Second-order nonlinear optics in isotropic liquids: Hyper-Rayleigh scattering in solution

ELSEVIER

Journal of Mdccdar

Liquids67 (1995)133- 155

Second-order nonlinear optics in isotropic liquids: Hyper-Rayleigh scattering in solution.

In honour of Prof. Em. Pierre Huyskens on the occasion of his retirement

Koen Clays, Eric He&-i&x,

Myriam Triest, and Andre Persoons

Laboratory of Chemical and BiologicalDynamics Centerfor Research in Molecular Photonicsand Electronics Universityof Leuven, Celestijnenlaan2000, B-3001 Leuven, Belgium

The incoherent second-order nonlinear light scattering in a macroscopically isotropic molecular liquid has emerged as a simple and widely applicable determination

of the ftrst hyperpolarizability

technique

technique has become widely known as hyper-Rayleigh scattering. field-induced

second-harmonic

molecular hyperpolarizabilities. also limits its applicability

for the experimental

of nonlinear optical molecules in solution.

The

Until recently, elecnic-

generation was the only solution technique

to determine

Apart from being more complex a technique, the applied field

to neutral and dipolar solutions.

In this paper, we present the

specific advantages of the new hyper-Rayleigh scattering technique and exemplify its wider scope with results from three different kinds of molecular materials: octopoles, biological chromophores, and quantum colloids. 0167-7322/95/$09.50 0 1995E1sevierScienceB.V. All rights reserved SSD/O167-7322(95)00872-l

134

I. Introduction

The high peak power available in the early pulsed laser sources led to the experimental discovery of nonlinear optical (IVLO) effects in the 1960’s. Frequency-doubling centrosymmetric scattering

crystal was the first of these effects to be 0bserved.l

in isotropic samples was discovered only a few years later.:!

in a non-

Elastic harmonic The spatial and

temporal profile of the optical output of the early pulsed lasers did not allow for accurate intensity measurements of the second-order scattered light, precluding the retrieval of a value for the hyperpolarizability of the molecules in solution. The application of an electric field over a solution of dipolar molecules3 induced the polar order necessary for second-order nonlinear optical effects to be observed on a macroscopic scale. The electric-field-induced

second-

harmonic generation (EFISHG) technique kcame the standard technique for the experimental determination

of the fast hyperpolarizability.4‘6

The electro-optically

Q-switched Nd:YAG

laser is a reliable source for the fundamental beam. The interaction between orienting field and dipolar molecules is well known.7

Over a period of some 20 years, EFISHG was used to

measure a wealth of hyperpolarizability

data on dipolar molecules,8~g leading to snucmre-

property relationships that are strongly biased towards the dipolar paradigm

The necessary application of an electric field to induce the polar order on a macroscopic scale has a number of disadvantages.

First of all, the technique is inherently

limited in

applicability to neutral and dipolar molecules. The interaction of the orienting DC field with the second hyperpolarizability contribution

also generates light at the second-harmonic

frequency.

This

is normally neglected. The experimental result is then the scalar product of the

vector part of the hyperpolarizability tensor with the dipole moment vector. Therefore, one has to know the magnitude and the relative orientation of the dipole moment with respect to the hyperpolarizability.

The angle between the two is normally assumed to be either 0 or 180

degrees. One is then left with the problem of estimating the dipole moment in its own reaction field.7 The calculation of the local field factor normally uses the Lorentz approximation.

The

ultimate result is only the vector part of the hyperpolruizability tensor. Finally, the cell design is not straightforward

and does not allow routine measurement

or even automation

of the

procedure.

Injection

seeding of Q-switched lasers is a technique

longitudinal mode to lase.1°-12 and spatial pulse profile. characteristics,

This preventsmode

to allow only one single

beating and results in a smooth temporal

Using this fundamental

laser source with much improved

we recurred to the original elastic harmonic light scattering to overcome the

135

limitations

of the EFISHG technique.

It proved possible to systematically

Rayleigh scattering @IRS) intensity of the nonlinearly

study the hyper-

scattered light as a function of the

fundamental light intensity and concentration of NLO molecules, which results in a value for the molecular

hyperpolarizability.

13 The systematic

study of structural,

solvent, and

wavelength dependence of this value has led to a reconsideration of the molecularstructural requirements for efficient second-order effects.

In this contribution the theoretical basis of hyper-Rayleigh scattering is briefly recalled in Section II. The experimental set-up, originally developed with Q-switched nanosecond pulsed lasers, but now also extended to tunable femtosecond continuous wave laser sources, is described in Section III. As a typical example of the new classes of materials that can be measured by HRS, octopolar molecules and their hyperpolarizability

are discussed in Section

IV. The discovery of a large nonlinear effect in the protein Bacteriorhodopsin systematic

study of the NLO properties of biological chromophores.

led us to a

An overview of the

results from this ongoing study is presented in Section V. The third-order NLO properties of quantum colloids

have been studied for some time.

In section VI, we present the first

preliminary results on the second-order susceptibility of these artificial materials.

II. Theoretical framework On the microscopic level, the induced dipole moment per molecule is

Here, pi is the component of the induced dipole moment along the molecule-fixed i-axis, is the &component

of the second-rank, first-order (3x3 = 9 elements) polarizabity

piik is the #-component hyperpolarizability

of the third-rank,

second-order

tensor fi, yijkl is the ijkl-component

first

third-order

tensor x and Ej is the electric-field

(3x3~3~3 = 81 elements)

second hyperpolarizability

component along the@&.

The classical Einstein summation convention applies.

At the macroscopic

tensor a,

(3x3~3 = 27 elements) of the fourth-rank,

aii

level, the analogous equation applies.

Limiting the analysis to

second-order effects, the induced dipole moment per volume unit Pi (2 0)becomes

(2)

136

The ikl-component Bikr (-2W;

of the

macroscopic

second-order

nonlinear

susceptibility,

0, W) is only zero when averaged over time or space. Translational fluctuations

(density fluctuations)

result in a nonzero linear susceptibility,

leading to first-order

linear

Rayleigh scattering. For second-order effects, spatial and/or temporal orientational fluctuations are the cause of a non-zero susceptibility

Bi~,(-261;0,0)

scattering. Correlations between the values Bikl,l(-20;

leading to hyper-Rayleigh

O, O) and Bj~,2 (-2 0; O, W) for

two different volumes 1 and 2 are assumed to exist only over distances small compared to the wavelength.

The intensity

of the hyper-Rayleigh

signal then becomes proportional

to

dv . For randomly oriented individual molecules, them are no specific phase( Bikl,l Bjmn,2) av relations between the scatteredfieldr. This allows the summation of the individual scattering intensities.

The intensity of the harmonic scattered light then becomes proportional

concentration direction

of the NLO molecules and to (&,,,flXYr)(IV.

cosines

over all possible directions

to the

Averaging the product of the

for an isotropic

system then gives the

transformation between molecule-fixed axis and laboratory coordinates. The resulting formulae ,143

where ij and k are the molecule-futed Cartesian coordinates, while X, Y and Z refer to the laboratory frame. These expressions form the basis of the analysis of the scattering intensities for different polarizations towards values for molecular hyperpolarizability tensor components. The number of non-zero tensor components depends on the specific symmetry of the molecule. consequence, symmetries.

is different for different molecular p ( ~)l(p:,) The first reports of harmonic light scattering did not include an actual value for the depolarization ratio,

hyperpolarizability be measured,

tensor components, but the relative ease with which depolarization ratios can

spurred the study of tetrahedral molecules.

hyperpolarizability depolarization

As a

There is only one non-zero

tensor component for this specific symmetry,

ratio of 3/2. The deviation of the experimentally

p,,

resulting

in a

observed ratio .from this

theoretical value was then interpreted as indicative of molecular interaction.2J5

137

For the historically important class of asymmetrically para-substituted electron systems, there is only one dominant tensor component.

conjugated IF-

This is the charge-transfer

component along the direction of the molecular z-axis. Tbe term &

is then by far the largest

in Eqs. 3 and 4. The total intensity of the harmonic scattered light can then be written as

The proportionality factor G includes all the theoretical factors, such as the wavelength, angular and distance dependence

of the scattered intensity and the average of the products of the

direction cosines (i.e. l/7 or l/35, depending on the polarization), as well as the instrumental factors, including the solid angle of photon collection, the detection efficiency and gain. The quadratic dependence of the second-order scattered light intensity on the fundamental

light

intensity is always experimentally observed. From this dependence, the quadratic coefficient I,,lG

1s

obtained.

N, is the number

density (the concentmtion in number of molecules per

cubic centimeter) of species with major hyperpolarizabiity simple two-component to a linear concentration

tensor component p,,,,.

For a

mixture of solute and solvent assuming the same symmetry, this leads dependence of 12w/Ii

as a function of

intercept is determined by the first hyperpolarizabiity,

N, of

the solute.

The

density and molecular weight of the

solvent, the slope by the concentration and the hyperpolarizability of the solute. Both contain the proportionality

factor G. When a value for the hyperpolarizability of the solvent is known,

this G can be calculated and used to obtain a value for the hyperpolarizability

of the solute, or

the other way around. This method effectively eliminates the need for local field correction factors at optical frequencies and is referred to as the internal reference method. hyperpolarizability

When the

of the solvent is not known, or when the solvent used is cenuosymmetric,

a

calibration with an external reference - with the appropriate local field correction factors - can be performed.

When solute and solvent, or unknown and reference, are of different symmetry, the averages of the products of the direction cosines can not be factor& out. They have to be taken into account when deducing a value for the hyperpolarizability harmonic scattered intensities.

from the relative second-

III. Experimental set-up and measurement procedure The originally developed instrument uses the high peak power pulses of a Q-switched Nd-YAG laser.

The intense infrared light pulses (8 ns, c 10 mI, 1064 nm) of an injection

seeded laser are focused in a small cell. The experiments are performed well below-threshold for other nonlinear

effects, such as stimulated

Brillouin

and Raman scattering.

The

fundamental light intensity is varied by means of a half-wave plate between polarizers, to check the quadratic dependence of HRS signal on IR intensity.

The second-order scattered light is

collected with a retroreflecting concave mirror and an aspheric condenser, discriminated against linear scattering by appropriate filters, and measured by gated integrators. procedure is computer-controlled.

The measurement

Insertion of an analyzing polarizer allows depolarization

measurements for the resolution into specific hyperpolarizability tensor components. A detailed description

of this nanosecond

version of the HRS instrument, including laser system and

modulation requirements, sample volume considerations and photon collection efficiency, has been given previously. l6 The special aspects of injection seeding and its advantages relevant for nonlinear

optical conversion

processes in general and hyper-Rayleigh

scattering

in

particular, have also been discussed. l7

With the advent of femtosecond conlinuous-wave mode-locked laser sources with high repetition

rate, hyper-Rayleigh

scattering experiments have become much more simple to

perform.

The 82 MHz pulse repetition rate of a self-mode-locked Titanium-doped

laser can for all practical purposes be considered quasi-continuous.

sapphire

Hence, we can think of this

laser as a source of continuous high power and increase the sensitivity with lock-in detection techniques.

The high peak power (1 Watt average power at 82 MHz in 80 fsec pulses gives

140 kWatt peak power) will broaden the femtosecond pulse by passing through optical elements with non-zero group velocity dispersion.

So-called femtosecond optics are thus

necessary in the femtosecond version of the HRS instrument.

The gated detection electronics

can be replaced by a chopper and a phase-sensitive detector. The intensity variation and photon collection is exactly the same as for the nanosecond version. The experimental details of the femtosecond version of the HRS instrument, including the special requirements for the optics, have been discussed recently. 18 The advantages of this system include the simpler, and hence cheaper, detection electronics, and the wavelength tunability.

139

IV. Octopolar molecules The first applications of the hyper-Rayleigh scattering technique were in the accurate determination of the solvent dependence of the hyperpolarizability values of dipolar molecules and in the sensitive measurement of the low values for some small saturated molecules.

This

enabled us to extend the Equivalent Internal Field model from conjugated monosubstituted benzene and stilbene derivatives to fully saturated molecules. l3 It was soon realized however, that HRS was also applicable to new classes of molecules that could not be measured with EFISHG. Ionic molecules are one example. lgv20 Another interesting class of molecules are the ones with an octopolar charge distribution.21

These octopolar molecules are characterized

by the absence of all vector-like properties, such as ground- and excited-state dipole moment, but they have a non-zero first hyperpolarizability.

However, before harmonic light scattering

emerged as an experimental tool to measure its value, the NLO properties of octopoles could not be studied on the molecular level, because the absence of a dipole moment also precludes EFISHG measurements.

The advantages of integrating nonpolar species for NLO applications

range from easier non-centrosymmenic total nonlinearity

crystallization, less dipolar aggregate formation, higher

(more hyperpolarizability

transparency trade-off.21

tensor components)

and better efficiency-

The major problem for device implementation

is the macroscopic,

ordering of apolar species in structures other than crystals. The familiar poling technique in polymer matrices is not applicable. One way of introducing order could be photo-assisted22 or all-optical poling.23

We have used hyper-Rayleigh hyperpolarizability

scattering

of the tricyanometbanide

for the determination

anion C[CN]S-.

of the first

For two reasons, this species

cannot bc measured by EFISHG: first, a charged ion will migrate in the field and no electric field can be established over the conducting solution and, secondly, an apolar molecule would not orient in the field. The potassium salt of cyanoform was synthesized following a known procedure24 and purified by crystallization. symmetry.

This highly polarizable anion is planar with D’jh

For this symmetry, all but four components of the hyperpolarizability

tensor are

zero, and they all have the same absolute value in the transparency regime. With the x-axis taken along a C-C-N bond direction and the z-axis perpendicular to the plane defined by the plane of the molecule, /3,

= - /?,

= - /3,

= - p,.

The value of this component was

determined in water, methanol, and ethanol. Methanol was used as the internal reference for the measurement in that solvent. Since methanol has another symmetry (approximately CSv) with other non-zero hyperpolatizability

components, a value for the pzZZ component

(0.26 x

lo-30 esu, with the z-axis along the C-O bond) was deduced by tensorial analysis, based on

140

quantumchemical

calculations.

The p._

value for the tricyanomethanide

anion in methanol

was found to be (7.0 f 1.5) x lo-30 esu at 1064 nm. Measurements in other solvents were referred to the measurement in methanol (external reference method). The p,

values for the

three solvents were identical within experimental error. The dielectric property of the solvent has little if no influence on the nonlinear optical properties of octopolar species. The-two-level model cannot be invoked to calculate a dispersion-free value for the hyperpolarizability, there is no (difference transparency

since

between the) dipole moment of ground- and excited state.

The

down to 300 nm ensures however that little if no resonance enhancement

is

observed.

This promising value of 7 x lo-30 esu for a small octopolar ion spurred the interest in this new class of molecules.

With the availability of a simple experimental

measure the hyperpolarizability

technique to

of these apolar molecules, more systematic and comparative

studies led us to step away from the strictly dipolar paradigm.25

V. Biological

chromophores

The study of the nonlinear optical properties of biological chromophores was prompted by the finding

of a very large NLO effect in the protein

Bacteriorhodopsin

(bR).26

Bacteriorhodopsin is the light-energy transducing protein present in the Purple Membrane of the bacterium Halobacterium Halobium.27-2g Under extreme conditions (oxygen deprivation), these halophilic bacteria can convert light energy to chemical energy (stored in adenosine uiphosphate,

ATP, molecules) through the establishment of a proton gradient over the Purple

Membrane.

Photoexcitation

protonation-deprotonation

of bR triggers a complex photocycle that involves a chain of from one side of the membrane to the other.

It is now firmly

established that the key element in the light absorption and the subsequent photocycle is the retinal chromophore.

This moiety is covalently linked to the protein backbone by a protonated

Schiff base linkage to the &-amino group of the Lysine-216 amino acid residue. Because of this unique photochemical received

considerable

behaviour and the excellent thermal and temporal stability, bR has attention

for potential

applications

in molecular

opto-electronic

The molecular hyperpolarizability of bR is unusually high and attempts have been made to measure its value using two-photon spectrosc~py~~~~~ and oriented poly(viny1 alcohol) ruatrice~.~~ With both these in&t

techniques, the actual value for the hyperpolarizabillty was

141

highly

dependent on the estimation of some critical parameters. Due to the presence of charged

amino acid residues on the protein surface, the more conventional Second-Harmonic scattering

Generation

was the natural

Electric-Field-Induced

(EFISHG) technique could not be used. technique

for the direct measurement

Hyper-Rayleigh of the molecular

hyperpolarizability of the protein, without any a priori assumptions.

The protein bacteriorhodopsin

(SIGMA) was solubilized in Triton X-100 (5% vol.) in

au acetate buffer (0.1 M, pH 5.0). The kinetics of the solubilization process have been studied in great detai1.37

It has been demonstrated

that this solubilization

finally results in one

monomeric protein molecule per one micelle of Triton X-1OO.38 The effect of the ongoing

30,000

25,000

0

20

40

60

80

Time (hours)

Fig. 1 : Time dependence of the hyperpolarizability of bR during the solubilization in Triton X-100 (5% vol.) in an acetate buffer (0.1 M, pH 5.0).

100

142

solubilization from oligomeric to monomeric form has a pronounced effect on the second-order scattered light, and, hence, on the effective value of the molecular hyperpolarizability. HRS intensity drops by a factor of 100 during the solubilization.

The

From the quadratic relation

between the second-order scattered light intensity and the hyperpolarizability. this intensity drop translates into a lo-fold drop in value for j.3. This is exemplified in Fig. 1. The data were taken with time intervals in the order of hours. The solid hue is a fit to the equation

Pqy= P*R(1+nexP - t/ Glrs1”

(6)

_-

a

0

I

I

I

I

20

40

60

80

time

100

(hours)

Fig. 2. Time dependence of the hydrodynamic diameter of the Triton X- 100 micelles with (squares) and without (circles) Bacteriorhodopsin.

143

The factor (1 + n exp

- f/‘cchs). (decaying to 1 upon complete solubilization)

takes into

account that at the onset of the solubilization bR is present as a mixture of oligomers, resulting from the slow decomposition of the purple membrane by the smfactant.

. The factor n thus

represents the initial degree of association. The relaxation time Zchrs for solubilization

of 37

hours, as determined by correlated HRS, is in good agreement with the time constant for solubilization obtained from quasi-elastic (linear) light scattering (Fig. 2). The micelle diameter d,# decreased according to

da

= dbR,sol

+ c

exp - ‘1~qds

(7)

A value of 36 hours was found for the decay time ZPers. The initial particle diameter d ea.0- dbR,sol + c = 17 nm determines the volume of the associated protein and surfactant molecules. The particle diameter found after complete solubiization, def,, = dbR.sol = 11 .S nm is in good agreement with previously reported values for bR in the same surfactant.39~40 The hyperpolarizability in good agreement

value found for bR after complete solubilization (2100 x lo-30 esu) is with the previously

reported values from two-photon

absorption

spectroscopy (2250 x lo-30 esu)34*35 and the value measured in oriented poly(viny1 alcohol) manices (2500 x lo-30 esu).36

In order to understand the high hyperpolarizability

of bR, a systematic theoretical and

experimental study of the NLO properties of various retinal derivatives was started. Since me hyperpolarizability is sensitive to the local electric field at the chromophore binding site, it was postulated that HRS on retinal derivatives would reveal information on the exact structure of the retinal binding pocket. The exact structure of this binding site is still subject to great uncertainty and in literature only modest agreement exists. interaction

It turned out, however, that a bulk solvent

could not simulate the highly specific chromophore-apoprotein

interactions.

Nevertheless, the measurements gave a lot of information on the influence of the molecular structure on the p value, when compared to quantum chemical calculations.

The experimental

and theoretical results are in excellent agreement for the effects of chain elongation nonlinearity-to-transparency

and

trade-off.

The first hyperpolarizability /3 of vitamin A acetate, retinoic acid, retinal Schiff base, retinal and protonated retinal Schiff base (PRSB), measured in methanol at 1064 nm, are given in Table I, along with the wavelength of maximal absorption and the two-level extrapolated values p0.

144

R

amax

(nm)

in MeOH

00

OICH

-If

3

ho64 (lo-30

PO esu)

( 10m30 esu)

in MeOH

in MeOH

326

140

80

351

310

160

365

470

220

380

730

300

445

3600

900

0 Vitamin A acetate

h

0 OYH

Retinoic acid

b

N’ Bu

Retinal Schiff base

AO Retinal

AN’

Bu A+

PRSB

Table I : Dependence of the experimental and static first hyperpolarizabiiity on the position of the absorption band maximum.

The observation that substituting the end gmup of the retinal polyene system for a more electron withdrawing group induces a bathochromic shift in the position of the absorption band maximum

was studied systematically

for the first time in 1967.41

After these early

considerations, a vast number of retinal derivatives have been prepared, especially for achieving a better understanding protonated

of the chromophore-apoprotein

Schiff base its characteristic

incorporated

in the bacteriorhodopsin

interactions

that give the retinal

absorption spectrum and photocycle

when it is

binding pocket.42 We have chosen for the tabulated

derivatives because of their commercial availability (SIGMA) and convenient wavelength of maximal absorption (326-445 nm).

The hyperpolarizability molecule

without

of retinal is higher than one would generally expect for a

a strong electron donor-acceptor

system.

Using quantum

chemical

calculations that take into account the polarity of the solvent, we have been able to demonstrate that this is due to the favourable degree of bond length alternation of the retinal polyene chain in polar solvents.26p43

Furthermore, the aldehyde group has been found to be a very efficient

electron acceptor for polyenes.44

The strong trade-off between nonlinearity and transparency, or the dependence of the hyperpolarizability contribution

on the position of the main absorption maximum confirms that the major

to the optical nonlinearity can be attributed to the first low lying, dipole allowed,

state. Quantum chemical calculations indeed show that the evolution of /3 is governed by the dipole moment variation between the two states and also by the position of the absorption band maximum Amax. For the protonated retinal Schiff base, these calculations also predict some two-photon resonance enhancement.45

The observed slope of a plot of log(&)/log(Amax)

is

7.7 and is to be compared with the slope of similar plots for benzene derivatives (4.4) and stilbene derivatives (8.7).8 Thus for a given ;Imax, the optical nonlinearity offered by retinal derivatives is intermediate between that offered by benzene and stilbene derivatives. disadvantage

A main

of these molecules is their instability when exposed to air and light for long

periods of time, which will limit their applicability in nonlinear optical devices.

The influence of the conjugation length on the hyperpolatizability is a recurring theme in second-order nonlinear optic~.~~~~~~~ An exponential increase of the hyperpolarizability the number

of double bonds has always been observed.

hyperpolarizability polyenes with 2,3,6

of /kyclocitral,

pionone,

We have measured

retinal and PApo-8’-carotenal.

and 10 double bonds, respectively.

with

the first

These are pure

146

The spectral properties of these molecules have been studied in detail to determine the nature of the electronic states of retinaL4*

The general similarity between the absorption

spectra of the polyenones, such as j%ionone, and the corresponding polyenals supports the fact that the hyperpolarizability polyenals.

of p-ionone can readily be compared to that of the other three

For j?-cyclocitral, the presence of a weak, but well-separated n-n* band is noted

below the onset of the main absorption band, that corresponds to the lAg-lBu four derivatives.

transition in the

Upon chain elongation, the n-rc* band is completely swamped by the

1Bu transition shifting to higher wavelengths.

1Ag-

As was the case for retinal, we expect this state

to give the largest contribution to pin the long and short chain derivatives.

2.55

Fig. 3. Transparency-nonlinearity

trade-off for all-tram derivatives in methanol.

The molecules are (with increasing /3 and &ax): Vitamin A acetate, Retinoic acid, Retinal Schiff base Retinal, PRSB.

2.65

147

The

observed exponential dependence of /I on the number of double bonds is given by

log(p) = 3.54 log(n) - 0.481 for the values at 1064 nm and log@)) = 2.35 log(n) - 0.248, where n is the number of double bonds in the polyene system, including the CO bond. The magnitude of the slope falls in the range of the observed slopes for the aw-diphenylpolyene derivatives, where 2 double bonds are counted for each phenyl unit. These derivatives were substituted with a strong electron donor-acceptor system and the magnitude of the slope was shown to be dependent

upon the nature of the end groups.

Because of the difference

in

counting schemes used and the different end groups, there is no simple way to compare these results.

It can be argued, however, that for a polyene system, substituted

electron donor-acceptor demonstrate

with a stronger

system the magnitude of the slope should be higher.

the superiority

This would

of the double bond to the phenyl ring for achieving

a large

hyperpolarizability.

C

Fig. 4: ~cyclocitml

(a), @ionone (b), retinal (c), and PApo-8’carotenal

Table II : Dependence of the experimental and static first hyperpolarizability on the number of double bonds in the polyene chain.

(d).

148

VI. Quantum colloids The properties of bulk material such as metals and semiconductors are determined by electrons that are not associated with individual nuclei as in single molecules.

The optical

nonlinearity in this class of materials is thought of as arising from the electronic characteristics of the bulk material. When a metal particle decreases in size, its properties deviate from those of bulk material and become size dependent. This phenomenon is referred to as the quantumsize effect. Many terms are used to describe these ultra small particles such as, quantum-dots, nanocrystals, Q-particles, clusters, etc. The particles in the quantum-size region show discrete large-molecule like electronic states that shift to higher energy with smaller particle size caused by charge carrier confinement.

This perturbation of the energy levels leads to new optical

properties that may find applications in the optical data processing field. There are two reasons for the choice of silver as the metal to study. surfaces are known to generate a second-harmonic

First, silver

signal in reflection. The first to report

second harmonic generation from a silver film was Brown. @ Wokaun subsequently observed SHG obtained

from silver island films50 and Bloembergen

harmonic generation

from metal surfaces.5l

started the study of second-

Since then considerable

progress is made in

understanding the nonlinear responses of simple metal surfaces5* In centrosymmetric approximation,

media there is no second-order optical response in the dipole

but at a surface or interface, where the inversion symmetry is broken, the

nonlinear susceptibility

is non vanishing in this approximation.

generated at the interface.

Thus a strong SHG signal is

Because of this surface sensitivity

SHG should be strongly

influenced by electronic properties localized at the interface, i.e. surface or interface states. On the other hand, quadrupole and higher-order terms may contribute to a bulk SHG response that may interfere with the surface response.

So both terms, the bulk and the surface response,

contribute to the induced nonlinear polarization of the medium, but their magnitudes and phases relative to each other are not known. The second reason for investigating silver particles is that the study of the enhancement of surface phenomena due to microscopic surface roughness53 included not only the SurfaceEnhanced-Raman-Spectroscopy enhancement

(SERS)54 but also other phenomena:

Chen observed an

of the SH signal when the silver surface was microscopic roughened.55

Even

more interesting was the measurement of a fifty-fold increase in the SH intensity of a silver surface covered with pyridine opposed to the SHG intensity observed in the absence of pyridine.56 With the I-IRS technique is it now possible to investigate whether these phenomena occur on silver colloid surfaces too.

149

All reagents used were of analytical grade and the aqueous solutions were prepared with distilled and filtered (milliQ system) water, The silver sols were prepared according to the method of Creighton by introducing

1mM silver nitrate (AgN03,

100mL) with vigorous

stirring into an ice-cold solution of 2 mhJ sodium borohydride (NaBH4, 300mL).57

The

yellow sol obtained was heated to about 60-62°C and then allowed to cool to room temperature. The colloids formed were stable (no precipitation or change in colour) over several weeks. The sols showed the characteristic single visible extinction band of silver particles near 400 nm, with little variation in the absorption curves depending on the particle sire. The size of the colloidal particles was determined with the Quasi-Elastic-Light-Scattering

(QELS) technique.58

The particles had a diameter in the range 20-35 run.

1,400

I

I

I

I

1200

1600

t

0

400

800

2000

fundamental intensity (a.u.) Fig 5. The enhancement of the HRS signal of silver colloids in the presence of pNA.

150

Figure 5 shows the results for the hyper-Rayleigh experiments on silver colloids. The open circles show the quadratic dependence for para-nitroaniline(RNA) at a concentration of 0.4 mM in water. The filled circles are for silver colloids with a diameter of 20 nm at a concentration

of 0.25 mM Ag in water. The triangles finally show the dependence

of the

hyper-Rayleigh signal at optical frequency 2w on the incident intensity at frequency o for paranitroaniline in the presence of silver colloids, both at the same concentration. increase of the SHG signal of pNA in the presence of silver colloids.

There is a clear

There are several

explanations for this effect. The simplest one is that the alignment of the pNA molecules upon adsorption on the silver colloid-surface

causes the increase in SHG.

The fact that pNA

molecules actually adsorb on silver colloids is shown in the absorption spectrum of the solution after the sol has coagulated and precipitated: there is in solution no pNA detectable. However, as SHG has been reported for centrosymmetric

molecules absorbed on silver surfaces, 5g the

alignment only could not explain for this enhancement. destabilization

There is also the possibility

of a

of the colloids upon adding pNA. The disturbing of the electric double layer

could result in a little aggregation of the colloids, but no significant change of diameter was found with QELS measurements. Other physical mechanisms for an enhancement originate either from the electrodynamic effect, associated with a localized surface-plasmon resonance, 60 or from the charge-transfer effect involving an electron transition between the molecule and the metal surface.6162

There is also an enhancement of the SHG signal observed by us of silver

colloids in the presence of pyridine. Which effect is responsible for the enhancement is not yet clear. The effect of the silver particle diameter on the SHG signal of silver colloids is shown in Fig. 6. There is a strong size-dependence of the second-harmonic intensity: when the particle diameter increases, the signal increases.

The fluorescence of the colloidal solution shifts

towards 532 nm above 35 nm particle diameter, disturbing the measurements

At this diameter

the quadratic dependence of the SHG signal on the incident beam is lost and becomes a thirdorder dependence.

Colloids with a 20-35 nm diameter are rather large to be called quantum-

dots and to exhibit quantum-size effects. However the surface plasmon is a collective excitation that is characteristic of solids, therefore its quantum-size effect is expected to occur at larger scales than those of atomic-based properties such as ionization energies or binding energies. Since the surface plasmon is a surface localized excitation, its intensity is roughly proportional to the surface area_63 This could explain the increase of the SHG signal.

The fmt results of actual measurements of the hyperpolarizabiity

of silver colloids are

shown in Fig. 7. To conduct these measurements it was necessary to use an external reference, pNA in methanol, as the hyperpolarizability of water is not known ($NA = 34 x lo-30 esu).

151

_

800

I

I

I

0

600 500 0 0

400 300 00

200 ??

100 0

??

0 25

I

I

I

I

27

29

31

33

35

diameter Ag-colldids (nm)

Fig. 6. The dependence of the quadratic coefficient in HRS on the particle diameter for the silver colloid particle.

As expected, the hyperpolarizability hyperpolarizability

of the colloids is dependent on their particle size. The

value for a colloid with 21 nm particle diameter amounts to (7 x 105) x lo-

30 esu per colloid particle, which becomes, with au average of 7 x 105 Ag atoms per colloid, a j3 of 1 x lo-30 esu per Ag atom in the colloid particle. The second-order nonlinear effect in these colloid particles is believed to be caused by defects, disturbing the symmetry of the colloids.

Hence, the hyperpolarizability

single atom. plasmons.

value cannot simply be divided down to a value per

The nonlinear scattering is a collective effect, very much the same as surface

Further measurements will be necessary to make any definite remarks on the size-

dependence of the hyperpolarizabiity

of silver colloids and on the importance of defects.

20

21

22 23 24 particle diameter (MI)

25

26

Fig. 7. The hyperpolarizabihty of the silver colloids with different sizes.

VII. Perspectives

We have demonstrated the wide applicability of the hyper-Rayleigh scattering technique: results were given for octopolar, biological and quantum-sized systems. The non-degenerate version of hyper-Rayleigh extension

scattering, with two different input frequencies,

of the existing technique.

In stead of the second-harmonic

is the natural

frequency

in the

degenerate case, sum and difference frequency are generated in parametric light scattering. This parametric

version of hyper-Rayleigh

determination of first hyperpolarizabities measurements.64

scattering can also be used for the experimental and has some specific advantages for depolarization

153

The wavelength-tunable

laser source for HRS, either the Optical Parametric Oscillator

(OPO) for the nanosecond version, or for example the Ti:sapphim laser with its femtosecond pulse train, opens the perspective for completely automated dispersion studies. The internal reference method will be very valuable, since the dispersion, i.e. the resonance enhancement of the larger, conjugated, solute molecule is in a wavelength region where the dispersion of the small, saturated solvent molecule is negligible. hyperpolarizability

An essentially dispersion-free value for the

of the solvent can then be taken as the reference over the wavelength range

of interest. Acknowledgements

Koen Clays is indebted to the Research Council of the University of Leuven for a postdoctoral fellowship.

Eric Hendrickx is a Research Assistant of the Belgian National Fund

for Scientific Research. This research is supported by grants from the Belgian (IUAP- 16) and Flemish government (EIT 1181) and from the Belgian National Fund for Scientific Research (FKFO 9.0012.92). References

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