centrosymmetric ordering

The two preceding slides clearly demonstrate that covalent bond potentials and nuclear repulsive (steric) interactions can result in order parameter increasing with concentration

The next slide shows another possibility: The sum of interactions favors the noncentrosymmetric ordering potential component of the electronic intermolecular interactions

Optimum Monte Carlo Calculated Structure--Noncentrosymmetric Order By Design--

• Three chromophores (End-on attachment) -- 20 Debye dipole each

• Best of Set of accepted M.C. moves.

• Result: Near perfect order of 3 Chromophores

• This is a limiting case: Very Large Field ( 3000 MV/m) Points on Z (up)

Chromophore

Magic Angle

Center

Another Experimental Demonstration: Comparison of chromophore/APC composite with pure three arm

chromophore dendrimer (D2PASS)

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

CF3FTCCF3FTCD2PASSD2PASS

r 33 a

t 1

31

0 n

m w

ave

len

gth

(p

m/V

)

Poling field (MV/cm)

S ON

TBDMSO

TBDMSO

CF3

NCCN

NC

CF3-FTC

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

CF3FTCCF3FTCD2PASSD2PASS

r 33 a

t 1

31

0 n

m w

ave

len

gth

(p

m/V

)

Poling field (MV/cm)

S ON

TBDMSO

TBDMSO

CF3

NCCN

NC

CF3-FTC

The demonstration of the advantage of incorporating a chromophore into a multi-chromophore dendrimer is shown in the figure to the right. An electro-optic activity approximately three times greater than the best value that can be obtained for a chromophore/polymer composite is achieved.

Summary of Multi-Chromophore Dendrimer Results

Electro-optic coefficients (at 1.3 microns wavelength) in the range 200-430 pm/V have been achieved with multi-chromophore containing dendrimers

Ultimate electro-optic values (supermolecular structures) have not yet been achieved so values can be expected to become larger in the future

Electro-optic activity can also been increased by inserting chromophores with greater molecular first hyperpolarizability into optimized supermolecular structures. We now turn our attention to optimizing chromophore hyperpolarizability

Comparison of Experimental Results and Theoretical Predictions

Fe

Fe

S

O

NCNC

CN Fe

O

NCNC

CN

F3C

1 2

3

O

NCCN

NC

Fe

S

O

NCCN

NC

F3C

4

Hyperpolarizability values relative to pNA measured by HRS and calculated by DFT.

Electro-optic coefficients determined by simple reflection

Cmpd #

r33(pm/V) 1.3@20%

1 ----

2 5

4 / 3 25 / ----

Experiment. relative to pNA

DFT Calculations

3.5 4.6

5.7 4.8

42.2 /33.3 43.5 / 35.5

2.4

3.6

44 / 11.4

,calcrel zzz

301

N

O

NC

N

CN

O

302

N

O

NC

N

CNCN

CN

µ = 11.7 D

ß1907 nm = 60.2 x 10 -30 esu

µß1907 nm = 704.3 x 10 -48 esu

max, ZINDO = 431 nm

N O

CN

NCNC

1

N O

CN

NCNC

CF3

2

N NH

NCCN

NC

O10

µ = 10.1 D

ß1907 nm = 31.6 x 10 -30 esu

µß1907 nm = 319.2 x 10 -48 esu

max, ZINDO = 390 nm

µ = 9.9 D

ß1907 nm = 46.6 x 10 -30 esu

µß1907 nm = 461.3 x 10 -48 esu

max, ZINDO = 403 nm

µ = 6.3 D

ß1907 nm = 62.4 x 10 -30 esu

µß1907 nm = 393.1 x 10 -48 esu

max, ZINDO = 430 nm

µ = 13.6 D

ß1907 nm = 91.7 x 10 -30 esu

µß1907 nm = 1247.1 x 10 -48 esu

max, ZINDO = 459 nm

Theoretical Prediction of Variation of Molecular First Hyper-polarizability and Dipole Moment with Chromophore Structure

(Semi-Empirical Calculation Predictions)

Determination of Molecular 1st Hyperpolarizability (relative to CHCl3) by Femtosecond, Wavelength-Agile Hyper-Rayleigh Scattering (HRS)

--Experiment confirms theoretical prediction--

N O

CN

NCNC

N N

CN

NCNC

OOO

N N

CN

NCNC

O

N N

CN

NCNC

OO

O

TCF

TCP1

TCP2

TCP3

2285

8288

7582

7943

chloroform = 0.16 x 10-30 esu [Kaatz et al, Opt. Commun. 157 (1998) 177]

chloroform = 0.49 x 10-30 esu [Clays et al, Phys. Rev. Lett. 66 (1991) 2980]

chloroform = 0.16 x 10-30 esu [Kaatz et al, Opt. Commun. 157 (1998) 177]

chloroform = 0.49 x 10-30 esu [Clays et al, Phys. Rev. Lett. 66 (1991) 2980]

293146CLD (Ref.)

385183D1-B2-A2

454223D1-B2-A4

1681794D1-B10-A4

1214585D1-B9-A4

990500D1-B9-A3

zzz/10-30 esuHRS/10-30 esuStructureDesignation

293146CLD (Ref.)

385183D1-B2-A2

454223D1-B2-A4

1681794D1-B10-A4

1214585D1-B9-A4

990500D1-B9-A3

zzz/10-30 esuHRS/10-30 esuStructureDesignation

Density Functional Theory (DFT) Calculations Predict The Same General Trends

NR

R

O

CN

CN

CN

RF3C

NR

R

O

CN

CN

CN

RF3C

Extended bridges:

Asymmetric bulky 3D shaped acceptors:

S

RR

S

R R

Stronger acceptors :

Pyrrolines

pyrrolizines

N

NC

O

CN

NC

R

N

NC

O

CN

O

OR

RO

N

NC

O

CNCN

CN

OR

RO

Stronger donors :

NN

N

NP

O

NCCN

NC

F3C

OR

O

NCCN

NC

F3CS

R

Strategy for Improving NLO Chromophores: Choose the Right Combination of Donor, Bridge, and Acceptor With Theoretical Guidance

Summary

Values of electro-optic activity greater than 300 pm/V (an order of magnitude greater than the commercial standard lithium niobate) have been realized for both single and multi-chromophore-containing dendrimers

Much greater values can clearly be obtained byUsing pseudo-atomistic Monte Carlo calculations to design dendrimers that lead to even larger values of N<cos3>Using quantum mechanical calculations to design chromophores with improved molecular first hyperpolarizability, .

Values of greater than 1000 pm/V are likely possibility. Such materials would likely have a transformative impact on a number of technological areas