P. Audebert

Gdansk Lecture: materials for opticsGdansk Lecture: materials for optics

Where we are :Where we are :

ECOLE NORMALE SUPERIEURE DE CACHAN (Paris area)

Main goal: Train future university and high school teachers

ECOLE NORMALE SUPERIEURE DE CACHAN (Paris area)

Main goal: Train future university and high school teachers

17 departments12 laboratories3 institutes

17 departments12 laboratories3 institutes

1320 students “normaliens”760 other students300 foreign students (China, US, Canada, Poland, India)260 PhD

345 professors and assistant professors70 Post-docs238 technical staff

1320 students “normaliens”760 other students300 foreign students (China, US, Canada, Poland, India)260 PhD

345 professors and assistant professors70 Post-docs238 technical staff

More than 100 international programs More than 100 international programs

OutlineOutline

IntroductionIntroduction– Basics on light and matterBasics on light and matter

Fluorescent molecules and materials.Fluorescent molecules and materials.– What is fluorescence-theoryWhat is fluorescence-theory– Fluorescent moleculesFluorescent molecules– Fluorescent materials Fluorescent materials – Plasmon resonnance and sensingPlasmon resonnance and sensing– ApplicationsApplications

Molecules and materials for NLOMolecules and materials for NLO– Second orderSecond order– Third orderThird order– Non-linear absorptionNon-linear absorption– Molecules and materials for NLOMolecules and materials for NLO– Figures of merit and influence of size.Figures of merit and influence of size.

– ConclusionConclusion

INTRODUCTION: Recalling what light is.

Wavelengths of “Light”Wavelengths of “Light”

nm: for near UV, visible, and near IR light

m: for IR and far IR light (sometimes wavenumbers preferred, n = 10000/ if n in cm-1 and in m)

Å: for x-ray. But in this regime people usually use photon energy in eV.

(nm)

1240eV

We have

Typical range of IR spectra recording

Light WaveLight WavePlane electromagnetic wavePlane electromagnetic wave

– kk: propagation constant or wave : propagation constant or wave numbernumber

: angular frequency: angular frequency– Phase of the wave (Phase of the wave (t –kz+t –kz+00) )

Wave front : A surface over Wave front : A surface over which the phase of a wave is which the phase of a wave is constant.constant.Optical field : refers to the Optical field : refers to the electrical field Ex. electrical field Ex.

)](expRe[

)](exp)exp(Re[

)-t ( cos E t)(x,E

00

00x

kztjE

kztjjE

kz

c

Ex

z

Direction of Propagation

By

z

x

y

k

An electromagnetic wave is a travelling wave which has timevarying electric and magnetic fields which are perpendicular to eachother and the direction of propagation, z.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

/2k

Traveling wave along Z

)exp( 00 jEEc

Propagation of LightPropagation of Light

Light is a kind of electro-magnetic wave. In the general case the field varies with all space ordinates (in addition to time)

A: amplitude vector. : phase.

Wave Vector and Wave numberWave Vector and Wave number

Wave Vector, k : Use to indicate the direction of propagation. The vector whose direction is normal to the wavefront, and magnitude is k = 2/.

For a plane wave, A is constant, and

t rkk

The magnitude of k, k = 2/, is also called the wave number.

Phase velocityPhase velocity

The relationship between time and space for a given The relationship between time and space for a given phase, phase, , that corresponds to a maximum field, can be , that corresponds to a maximum field, can be described by:described by:

So, during a time interval So, during a time interval tt, this constant phase (max. field) moves , this constant phase (max. field) moves a distance a distance zz. From the relation above it comes : . From the relation above it comes :

Therfore it defines the phase velocity of this wave as:Therfore it defines the phase velocity of this wave as:

constkzt 0

)2(

,/

frequencyiswhere

kdtdzv

0 kdzdt

Basics of fluorescence

What happens to molecules upon photoexcitation?

Fluorescence deals with light reemission after absorption; It competes with plenty of other phenomena that can also occur after a photon absorption. Absorption is a linear process, which occurs when the incident photon energy matches a molecule/atom orbital gap + some additionnal conditions…

Optical absorption basics: What are the possible transitions in a simple molecule?

Not all transitions are allowed (there are symetry rules) and

some of them, eg the n* are associated to a partial charge transfer (results in a increase of the transition dipole).

Singlet and triplet states

From Hund’s rule, the triplet state lies always below the singlet state. Conversion is sometimes possible,

but not always.

Experimentally, the e ciency of light absorption at a wavelength ffi by an absorbing medium is characterized by the absorbance A() or the transmittance T() , defined as

Transmittance and absorbance; the Beer-Lambert law.

In a (very) large majority of case, the absorption of a solution is given by the

Beer-Lambert law below. The unit of is therefore L.mol-1.cm-1

We can define the decadic absorption coefficient:

And the Naperian absorption coefficient:

Which allows to introduce in turn the

molecular absorption cross-section:

Absorption coefficients and cross section

Relation between and

This is exactly the Beer-Lambert law with = (1/2.3)Na

Examples of values

The molar absorption coefficient is a very widespread value to estimate the absorption efficiency of a given compound. Here are reported the values for classical organic chemicals and dyes (at maximum).

Origin of emission from a molecule : The Perrin-Jablonski diagram.

Emission (or non-emission) from a molecule : The time scale for the processes.

Absorption and emission from a molecule : The fine structure.

Molecules can be in different vibrational states; the relative proportion of molecules in the different states is given by the Boltzmann law:

N0/N1 = exp[-(E1-E0)/kT]This can induce a fine structure in the spectrum, if the vibrationnal levels have enough spacing.

In the case of anthracene, the spacing is around 1400 cm-1, which comes to 2.8 10-20 J, and has the consiquence that virtually all molecules are in the ground state (N0/N1 = 0.001). In this case the spectrum has the shape represented on the left.

In the general case, the levels are tighter spaced (quasi continuum) which leads to overlap between absorption and fluorescence spectrum)

Summary of all the possibilities for desactivation of a molecule.

Each process can be favoured according to the position of the different energy levels and the molecular structure (presence of heavy atoms favour intersystem crossing.

Fluorescence life-times

Once a molecule has been excited by absorption of a photon, to its excited state that we will call A*, it has therefore several paths of deactivation, fluorescence being one of them. This is quite well exemplified in the scheme below:

We can call knr the constant summarizing all the non radiative processes, against kr which summarizes the radiative ones (mainly fluorescence). The disparition of A* follows a classical 1rst order kinetics, and its life-time can be measured.

Fluorescence intensity

The fluorescence intensity is directly linked to the amount of excited molecules still remaining inside the solution, and the radiative rate constant:

Most of the time the decay is monoexponential, and parallels what is observed in radioactive decay, although with much faster decay rates!

Quantum yields

A very important property for a fluorescent molecule is the radiative quantum yield, that is, the proportion of reemitted light against the absorbed light.

The fluorescence yield is therefore nothing else than the ratio of the radiative rate constant against the sum of the deexcitation constants.

It is also possible, on the same basis, to define the yield for the intersystem crossing (isc) and the phosphorescence, which are usually lower than for fluorescence.

Or otherwise:

Some values for classical fluorophores

Aromatic hydrocarbons are usually good fluorophores, here are some examples with life-times and quantum yields.

Emission spectra and Stokes shift

Since the quantum yield concerns all photons emitted from a molecule, it can also be described from the integral of the emission spectrum.

The Stokes shift is a very important parameter, which describes the energy gap (often expressed in nm) between the absorption and the emission spectra.

Examples of Stokes shift

Examples of a large and small Stokes shift in two classical dyes, a benzoazinone and a rhodamine.

Heavy atom effect

The presence of heavy atoms in fluorescent molecules has huge effects on the intersystem crossing, and favors the phosphorescence at the expense of fluoresence, especially with bromine and iodine, as exemplified with the naphtalene derivatives below.

Fluorescence quenching

The excited state of a molecule can react with several type of substrates, exchanging energy, electrons or chemical species (mainly protons) leading to fluorescence quenching.

The kinetic analysis is very similar to deactivation processes, except that it is now a bimolecular rate! (which can comes to a 1rst order kinetics in case of quencher excess)

Fluorescence quenching : Main paths

Summary of all possible deactivation paths:

Fluorescence quenching : Three main situations, relatively to the process.

1) The excited state of a molecule can react immediately with quencher in large excess (interactions already exist between the quencher and the fluorophore): We have extinction of part of the fluorophores. Two life times can be distinguished according to the association of the quencher with the fluorophore or not.

2) The quencher is not in larger excess, but the life-time of the fluorophore is short enough and long-range interactions (eg energy transfer) can occur. Again, part of the fluorophore that are in the vicinity of the quencher are extinct, while others are not. This case is kinetically analogous to 1) for part of the fluorophores, and again two life times can be distinguished according to the presence or not of the quencher in the vicinity of the fluorophore. In the two above cases, the response are concentration dependent. These cases are called : Static quenching.

3) The quencher is not in large excess, and transport can occur during the quenching process (long life-time and/or fast diffusion). Then the pseudo first order may not applies any longer. This case may be more complex.This last case is called « dynamic quenching » and the apparent rate constant sometimes change with time.

Static fluorescence quenching : Illustration

In the first case (sphere of effective quenching) the quenching efficiency is related to the number of quenchers, equal to Na Q Vq , where Q is the quencher concentration, Vq the sphere volume, and Na the Avogadro number. It can be shown that:

In the second case (preequilibrium) there is an equilibrium M + Q = [MQ]. MQ does not fluoresce while the fluorescence of M is unaffected. Therefore:

And, at steady state:

Fluorescence quenching : Calculation of the two cases of static quenching

Dynamic fluorescence quenching : Stern-Volmer kinetics

This is what happens in cases 1) or 2) (for selected fluorophores), let be M the fluorophore, and Q the quencher, we have:

It comes to:

Since the fluorescence intensity is proportionnal to the M* concentration:

Fluorescence quenching : Stern-Volmer kinetics (2)

Since the fluorescence intensity decay is therefore a single exponential, whose characteristic time comes from the factor inside the exponential:

And therefore we have the relation, known as the Stern-Vomer law:

For quantum yields we have :

Fluorescence quenching : Stern-Volmer kinetics (3)

Under steady-state illumination, we have:

Where I0 and I are the steady-state fluorescence intensities in the

absence and presence of quencher respectively, and KSV = kq 0 Q, proportionnal to the quenching rate, is called the Stern-Volmer constant. The relation is called the Stern-Volmer relation.

Fluorescence quenching : Summary, including life-time dependance.

The table below shows the different I/Q and lg(I)/t curves that can be expected from the various mechanisms previously detailed.

Examples of classical fluorophores and their syntheses.

RhodamineCoumarines (coumarine and umbelliferone)

Malachite greenTétracene

Rhodamine 6G

Very classical fluorescent laser dyes (1)

Fluorol

Acridine orange

Acridine yellow

Pyrilium dye

Phenoxazine dye

Classical laser dyes (2)

Cresyl violet

Cyanine

isoindolinone isoindoline

Other fluorescent dyes

Flavanthrone

quinophtalone

BODIPY TR-X

Classical fluorescent dyes: Metal complexes and analogues.

Iridium complex Zinc octaethylporphyrin

Magnesium tetraphenylporphyrin

Magnesium phtalocyanin

Fluorophore

Anchoring group

FluoresceinFluorescein (A. von Baeyer, 1871)(A. von Baeyer, 1871)

Fluorescein : synthesis

Fluorescein: pH sensingFluorescein: pH sensing

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sont requis pour visionner cette image.

2 excitation ex1 ex2, 1 emission em

Rhodamin synthesis and activation

Synthesis of the core

Functionnalisation

Synthesis of indolium dyes (1)

Fischer indole synthesis

Near infrared dye

Synthesis of indolium dyes (2)

Sensing with fluorescence

What kind of parameters may modulate fluorescence ?

Fluorescence Fluorescence pHpH

pressurepressure

viscosityviscosity

temperaturetemperaturepolaritypolarity

ionsions

H bondingH bonding

quenchers quenchers

Electric potentialElectric potential

pHpH

pOpO22

ionsions

Ion sensing fluorophores

Calcium green

Sodium green

pH sensing : principlespH sensing : principlessingle wavelength measurementsingle wavelength measurement

IFAH = a.C0 with a AH , F

AH

IFB = b.C0 with b B , F

B

IF = a.[AH] + b.[B]

with C0 = [A] + [B]AH = H+ + B-

I

I

B-IFB-

I

AHIFAH

pH in

crea

se

IF

pH pKa log

B

AH

log [B ]

[AH]

pH pKapp logIF I

FAH

IFB I

F

[B ][AH]

= IF I

FAH

IFB I

F

pH sensing : principlespH sensing : principlessingle wavelength measurementsingle wavelength measurement

AH = H+ + B-

I

I

B-IFB-

I

AHIFAH

pH in

crea

se

IF

Disadvantages of single wavelength Disadvantages of single wavelength measurementmeasurement

Measurements of all intensities MUST be done in the very same conditions

Measurements of IFAH and IF

B are difficult in-vivo

Calibration may depend upon [probe]

Needs for ratiometric measurements (independent of [probe])

pH sensing : principlespH sensing : principlesdual wavelength measurementdual wavelength measurement

RI(

1)

I(2

)

pH pKapp logR R

AR

B R

+ loga

2b2

pH pKapp logR R

AR

B R

+ logIA

(2

)

IB

(2

)

IAH = H+ + B-

IB-

I

AH

pH in

crea

se

1 2

Advantages of dual wavelength Advantages of dual wavelength measurementmeasurement

Independant of [probe]

Independant of source fluctuations intensity

Independant of instrument sensitivity

FluoresceinFluorescein

2 excitation ex1 ex2, 1 emission em

Fluorescent polymers

* (LUMO)

* (LUMO)

* (LUMO) *

(LUMO)

(HOMO)

(HOMO)

(HOMO)

(HOMO)

BC

BV (pleine)

Energie vide

Ethylène Butadiène Octatétraène Polyène

2 n

Organic polymers model

As much as the conjugation length increases, the levels get closer and closer

n

O

O

MEH-PPV

R R

n

Fluorescent polymers (of interest in emitting devices)

PPV family

Polyfluorene family

SCl

n

CH2ClClH2C S

CH3OH T = 65°C S

S ClCl

S

Cl

1) NaOH, MeOH/H2O, T = 0°C or Bu4NOH, MeOH, T = 0°C

2) HCl

Soluble precursor Quinodimethane

PPV SYNTHESIS

The Wessling route

Precursor conversion :

n

T = 180-300°C

vacuum 12h

SCl

n

Insoluble

S+

BY PRODUCTS

+ HCl

THT

PPV SYNTHESIS

The Wessling route

Mechanism of the polymerisation of the para quinodimethane has not been completely elucidated yet

S

Cl

T = 50°CSCl

nCH3OH

OCH3

n

SOLUBLE

- radical polymerisation?- anionic propagation?

Molar mass determination :

Mn > 100 000 Da

R. A. Wessling, J. Polym. Sci., Polym. Symp., 72, 55-66, (1985)

PPV DERIVATIVES SYNTHESIS

MEH-PPV synthesis

D. Braun, A. J. Heeger, Appl. Phys. Lett., 58, 1982, (1991)

ITO/MEH-PPV/Ca EL = 1%

n

O

O

MEH-PPV

Synthesis : Gilch polymerisation

O

OH

O

O

KOH, EtOH reflux

Br

O

O

CH2ClClH2CHCHOHCl dioxane

O

OtBuOK

THF, T = 20°C

n

O

On

O

O

PPV DERIVATIVES SYNTHESIS

Dialkoxy-PPV derivatives

* A lot of polymers have been prepared following the previously described synthetic route.

* Two homopolymers have emerged :

MEH-PPV OC1C10-PPV

Philips HoechstEL

max= 610nm PL = 15%

EL

max= 592nm = 575nmPL

max

PPV DERIVATIVES SYNTHESIS

R1O

OR2

CH2ClClH2C

R1O

OR2

CHH2C

1 eq tBuOK

OR2

OR1

nCl

OR2

OR1

Cl

OR2

OR1

OR2

OR1

Cl

OR2

OR1

Cl

Cl

OR2

OR1

n

OR2

R1O

OR2

R1O

OR2

R1O

OR2

R1O

1 eq tBuOK 1 eq tBuOK

Main reactionSide reaction

Cl

Side reaction in the GILCH polymerisation

H. Becker et al., Macromolecules, 32, 4925, (1999)

For OC1C10-PPV, the defect concentration is in the range of 1.5 – 2.2%

Tolane bis benzyl moiety (TBB)

PPV DERIVATIVES SYNTHESIS : Cyano PPV

The Wessling route is ineffective when e- withdrawing substituents are involvedKnoevenagel condensation

C6H13O

OC6H13

CH2ClClH2C

C6H13O

OC6H13

CHOOHC

C6H13O

OC6H13

CN

NC

C6H13O

OC6H13

C6H13O

OC6H13

CN

NCn

NaCN

1) NaOAc

2) KOH, EtOH

3) PCC

t-BuOK or Bu4NOH

t-BuOH/THF 50°C

CN-PPV

Synthesis of polymer with high electron affinity

The synthetic route is flexible many cyano PPV derivatives

C6H13O

OC6H13

C6H13O

OC6H13

CN

NCn CH3O

O

CH3O

O

CN

NCn

C6H13O

OC6H13

CN

NCn

CN-PPV MEH-CN-PPV

PPV DERIVATIVES SYNTHESIS : Heck coupling reaction

OR2

R1O

II

OR2

R1On

+Et3N, Pd(OAc)2 , DMF

3P

Precursor synthesis :

R. Heck, Org. React.,27, 345, (1982)

OR2

R1O

II

OR2

R1O

I2, HIO3

H2SO4, AcOH, CCl4

Preparation of alternating copolymers derived from PPV :

* The Heck coupling reaction approach is versatile* But the obtained molecular weights are limited

Z. Bao, Y. Cen, R. Cai, L. Yu, Macromolecules, 26, 5281-5286, (1993)

POLYFLUORENE DERIVATIVES

R R

n

* Good opportunity for getting soluble blue emitting polymer* Chemically and photochemically stable* Good hole injecting materials* Good electron transporting materials

First attempts for preparing poly(9,9-dihexylfluorene) (oxidative polymerisation)

2 n-BuLi T = -78°C

2 RBr

R R R R

n

FeCl3

CHCl3

Not really suitable for application for the moment…* very low molecular weight* branching* non conjugative linkages through other positions than 2 and 7

Y. Ohmori et al., Jpn. J. of Appl. Phys., 30(11B), L1941-L1943, (1991)

POLYFLUORENE DERIVATIVES

Yamamoto reaction (Dow Chemical Company) :

R R R R

BrBr2 Br2

CHCl3

BrBr

R R

n

bis(1,5-cyclooctadienyl) Nickel (0)

DMF T = 80°CN N

Polymers were end-capped with monobrominated aromatic derivatives

BrBr

R R

n

R R

nBr

Yamamoto coupling

2

Ni-catalysedNi-catalysed Oxydative couplingOxydative coupling

DPnDPn 4848 1414

Mw/MnMw/Mn 2.42.4 6.86.8

Tg (°C)Tg (°C) 9595 5555

MesomorphismMesomorphism 193 N 249193 N 249 nonenone

Fluorescence (nm)Fluorescence (nm) 424, 448, 475424, 448, 475 425, 495425, 495

M. Bernius, et al., Proc. SPIE, 3797, 129-137, (1999)

POLYFLUORENE DERIVATIVES

R R

BrBr

OB

O2)

1) 2.1 eq n-BuLi THF -78°C

R R

BBO

OO

O

R R

BrBr

R R

n

Pd(0)[(PPh3)4]

Toluene, Na2CO3

Reflux 48h, Ar

Drawback of the Yamamoto route : low solubility of the polymer in DMF Adaptation of the Suzuki reaction (Dow Chemical + others)

Possibility of making fluorene based copolymers with a wide variety of comonomers :

N

R

N

R

N

R

N

R

N

R

S

RO

OR

NS

N

Possibility of finely tuning properties of the EL polymers

COPOLYMERISATIONFluorene based copolymers

Poly(9,9-dialkylfluorene)s tend to aggregate upon annealing or during operation

W. L. Yu, et al. Chem. Commun., 1837-1838, (1999)

Use of a lower band gap comonomer

C6H13 C6H13 OC10H21

C10H21O n

PDHFDDOP

PL = 40%

PL spectra of PDHF

PL spectra of PDHFDDOP

Quantum confinement – Perovskite Quantum confinement – Perovskite layers and Q-dotslayers and Q-dots

Luminescence from quantum confinement

When a wave lenght can be held into a small size environment, this is called quantum confinement

Exemple 1 : Plasmon resonnance into a gold nanoparticle of a Q-dot

Exemple 2 : Confinement into a bidimensionnal layer of an hybrid organic-inorganic perovskite

Résolution in the harmonic case

Hypotheses Solutions

A second order developpment shows the fonctions are paraboles

Avec:

2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3,0 3,1 3,2

Energie (eV)

Optical Density Photoluminescence

Alternance of infinite organic/inorganic plans

Eliaison≈ 220 meV

« strong » excitons observables at 300 K

[2]

Schematic electronic structure

• Luminescence at room temperature

Exemple : Organic-inorganic perovskites – (2 d-Q-well)

Q-dots - Size effects

The Q-dots are very small nanoparticles of chalcogenides, where the wavelength is confined and the emission is size-dependant.

Chemical synthesis

Inorganic materials where optical properties are linked with electron confinement

Type of materials: Various metal chalcogenides

Composition effects

Blinking as a consequence of single photon emission!

Second part of the course: Basics of

Nonlinear Optics (NLO)

Basics of Nonlinear Optics

At the molecular scale, molecules are influenced by electromagnetic fields without need of absorption.

The first effect is simply diffraction (linear index change) as a result of the « slowing down » of the propagation in matter vs vacuum. Simple one-photon absorpation is also a linear effect.

There are higher order effects, whose intensity is much smaller (not observable at standard intensities)

Macroscopic situation: Intense light modifiy matter polarization.

Upon application of an electric field, induced dipolar moments

appear in the matter, which cause induced polarization P.

The linear (1) term is a second order tensor.

For low powers, P = (1) E This is the linear response of matter to light, the polarisation has the same direction than the incident light, and can be related to the linear refraction index.

We have the simple relation = 1 + 4(1) = n2

Simplified situation: Only one light beam, and only one direction counts

If the light is polarized, only the field direction counts, the equation becomes scalar, and the powers 2 and 3 in the trigonometric equations can be linearized.

With:

We have:

It comes out that, in this very classical situation, second order NLO will give rise to generation of frequency doubling and an additionnal constant electric field, while third order NLO will give rise to frequency tripling + generation of an harmonic at the same wavelength.

Second order NLO

The non-linear (2)

The non-linear response is a third order tensor and therefore can mix responses to two different incident beams.

P2 = (2) E1E2 and therefore implies the possibility of frequency mixing.

(2) different from zero implies non-centrosymetry in both the material, and the active component, otherwise the effects cancel.

The non-linear (2) term is a third order tensor.

The P2 tensor comes down to a scalar, like

(2) .We have:

Pzzz = (2) zzz E2

z.

For most NLO effects,the response of a material is usually much higher in a privileged direction,

usually chosen for z axis (sometimes called x).

Privileged direction (z)

1

2nd order NLO active material

2

1

2

1 21 12

Second order NLO, the general case:

If beams have same direction and polarization, and phase matching, we come back to the directionnal case, with simple wave mixing. We have:

Etotal = E1cos(1t) + E2cos(2t)

Calculation (of the simplest case)

P2 = (2) Etotal2 , therefore:

P2 = (2) {1/2[ E12 + E2

2 + E12 cos(21t)+ E2

2cos(22t)] +

E1E2cos(1+2)t + E1E2cos(1+2)t

The first term (in white) corresponds to the induced static polarization, the second (in red) to the second harmonic generation (frequency doubling) the third (in yellow) to the frequency sum generation and the last one (in green) to the frequency difference generation.

The frequency doubling

This is by far the largest application of second order NLO

P2 = (2) EE and therefore generates a wave with doubled frequency.

The main application is the UV laser (of weak power) for eg information storage..

Red Blue (sum frequency)

NLO active material

Other possibilities

1) The non-linear response can be used to generate sum and difference frequencies to detect eg IR beams.

IR

Yellow

Orange (frequency difference)

Green (frequency sum)

2) The non-linear response can be used to generate modulation of the linear refraction index through application of a constant field, this is the electrooptic effect (or Pockels effect).

The electrooptic effect

P2 = (2) EE therefore P = (1) (E0+E) + (2) (E0+E)2

P = (1) E0 + (2) E02+ (2(2)E0+ (1)) E + (2) E2

Applying an external field comes to submit the medium to a sollicitation E = E0 + E(). E0 is usually large compared to E. If the field is aligned with the light direction the tensor solves to the scalar, along this direction.

Static term « new » refraction ≈ n2 Small

Therefore we have the « new » refraction index given by:

n2 – n02 = 2(2)E0

Third order NLO

The 3rd order NLO

One wave is generated at triple frequency, and one at the same frequency.

Applications in optical gates (Kerr effect) and UV lasers.

Red

UV (frequency tripling)

NLO 3rd order active material

red (harmonic generation at same frequency)

The P3 tensor is reduced, but not to a simple scalar, we have:

Pzzzz = (3) zzzz E3

z.

However, this time, the (3) term contains two components, because not only frequency tripling

can occur, but also generation at the same frequency, by simultaneous frequency addition and

soustraction

Again the z direction can be privileged along the field direction.

Privileged direction (z)

The non-linear (3)

The third order non-linear response is a fourth order tensor and therefore can mix responses to three different incident beams.

P2 = (3) E1 E2 E3 and therefore implies many possibilities of frequency mixing. The general case is extremely complicated…

(3) different from zero also for centrosymetric molecules and materials always observed!

The 3rd order NLO

Generation of triple frequency occurs just like frequency doubling,

only the (3) zzzz values are usually smaller than (2)

zzz values .

Generation of same frequency through 3rd order NLO effects leads to a light induced apparent refraction index change called optical Kerr effect. The effect looks like the previously presented Pockels effects, except that there is no applied permanent electric field.

However, if a permanent electric field is applied on a 3rd order optical material, it has also an effect on the apparent refraction index (analogous to Pockels effect) which is called static Kerr effect.

For a nonlinear material, the electric polarization field P will depend on the electric field E:

where ε0 is the vacuum permittivity and χ(n) is the n-th order component of the electric susceptibility of the

medium. The ":" symbol represents the scalar product between matrices. We can write that relationship explicitly; the i-th component for the vector P can be expressed as:

where i = 1,2,3. It is often assumed that P1 = Px, i.e. the component parallel to x of the polarization field; E2 = Ey

and so on.For a linear medium, only the first term of this equation is significant and the polarization varies linearly with the electric field. For materials exhibiting a non-negligible Kerr effect, the third, χ(3) term is significant, with the even-order terms typically dropping out due to inversion symmetry of the Kerr medium. Consider the net electric field E produced by a light wave of frequency ω together with an external electric field E0:

where Eω is the vector amplitude of the wave.

Combining these two equations produces a complex expression for P. For the DC Kerr effect (E° surimposed) , we can neglect all except the linear terms and those in

Static Kerr effect

Therefore :

Optical (or AC) Kerr effect

In the optical or AC Kerr effect, an intense beam of light in a medium can itself provide the modulating electric field, without the need for an external field to be applied. In this case, the electric field is given by:

where Eω is the amplitude of the wave as before.

Combining this with the equation for the polarization, and taking only linear terms and those in χ(3)|Eω|3:

As before, this looks like a linear susceptibility with an additional non-linear term:

and since:

where n0=(1+χLIN)1/2 is the linear refractive index. Using a Taylor approximation, since χNL

<< n02, this gives an intensity dependent refractive index (IDRI) of:

where n2 is the second-order nonlinear refractive index, and I is the intensity of the wave. The refractive index change is thus

proportional to the intensity of the light travelling through the medium.The values of n2 are relatively small for most materials, on the order of 10-20 m2 W-1 for typical glasses. Therefore beam

intensities in the GW cm-2 range are necessary to produce significant variations in refractive index via the AC Kerr effect.

Two-photon adsorption

This process corresponds to the simultaneous absorption of two photons, which is possible if there is of course phase matching. This is a 3rd order

process. This is a resonnant process involving the imaginary part of (3).

2-photon absorption may generate classical fluorescence !

Two-photon adsorption : Very localized fluorescence

Molecular scale: What happens

Molecules for NLO

At the molecular scale, molecules are influenced by electromagnetic fields without need of absorption.

A molecule which is sensitive to an electric field is a molecule with electronic delocalization

For 2nd order NLO, it has to be non-centrosymetric, and it is good to exhibit a high dipole moment

For 3rd order NLO, it is enough to have flexible delocalized electrons.

Molecules for NLO

At the molecular scale, the molecules are individually polarized. We have:P = P(0) + E() + E(1)E(2) + E(1)E(2)E(3) +…

Where P(0) represents the permanent dipole moment of the molecule, and the other terms the induced dipoles, through interaction with light.

Despite a molecule may have a distorted dipole moment, most of the molecules, and especially the one used in NLO, have a main axis through which the largest component appears, and which will be choses as z. Therefore, the best molecules will present a high dipole moment in a privileged direction.

Molecules for 2nd order NLO

AD

µ0

AD

µ1

µ1 - µ0 depends on the spacer length

Molecules with high dipole moment are prefered.

Typical example: The paranitroaniline (one of the first molecules studied)

NO2H2N

µ0

NH2N

µ1

O-

O

zzz = TCUnidirectional molecule:

Molecules for 2nd order NLO: The two levels model for SHG

zzz = CT (-2, ,) = (3 e2h/4m) F()f

Calculations show that:

Where m and e are respecitvely the mass and the charge of the electron, h the Planck constant, F() a frequence dependant factor and the difference between the dipole moments in the fundamental and first excited state ( = e-g), and f the oscillator strength. E represents

the energy of the incident light (h) and E° the energy of the electronic transition between the two levels.

F() = )4)(( 220

220

0

EEEE

E

= )4)(( 220

220

40

EEEE

E

Molecules for 2nd order NLO: The two levels model for SHG (2)

When E 0, the term does tend towards 0, but towards a value that is really representing the polarizability of the molecules, ie its nonlinear reaction to an electric field sollicitation. This term is called (0) and we have :

CT = (3 e2h/4m) E0-3 f

Then, the at any frequency can be expressed as a function of b(0) and the frequency. It comes:

The first term is an intrinsic characteristics of the molecule, and the second a frequency factor that rises when one gets close to the one photon or the two-photon transition (but also absorption !!).

Molecules for 2nd order NLO: The two levels model for SHG (2)

The at any frequency can be also expressed as a

function of (0) and the pulsations. It comes:

Molecules for 2nd order NLO: The relation between and .

Basically, the macroscopic polarisability is the integrated sum of the microscopic ones.

When all molecules are oriented, with an angle, with the incident field:

f is the local electric field correction factor, which depends on the polarity of the solvent/medium.

Non polar Polar( = n2)

Ideal molecules for NLO response:Donor-acceptor conjugated molecules

Donor Bridge Acceptor

-conjugated

Most prepared and studied families

AR2N

AR2N

AR2N N

N

AR2Nn

SAR2N

SSn

PNA family Oligophenylenes family

Stilbene family Azo dyes family

Oligothienylenes family

Ground and excited state

In the 2-level approximation, people consider that the first excited state corresponds to the complete charge transfer between the donor and the acceptor group, as represented for the classical NLO-phores shown left.

Examples of molecules and values

Examples of molecules and values (2)

Examples of molecules and values (3)

Examples of molecules and values: Organometallics

Examples of molecules with other geometries (distorted and V-shaped)

Examples of molecules with other geometries (calixarenes)

Examples of molecules with other geometries (octupoles)

Synthesis of azodyes: Para red

Molecules for 3rd order NLO

We recall:P = P(0) + E() + E(1)E(2) + E(1)E(2)E(3) +…

Therefore, the best third order molecules will also need to present a high electronic flexibility, but a high dipole moment in the ground state is no longer mandatory.

However, we have, for a 2-states molecule:

xxxx (-, , -, )

014

02 2 3

012

1 02

02 2 2

02 24( )

( )

( ) ( )

0

1

D A1 , µ1

D A0 , µ0

µ01, 0

Quadrupoles are OK, despite the momentum of the ground tate is zero!

Molecules for 3rd order NLO

D A1 , µ1

D A0 , µ0

µ01, 0

D---A---D or

D-spacer-D or

A-spacer-A

Examples of molecules only for 3rd order NLO

R R

n

N N

NN

FeFe

X X

X = -, Ph , ,

Optical limitation

(2-photon absorption)

Optical Kerr effect

Figures of merit for Kerr effect

So the important parameter is n2, nut it may be considered relatively, compared to the 2-photon absorption and the standard absorption .

W = n2/ and T = /n2 , where and are as defined above,

are the figures of merit to consider sonce they represent respectively the relative efficiency and transparency of the molecule

NN

NO2

NN

NO2

NH2

N

DO3 PYDO3

Figures of merit for Kerr effect: Comparison between two record molecules

DO3 is a classical dye while PYDO3 is non classical annd belongs to the pull-push-pull group.

One and two photons absorption, along with One and two photons absorption, along with ofofDO3 DO3 and its pyrrole counterpart PYDO3and its pyrrole counterpart PYDO3

NN

NO2

NN

NO2

NH2

N

DO3 PYDO3

1.0

0.8

0.6

0.4

0.2

0.0

1000 800 600 400

Wavelength (nm)

250

200

150

100

50

0

DO3

PYDO3

A la fois les absorptions à un et deux photons sont décalées vers le bleu du DO3 au Pyrrole-DO3

Gammas at 1280 nm, out of resonnance for the two molecules

PYDO3 : (+137±70)10-36 esu, DO3: (+256±94)10-36 esu.

P. AUDEBERT, K. OHTA, K. KAMADA and M. ANDO Chem.Phys. Lett, 2000.

The are almost the same, despite the large offset from resonnance in the pyrrole !

1 photon

2 photons

Bibliography:

1)Fluorescence:

2)NLO Personnal and Zyss’s group data + T. Verbiest, S. Houbrechts, M. Kauranen, K. Clays and A.

PersoonsJ. Mater. Chem., 1997, 7(11), 2175–2189

Dzekuje bardzo !