Nonlinear Optical Properties of Correlated Chromophores in Organic Mesoscopic Superstructures

Nonlinear Optical Properties of CorrelatedChromophores in Organic MesoscopicSuperstructures**

By Koen Clays,* Eric Hendrickx, Thierry Verbiest, andAndrØ Persoons*

A new design strategy for enhanced nonlinear optical properties, based on a simple vector model and situated at the meso-scopic level, between the microscopic molecular level and the macroscopic bulk, is explained and exemplified by a number oforganic superstructures. The second-order nonlinear optical properties of the structures are analyzed in terms of the corre-sponding properties of the individual monomeric chromophores that constitute the structure. The chromophores can be con-sidered as electronically independent with a high symmetry. A simple vector model can then account for the large second-order nonlinear optical polarizability of the mesoscopic superstructure. Another important advantage that is clear from thevector analysis is the improved chromophore alignment, owing to the enlarged mesoscopic dipole moment.

1. Introduction

Organic molecular materials have been proposed as po-tential candidates for constructing a number of nonlinearoptical (NLO) devices, such as frequency-doublers, electro-optic modulators, all-optical modulators, and holographydevices. The former two are situated in the field of second-order nonlinear optics. Such devices are already heavilyused in information transmission and two-dimensional datastorage, albeit on an inorganic basis. The latter two devices,based on organic materials, are on the verge of being usedfor information handling and three-dimensional data stor-age, based on third-order NLO effects. In our modern so-ciety with ever increasing need for information retrieval,handling, and storage capacity, there is a need for fast de-vices that can manipulate all-optical information. Owing tothe purely electronic nature of the NLO response in organ-ic molecular materials, devices based on organics are inher-ently fast. Modulation bandwidths of 100 GHz for electro-optic modulation in a polymer have been reported. Themagnitude of the nonlinear response at the molecular levelcan also be extremely large. Incorporation of the individualmolecules, with their large molecular first hyperpolarizabil-ity and fast response, into bulk devices with large andstable NLO susceptibilities, is not so straightforward as in-

organic crystal growth. In this article, we will describe astrategy to enhance the NLO response at the mesoscopiclevelÐbetween the microscopic level of the individual mol-ecule and the macroscopic level of the bulkÐin the field ofsecond-order nonlinear optics. With the advent of unifyingtheories for linear and nonlinear polarization in organicchromophores[1,2] and with the intrinsic relation betweenphotorefractivity and second-order nonlinear optics,[3] theresults are automatically also relevant for third-order non-linear optics.

In the following part, we point out the boundary condi-tions for this analysis. The complementary nature of thetwo experimental techniques for the determination ofthe molecular first hyperpolarizability, i.e., electric-field-induced second-harmonic generation (EFISHG) and hy-per-Rayleigh scattering (HRS), are shown in the third part.The fourth part gives selected examples of this vector anal-ysis. The part following this indicates when the model fails.The concluding part then summarizes the molecular engi-neering concepts that can be deduced from this analysis.

2. Boundary Conditions for the Simple VectorModel

Our strategy to enhance the second-order NLO responseis based on correlated individual chromophores covalentlyincorporated in a superstructure. These chromophores donot show nonlinear interaction. Because of the electronicnature of the molecular response to electromagnetic radia-tion of the wavelength considered, the electronic linear ab-sorption spectrum does not show evidence of electronic in-teraction between the chromophores. It has been shownthat it is also possible to obtain NLO response from thenonlinear interaction of individual molecules that only

Adv. Mater. 1998, 10, No. 9 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1998 0935-9648/98/0906-0643 $ 17.50+.50/0 643

±

[*] Prof. K. Clays, Dr. E. Hendrickx, Dr. T. Verbiest, Prof. A. PersoonsLaboratory of Chemical and Biological DynamicsCenter for Research on Molecular Electronics and PhotonicsCelestijnenlaan 200D, B-3001 Leuven (Belgium)

[**] This research was supported by research grants from the Fund forScientific Research, Flanders (FWO-V, G.0308.96), from the Belgiangovernment (IUAP P4/11, ªSupramolecular Chemistry and Supramo-lecular Catalysisº) and from the University of Leuven (GOA/95/01).

644 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1998 0935-9648/98/0906-0644 $ 17.50+.50/0 Adv. Mater. 1998, 10, No. 9

show linear optical properties.[4] For these effects to be ob-served, a large molecular first hyperpolarizability is notneeded. This is an alternative strategy that will not be con-sidered in this review.

Our strategy is also different from single-molecule opti-mization. This approach is a typical synthetic one, where in-dividual chromophores are designed and synthesized basedon monomolecular engineering guidelines. A classical ex-ample of such a guideline in optics in general is the relationbetween electron density and (linear) polarizability, as ithappens, both expressed in units of (reciprocal) volume.For a second-order first hyperpolarizability to be present,non-centrosymmetry needs to be induced. This can be doneby introducing electron-donating and -withdrawing substi-tuents. Classical organic chemistry strongly suggests ortho,or even better, para substitution. Intuitively, one would ex-pect stronger second-order nonlinearity for stronger elec-tron-donating and -withdrawing substituents. This is whererecent research has provided new insights and better engi-neering rules at the single-molecule level.[5] On the otherhand, for third-order nonlinear optics, where, at first sight,non-centrosymmetry does not play a role, it has been theo-retically predicted and now also experimentally demon-strated that substitution with increasingly stronger electronacceptors increasingly enhances the third-order response.[6]

So, in both second- and third-order molecular nonlinearoptics, single-molecule optimization has also proven a verysuccessful approach.

The strategy that we want to describe here has the intrin-sic advantage that it can be applied to any monomolecular

material available. Hence, whatever monomolecular mate-rial single-molecule optimization approaches may bring inthe future, they can without any difficulty be introduced ina correlated way into a mesoscopic superstructure.

Another strategy to enlarge the second-order NLO re-sponse is situated at the macroscopic level of inducing astable bulk non-centrosymmetry. This strategy is typically acombination of physical aspects of inducing a large degreeof order in the bulk, combined with chemical aspects ofcrosslinking or imidization. Large advances have beenmade in this field also.[7] Once again, all approaches viableat the macroscopic level can be applied to the superstruc-ture at the mesoscopic level.

The enhancement of the orientation of individual mono-meric chromophores in a liquid-crystalline (mesogenic)bulk material along the liquid-crystalline director is an-other important and viable approach that is also outsidethe scope of this article. It does not relate to the chemicalpre-organization into stable covalently linked entities. In asmuch as mesogenic mesoscopic materials could be de-signed and synthesized, enhanced orientation of the meso-scopic entity induced along the mesogenic director wouldstill be possible.

The individual molecules that have been incorporated insuperstructures all have relatively high symmetry. Theirmolecular first hyperpolarizability can be approximatedwith good accuracy by a single component of the third-ranksecond-order first hyperpolarizability tensor. This singlecomponent can be treated as a vector, completely de-scribed by its magnitude and direction. Therefore, coordi-

K. Clays et al. / Correlated Chromophores in Organic Mesoscopic Superstructures

AndrØ Persoons obtained his Ph.D. in chemistry at the Catholic University of Leuven in 1965under the supervision of Prof. J. C. Jungers. After working with Leo De Maeyer on instrumen-tal techniques for the study of fast reactions at the Max Planck Institute for Physical Chemistryin Göttingen, Germany, he returned to the University of Leuven, where, together with DeMaeyer, he founded the Laboratory of Chemical and Biological Dynamics. He became fullprofessor at Leuven in 1977 and extraordinary professor at the University of Brussels in 1987.Recently he and Jean-Luc BrØdas founded the Center for Research on Molecular Electronicsand Photonics. Persoons' research efforts are currently focused on the nonlinear optical prop-erties of organic and polymeric materials, particularly chiral molecules, and the developmentof new experimental techniques.

Koen Clays received his Ph.D. in chemistry from the University of Leuven in 1989, for hiswork on hybrid multifrequency phasefluorometry with pulsed excitation under the supervisionof Prof. AndrØ Persoons. In 1991 he went to the Corporate Research Laboratories of the East-man Kodak Company in Rochester, New York, where he was a postdoctoral researcher in thegroup of David J. Williams. He then returned to the Chemistry Department, University of Leu-ven, initially as a Senior Research Associate of the Fund for Scientific Research in Flanders,and later as associate professor. His research interests lie in the development of instrumenta-tion for physical measurements in chemistry. He is currently working on nano- and femto-second static and dynamic hyper-Rayleigh scattering for molecular nonlinear optics.

nate transformations from molecular axes to laboratoryaxes or averaging of direction cosines over all possible an-gles can be used to express the experimentally measuredbulk susceptibility in terms of molecular hyperpolarizabil-ity and the relative positions of the molecules. By the sametoken, experimentally determined hyperpolarizability ten-sor components for the superstructure can be related to thesingle tensor component of the constituent monomer.

Such coordinate transformation is based on a fixed rel-ative position of the monomeric chromophore with respectto the macroscopic structure, or with respect to the super-structure. For both of the latter, a certain symmetry has tobe assumed. A complete description of the position of thechromophore in the bulk structure can be given in crystals.Therefore, an exact transformation from molecular hyper-polarizability to crystal susceptibility, based on the direc-tion cosines, is possible for crystals.[8,9] Crystals also havethe intrinsic advantage of high thermodynamic stability.Other examples of bulk structures are thin films of orientedmolecules. The technique to orient the molecules can beLangmuir±Blodgett deposition or electric-field poling.Both techniques result in a C¥v symmetry of limited tem-poral and/or thermal stability. For poling, the relation be-tween molecular and bulk nonlinearity includes the dipolemoment of the chromophore, the static orienting field am-plitude, and the poling temperature. For Langmuir±Blod-gett films, the tilt angle between the molecular axis and thenormal to the plane of the film enters the coordinate trans-formation. For these typical examples of bulk structures oforiented molecules with specific phase relations betweenthe individual chromophores, a coherent second-harmonicsignal can be obtained by shining a powerful laser beam onthese bulk structures. With the knowledge of the relationbetween the observed second-harmonic intensity, i.e., thebulk susceptibility, and the molecular nonlinearity, it is pos-sible to derive an experimental value for the first hyperpo-larizability. For the determination of hyperpolarizabilitiesof molecules in solution, this technique is called electric-field-induced second-harmonic generation (EFISHG).Averaging over all possible orientations, on the other hand,is what is necessary in hyper-Rayleigh scattering (HRS)from isotropic solutions. The complementary nature ofthese two experimental techniques for the determinationof molecular first hyperpolarizabilities will be addressed inthe following part.

3. Complementary Nature of EFISHG and HRSin Experimental Nonlinear Optics

Although incoherent second-order nonlinear light scat-tering was discovered[10] prior to coherent second-harmonicgeneration under the influence of an orienting electricfield,[11] HRS did not evolve into a generally accepted ex-perimental technique until the advent of injection seededlasers. The more efficient technique of generating a coher-

ent second-harmonic beam did not have to await this anddeveloped into the first standard technique to measure hy-perpolarizabilities of molecules in solution.

For the experimental determination of the second-orderfirst hyperpolarizability, some sort of non-centrosymmetryhas to be present in the solution. This can be achieved byapplying a static electric field over a solution of neutralmolecules with dipolar chromophores. Implicitly, this de-scription limits the applicability of this EFISHG technique:i) No ionic species can be measured: they would migrate

instead of orient under the influence of the static field.ii) Only dipolar molecules can be measured, because inter-

action with the electric field is necessary to induce thenon-centrosymmetry.

The latter limitation did not prove a disadvantage untilrecently. The paradigm of second-order nonlinear opticsused to be an asymmetrically para-substituted (azo)ben-zene or stilbene, hence a dipolar molecule.

EFISHG[12±14] is inherently a third-order process: Twooptical fields are necessary to generate the optical harmon-ic, but a third (static) field is also present. A completeanalysis of the different contributions to the second-ordersignal obtained from EFISHG reveals that there are differ-ent contributions to the molecular third-order NLO polar-izability, which is inherently determined by the third-orderprocess. There is a purely electronic third-order contribu-tion, inherently third order; a purely vibrational contribu-tion, also third order in nature; and a so-called average di-polar rotational contribution, gr. The latter contribution isin fact a combination of a second-order parameter with an-other field, yielding a third-order contribution. For theanalysis towards a value for the second-order nonlinear po-larizability b of dipolar molecules, we have to focus on thiscontribution. The experimental conditions are parallel po-larizations of fundamental, second-harmonic, and staticfields.

The rotational contribution stems from the second har-monic that is generated by partially oriented dipolar mol-ecules. The orientation is induced by the lowering of theenergy when a dipole moment orients parallel to the field.The orientation of the molecules induces a specific phaserelation that leads to the generation of a coherent second-harmonic signal. The coherence length of the solution andthe interaction length, i.e., the length of the cell containingthe solution, ultimately determine the magnitude of this co-herent signal. The wedge-shaped cell is therefore instru-mental to factor out this length dependence and to accu-rately determine the amplitude. Referencing can be donein different ways. Either a piece of quartz can be used, withthe appropriate w(2) value, or a solution containing a knownconcentration of a dipolar chromophore with a known firsthyperpolarizability value can be used.

What is important in EFISHG, especially in the light ofthe complementarity with HRS, is: what is actually experi-mentally determined? The expression for the rotationalcontribution is determined by the scalar product of the di-




pole moment vector with the vector part of the third-rankhyperpolarizability tensor (Eq. 1).

gr �m�bvec

5kT� m�bJ�1

5kT(1)

The reduction spectrum of rank-three tensors contains,in the general case, one (pseudo)scalar (weight J = 0),three vectors (J = 1), two (pseudo)deviators (J = 2), andone septor (J = 3).[15] As seen from Equation 1, we onlyhave to deal with the vectorial parts (J = 1). They trans-form as a vector. Hence, the scalar product of the dipolemoment vector with a vector part of the first hyper-polarizability tensor can be written as the simple productof two scalars (Eq. 2), when we designate y as the anglebetween the molecular axis (z-axis) and the dipolemoment axis.

gr �mzbz cos y

5kT(2)

The assumption is often made that the two vectors arecollinear, leading to the familiar expression for EFISHG,Equation 3.

gr �mzbz

5kT(3)

From the measurement of the intensity of the generatedsecond harmonic for a dipolar molecule and with knowl-edge of the value for the dipole moment, an experimentalvalue for b can be obtained. This value relates to the hyper-polarizability tensor components as follows, for the com-pletely general case (bk = (bkmndnm + bnkmdnm + bnmkdnm)/3).

bz = bzzz+13

(bzyy + bzxx + byzy + bxzx + byyz + bxxz) (4)

In the more specific case of second-harmonic generation,with degeneracy between the optical fields (bijk = bikj),Equation 4 reduces to Equation 5.

bz = bzzz+13

(bzyy + bzxx + 2byzy + 2bxzx) (5)

When Kleinman[16] symmetry is applicable (bijk = bjik)Equation 6 holds.

bz = bzxx+ bzyy + bzzz (6)

These relations between the experimental observable inEFISHG, bz, and the molecular third-rank hyperpolariz-ability tensor components, do not reflect the (approximate)symmetry of the molecule yet. When we accept (approxi-

mate) C2v symmetry for a molecule with a planar conju-gated p-electron system (in the xz-plane), we are still leftwith these three non-zero and independent tensor compo-nents.

For C¥v symmetry, there are only two independent ten-sor components bzzz and bzyy = bzxx, resulting in Equa-tion 7.

bz = 2bzxx+ bzzz (7)

In most cases, for charge-transfer molecules, only a singlemajor non-zero tensor component can be assumed. Then,Equation 7 finally reduces to Equation 8.

bz = bzzz (8)

It is important to make the difference, and state the exactrelation, between the measured observable and the actualhyperpolarizability tensor component(s), even if, for speci-fic experimental conditions and molecular symmetries,their values turn out to be identical. What is also importantis the fact that only one experimental condition is favorablefor EFISHG, namely, parallel polarizations for all opticaland static fields. This leads to only one observable, result-ing in only a single value to be deduced. It is not possiblewith EFISHG to determine more than one tensor compo-nent, hence, one often contends with the approximationthat either bzzz was determined, or with the statement thatbz was obtained, in any of the above mentioned relations tothe individual tensor components. Even then, the assump-tion that the dipole moment vector and the vector part ofthe third-rank tensor along the molecular z-axis are col-linear, is implicitly made. However, even if one was to beinterested in checking this assumption, it would not bepossible, since EFISHG can only provide one independentobservable.

In HRS,[17±19] no extrinsic non-centrosymmetry is in-duced in a solution. Advantage is taken of the temporaland spatial deviation from the average centrosymmetrycaused by fluctuations. Owing to the isotropic distributionof chromophores in a solution without orienting field, therelations between the experimental observable and the hy-perpolarizability tensor components are determined by theaveraging of direction cosines over all possible orientationsin solution. The results have been obtained for the generalcase, i.e., as a function of all 27 possible hyperpolarizabilitytensor components.[20,21] Again, degeneracy of the opticalfields in HRS (bijk = bikj, dispersive HRS)[22] reduces thisnumber to 18, while Kleinman symmetry (bijk = bjik) resultsin only 10 independent components. Molecular symmetrythen ultimately determines the number of non-zero compo-nents.

Since in HRS, there is no preferred orientation inducedby an additional static field, there is the possibility of vary-


ing the experimental conditions in order to increase thenumber of independent observables. The number of theo-retically possible independent observations, and hence thenumber of tensor components that can be obtained byHRS, is at most five. For sum frequency generation, thisnumber is six, owing to the possibility of distinguishing be-tween the two optical fundamental fields.[22] The experi-mental difficulty has precluded the determination of thisnumber of components. What is experimentally realistic inHRS, is an additional depolarization measurement, apartfrom the classical measurement of the intensity of the sec-ond-order incoherent scattered light. The two measure-ments, the total intensity measurement and the depolariza-tion ratio (or two intensity measurements, one with paralleland one with perpendicular polarization for fundamentaland second harmonic), represent two independent observa-bles and allow the experimental determination of two ten-sor components. In general practice these are bzzz and bzxx,resulting in Equation 9 for the total intensity measurementand in Equation 10 for the depolarization ratio r, where q= bzxx/bzzz.

b2HRS

D E� 6

35b2

zzz� 16

105bzzzbzxx �

38105

b2zxx

(9)

r � 15�18q�27q2

3ÿ2q�11q2(10)

The total intensity HRS experiment basically consists ofmeasuring the amount of incoherently scattered opticalsecond harmonic (parallel and perpendicular output polari-zations) versus a reference. When only this single measure-ment is done, only one independent tensor component canbe obtained. For charge-transfer molecules, this is generallyapproximated by bzzz. The depolarization measurement isgenerally performed with a rotating analyzer inserted be-tween scattering cell and photomultiplier, but with reducednumerical aperture of the condensing system.[23±25] Fromthe theoretical depolarization ratio calculated as a functionof bzxx/bzzz (Eq. 10), it is then possible to derive from theexperimentally observed depolarization ratio, the ratio ofbzxx/bzzz. This then not only gives a value for bzxx, but addi-tionally a relative sign and a check on the assumption thatbzzz is responsible for most of the scattered light. For do-nor±acceptor charge-transfer molecules, this is always thecase.

The situation is drastically different at the mesomolecu-lar level for superstructures of these charge-transfer mol-ecules. Since the microscopic first hyperpolarizability ten-sor, associated with the constituting monomeric molecule,has only a single major component, bmono = bzzz,monomer,and this component belongs to the vector part of the third-rank tensor, it transforms like a vector. This allows the sim-ple vector calculation of the mesoscopic second-order non-linear polarizability tensor components bIJK of the super-structure, based on the single individual monomolecular

bmono and the relative angles between the vectors. For asuperstructure with a relatively high symmetry, a single an-gle and bmono can completely determine the mesoscopicnonlinear polarizability tensor. Depending on the symme-try of the mesomolecular superstructure, a certain numberof non-zero and independent nonlinear polarizability ten-sor components can be calculated. Their value is, however,only a function of the microscopic first hyperpolarizability,bmono, and this angle. Therefore, two independent observa-tions allow the experimental determination of bmono andthis angle. These two independent observations can be in-tensity and depolarization measurements in HRS. It canalso be EFISHG and HRS, since these techniques measuredifferent functions of the tensor components. It followsimmediately that, by combining EFISHG with intensityand depolarization in HRS, three independent non-zerotensor components can be determined. This technique hasbeen used successfully previously for the analysis of mono-meric dipolar chromophores with large off-diagonal hyper-polarizability tensor components.[26]

Other input for the analysis can also be used. Moleculargeometry is often obtained from theoretical calculations.Then, the over-determination by combining EFISHG withHRS results enables consistency checks or error estimationon the retrieved value for the bmono.

It is important to realize at this point that the value forbmono is not necessarily always identical to bzzz for themonomolecular model compound. Geometric interactionscan cause a change in linear and NLO properties. The dif-ference between bzzz and bmono can be used to estimate thedegree of geometric interaction. This kind of interactionmay lead to changes in the linear absorption spectrum, butis different from a purely electronic interaction. In ouranalysis, we neglect purely electronic interaction betweenthe individual chromophores. The monomeric constituentsof the superstructure are assumed to be electronically inde-pendent. Shifts in the linear absorption spectrum that areobserved for the superstructure are not attributed to elec-tronic interaction in aggregates. Exciton effects are notconsidered. Shifts in the electronic absorption spectrumcan be attributed to changes in electronic properties at themicroscopic level of the individual chromophore, as evi-denced also in the correlation between the linear absorp-tion spectrum and the first hyperpolarizability for the con-stituent.

4. Vector Analysis of the Second-OrderNonlinear Optical Properties of Mesostructures

Historically, the first report on large hyperpolarizabilitiesof organic superstructures dates back to the early develop-ment of EFISHG as an experimental technique for the de-termination of these molecular quantities.[27] The structurewas an a-helix-forming polypeptide. The (mono)peptide isthe microscopic constituent of the mesoscopic superstruc-




ture. Hydrogen bonding in appropriate polar solvents (e.g.,ethylene dichloride) allows for the formation of the specificright-handed a-helix configuration, characterized by3.6 peptides per turn of 0.54 nm, and the amino-acid resi-due on the outside. The first report was on poly(g-benzyl-L-glutamate), with a molecular weight of 550 000. This means2500 peptide units constituting the mesoscopic a-helixsuperstructure. The vector sum of the dipole momentsamounted to 6000 D, while for the mesoscopic second-order nonlinear polarizability, a value of 500 ´ 10±30 esu wasobtained. No more detailed information was given aboutthe geometry of the substituent on the helix. Hence, onlythe most simple geometry can be used, leading to a scalaranalysis in term of only the number of constituents. Thisresults in a microscopic value of 0.2 ´ 10±30 esu for themolecular first hyperpolarizability of a single constituent.Already from this very early report and over-simplisticanalysis, it is clear that large enhancements in nonlinearoptical response can be achieved.

Although the mesoscopic dipole moment does not di-rectly relate to the nonlinear optical response, its enhancedvalue will add to creating the non-centrosymmetric macro-scopic bulk structure. In fact, electric field saturation hasbeen observed. The alignment of the mesoscopic super-structure into a non-centrosymmetric macroscopic bulkstructure is, hence, almost complete. The bulk susceptibilitywill, therefore, in its turn, be enhanced by the geometricalstructure at the mesoscopic level.

Apart from this early report of enhancement, a slightlymore elaborate analysis in terms of the molecular first hy-perpolarizability and an average (cosine of the) angle be-tween the chromophores and the net dipole moment hasalso been reported for functionalized poly(g-methyl-L-glu-tamate).[28] However, no systematic study on optimizingmolecular structures had been performed until HRS wasdeveloped. Since then, additional information on the geo-metrical structure of the constituents in the superstructurehas become accessible.

The importance of the enhancement of the value for themesoscopic dipole moment can very elegantly be evi-denced by poly(g-methyl-L-glutamate). The generic struc-ture for a rigid multichromophore system is shown in Fig-ure 1. Within the limits of our vector model, we can writemmeso = nmmonoácosyñ. It is often also written that bmeso =nbmonoácosyñ, resulting in an actual decrease in hyperpolar-izability per chromophore. Our approach will consist of ex-actly stating the relationship between the individual bmono

and bmeso instead of taking the average, leading to a com-plete tensor analysis of the mesoscopic hyperpolarizability.However, it should be clear that the purely vectorial dipolemoment for the mesoscopic superstructure will be largerwhenever nácosyñ > 1.

The observation that the same condition has been de-rived for the enhancement of mb per chromophore is, again,the result of neglecting the tensor properties of the result-ing mesoscopic hyperpolarizability. Within this approxima-

tion, experimental enhancement factors up to 48 have beenreported for the dipole moment, while only 35 wasachieved for mb per chromophore.[28] However, when con-sidering only the improved orientation due to the dipolarinteraction with a field, an enhancement factor of 48 forthe dipole will result in a substantial enhancement of therelevant orientation factor, ácos3yñ, equal to the third-orderLangevin function, which is, before Langevin saturation oc-curs, linearly proportional to mE/kT.[29]

The analysis of the HRS intensity for the case of specificcorrelations between the individual scatterers has been giv-en previously.[21] The first time this so-called cooperativescattering was invoked to explain a large intensity of theHRS signal, and, hence, a large apparent first hyperpolariz-ability, was, coincidentally, also for a protein.[30] The tem-poral decay of the large apparent first hyperpolarizabilityof bacteriorhodopsin was explained by the on-going solubi-lization, as evidenced by time-resolved dynamic light scat-tering. The data could be quantitatively analyzed in termsof an initial degree of association and a time constant. Thetime constant for the decay of the first hyperpolarizability(37 h) was in good agreement with the one for the solubili-zation (36 h).[31] The initial degree of association (derivedfrom the curve fit to be at least 2.5) was already indicativeof the three-fold octopolar symmetry in the bacteriorho-dopsin trimers.

A complete analysis of the symmetry in bacteriorhodop-sin aggregates was performed by combining HRS intensityand depolarization measurements with the topography ofthe purple membrane fragments.[24] The proposed geom-etry of the aggregate was a trimer consisting of three mono-meric bacteriorhodopsin protein molecules around a three-fold axis of symmetry, with the three retinal moieties in themolecules at an angle y away from the plane of the purplemembrane, resulting in overall C3v symmetry (see Fig. 2).This geometry is very sensitive to the value of the tilt angley. Two limits can immediately be identified: i) y = 0�, whichmeans that the three retinals are in a single plane, resultingin a purely octopolar geometry with D3h symmetry and no


Fig. 1. Schematic representation of individual chromophores distributedalong the net dipole moment of a supramolecular structure.

dipole moment; ii) y = 90�, resulting in a purely dipolarC¥v symmetry with a mesoscopic dipole moment threetimes the monomeric one. From the corresponding limitingvalues for the experimental depolarization ratio in HRS(see Fig. 3), i) r = 1.5 for octopoles, ii) r = 5 for pure di-poles, it can already be seen that experimental determina-tion of this ratio will elucidate the geometry of the trimer.

Fig. 3. HRS depolarization ratio as a function of the angle between theplane of the purple membrane and the polyene chain of the retinal in bacte-riorhodopsin. The limits indicated are discussed in the text.

Based on the model, 11 non-zero first hyperpolarizabilitytensor components bIJK,T for the mesoscopic trimer can bewritten in terms of the tilt angle and the single tensor com-

ponent bmono of the microscopic monomeric protein mol-ecule (see set of Eqs. 11).

bXXZ,T = bXZX,T = 1.5(cos y)2(sin y)bmono

bXXY,T = bXYX,T = ±0.75(cos y)3bmono

bYXX,T = ±0.75(cos y)3bmono

bYYY,T = 0.75(cos y)3bmono (11)bYYX,T = bYXY,T = 1.5(cos y)2(sin y)bmono

bZXX,T = 1.5(cos y)2(sin y)bmono

bZYY,T = 1.5(cos y)2(sin y)bmono

bZZZ,T = 3(sin y)3bmono

From these expressions, the theoretical depolarizationratio can be calculated as a function of (sines y and cosinesx of) the tilt angle y only, since the value of bmono cancelsout (see Eq. 12).

r �97y

6�5435x

2 y4�5435x

4 y2�0:1286x6

935y

6ÿ 635x

2 y4�37x

4 y2�0:08571x6(12)

Then, from a simple, but accurate measurement of thedepolarization ratio r, an accurate value for the tilt angle ycan be derived. A value of (10 ± 1)� was obtained from thedepolarization ratio of 1.78 ± 0.08. This ratio is close to 1.5indeed, resulting in a small tilt angle, and, hence, to a largedegree, cancellation of the vector parts of the microscopicfirst hyperpolarizability tensors. It has been concluded thatthere is a significant octopolar contribution to the first hy-perpolarizability tensor in the bacteriorhodopsin trimers.

Although there must also be a (small) resulting dipolemoment, it may be necessary at this time to recall thatEFISHG is not possible with proteins. The charged amino-acid residues will always determine the interaction with theapplied static field in EFISHG. When there is a net charge,migration in the field will occur, instead of orientation. Atthe isoelectric point, with no net charge, the rotation of theprotein will be determined by the distribution of the aminoacid charges instead of by the direction of the dipole mo-ment of retinal. Hence, EFISHG can not provide an addi-tional independent observation. Additional informationcould, however, this time be obtained from topographicalstudies of the purple membrane containing the bacterio-rhodopsin trimers. Combining the size information (averageparticle size of 390 000 nm2 or median of the distribution of25 500 nm2) with the results from high-resolution electroncryomicroscopy (nine protein molecules per 101 nm2)yields as a conservative estimate of the first hyperpolariz-ability for the monomer bmono a value of (2000 ± 400) ´10±30 esu. This value is in good agreement with the one de-rived from classical HRS on completely solubilized, i.e.,monomeric, proteins.[31]

From these results, it was concluded that guidelines de-rived from protein structures could be used for the engi-neering of supramolecular structures with very high opticalnonlinearities, for example, with a more suitable relativeorientation, such that vectorial cancellation would occur to



Fig. 2. Top view and side view of the geometry for the mesoscopic bacterio-rhodopsin trimer in purple membrane. The arrows represent the vector partof the first hyperpolarizability tensor of the bacteriorhodopsin monomer.


a lesser extent. One such approach combined the helicityof a poly(isocyanide) helix with the nonlinear optical prop-erties of a side-chain chromophore.[32]

The individual chromophore in this study was a dialkyl-aminonitrostilbene dye. The mesoscopic superstructure wasinduced by the rigid helicity that is typical for poly(isocya-nides). This class of polymers has been proposed for thestudy of the persistence-length concept in dynamic lightscattering (or quasi-elastic light scattering), for the possibi-lity of synthesizing rigid-rod polymers of certain lengthwith uniform size distribution. For second-order nonlinearoptical effects, it is not the length or size distribution that isimportant, but the pre-packing of the chromophores asside-chains in a rigid, non-centrosymmetric way.

In this pre-package, the four chromophores per turn ofthe helix all make an angle y of 60� with respect to the axisof the helical backbone (see Fig. 4), as deduced from mo-lecular mechanics calculations using the consistent forcefield method.[33] With this value, and assumed C¥v symme-try, the two non-zero and independent tensor componentsfor the polymer helix bIJK,H can be expressed in terms ofthe molecular first hyperpolarizability bmono of the dyemonomer and the number of correlated pre-packaged dyesnc (Eqs. 13 and 14).

bZZZ,H = nc cos3ybmono (13)

bZXX,H = bXXZ,H =12

nc sin2y cos ybmono (14)

In this study, an enhancement factor for the first hyper-polarizability of the polymer versus the monomer was cal-culated. This theoretical value is a sole function of thenumber of chromophores with a rigid conformation. Thisnumber has been estimated by subtracting a number ofchromophores at both ends of the polymer, since there theturns of the polymer backbone are assumed to be loose, in-stead of in the rigid helical conformation. The predictedvalue for the enhancement is not achieved. This has beenattributed to a number of factors.[32] The more interestingobservation is, however, that the largest enhancement was

obtained for the chromophore side groups with a specificgeometry of the exterior electron-donating group. Thisparticular group resulted, on the one hand, in a lower valuefor the monomolecular first hyperpolarizability of the dyeitself, probably exactly because of this geometry, but on theother hand, in a larger enhancement factor. This points tothe additional rigidity caused by the specific geometry ofouter groups on the helix. These groups can be, as is thecase here, part of the nonlinear chromophore. In this case,they should not have a diluting effect on the overall num-ber density in the macroscopic bulk structure. It should bepossible, unlike the case here, to combine larger first hyper-polarizabilities with improved mesoscopic rigidity, to resultin even larger second-order nonlinear polarizabilities atthis mesoscopic level.

The other important aspect of this example is the greatlyenlarged value of the dipole moment for the mesoscopicsuperstructure. The enhancement factor here is experimen-tally found to be 43, in good agreement with the vectormodel of 82 correlated chromophores in a fixed, rigid con-formation with a tilt angle of 60� (cos 60� = 0.5). Again, thislarger dipole moment will result in an improved orientationfactor.

Another example where increasing the rigidity of thecovalently linked chromophores has been demonstrated,albeit resulting in a reduction in the nonlinear optical re-sponse, is in dendrimers. The reduction of the first hyper-polarizability of the dendritic mesoscopic superstructurehas been used to verify independently, with molecular(nonlinear optical) spectroscopy, the globular structure ofthe higher generation dendrimers, as postulated from in-trinsic-viscosity measurements (see Fig. 5). Therefore, thepoly(propylene imine) dendrimers were functionalizedwith chromophores with a single major hyperpolarizability


Fig. 4. Side view and top view of the geometry for the mesoscopic helicoidalpoly(isocyanide). The arrows represent the vector part of the first hyperpo-larizability tensor of the monomeric chromophore.

Fig. 5. Two-dimensional representation of the mesoscopic dendrimer func-tionalized with chromophores. Note the two-dimensional circular geometry,representative of the three-dimensional globular structure.

tensor component (depolarization ratio between 4 and 4.5).Two different coupling reactions with the amine outer shellof the dendrimers were used: an aldehyde was used to cre-ate the imine linkage without the possibility of hydrogenbonds, and an amide linkage was synthesized with an acidchloride, so as to induce the possibility of hydrogen bond-ing between adjacent chromophores. This hydrogen bond-ing would induce more rigidity amongst the chromophores.

A first result, valid for both the imine and the amidelinkage, is the leveling off of the mesoscopic second-ordernonlinear polarizability of the functionalized dendrimer forincreasing generations.[34] Alternatively, the apparent firsthyperpolarizability per chromophore on the dendrimerdrops. At first, in the dendrimers with low generation num-ber, there is a linear increase with number of end groups(related to the generation number). This indicates that theindividual chromophores have the same conformationalfreedom as in isotropic solutions. For the higher genera-tions, the leveling off is a consequence of the restricted mo-bility.

When comparing the imine with the amide linkage, notso much a leveling off, but actually a decrease of the meso-scopic second-order nonlinear polarizability is noticed forthe amide, with the possibility of hydrogen-bond forma-tion.[25] The even further increased rigidity amongst chro-mophores further lowers the mobility.

When now comparing the effect of the reduced mobilityor increased rigidity with the previous example of thepoly(isocyanide), it should be clear that the chromophoresin the dendrimer are in a rigid conformation that is not fa-vorable for second-order nonlinear optics, i.e., in a confor-mation where the vectorial properties cancel. This shouldbe close to a highly symmetric, centrosymmetrical struc-ture. The most likely approximate symmetry that still al-lows for second-harmonic generation, is the octopolar tet-rahedral symmetry. This was confirmed by depolarizationmeasurements on the dendrimers. A fairly low ratio be-tween 1.5 and 2 does indeed confirm a globular shape forthe dendrimers. In this way, this topology, already proposedon the basis of the intrinsic viscosity, which falls for highergenerations, has been independently confirmed.

It may be worthwhile here, after the dendrimers havebeen exemplified, to elaborate further on the other typesof polymers that are so often used in second-order non-linear optics. In general, the polymers themselves are nor-mally used only as a matrix which incorporates the non-linear optical chromophores. This then leads to the clearseparation of function and chemical moiety: The processa-ble polymer matrix is characterized mainly by its glass tran-sition temperature and the active chromophore used for itshyperpolarizability. In the ideal world, these two param-eters can be independently optimized: larger glass transi-tion temperatures for better temporal stability and higherpolarizability for larger nonlinear optical effects. Unfortun-ately, in the real world, a large hyperpolarizability is relatedto a small energy gap between the ground and excited state,

leading to an only fair temporal stability and high suscept-ibility to oxidation. Off course, this is also backed up bytheory. The search for polymers with a high glass transitiontemperature could only result in useful materials for sec-ond-order nonlinear optics after the chromophores withthe necessary thermal stability had been developed. Inthe ultimately stable polyimides, part of the chromophoreis incorporated in the main chain of the polymer. This isanalogous to the main-chain polymers originally proposedand developed by Willand and Williams,[35] where the chro-mophore is completelyÐfrom electron donor to electronwithdrawing groupÐincorporated in the polymer back-bone. This imbedding of the individual chromophore in thepolymer backbone is, in fact, only realized as being able toincrease the temporal stability of the orientation of thechromophores, which still has to be induced, most of thetime by electric-field poling, i.e., orientation of the dipolarchromophores under the influence of an electric field. Inthis sense, these polymers all fundamentally differ from theother examples given above: there is no preferred orienta-tion of the individual chromophores in these polymersprior to this poling.

One can wonder whether, on the other hand, for highloading of the polymer backbone with side-chain chromo-phores, unfavorable centrosymmetrical aggregation mightoccur. This would be revealed as a decrease in the first hy-perpolarizability per chromophore, as was the case for thedendrimers. This has not been observed in a comparativestudy, where both a highly nonlinear thiophene and a clas-sical azobenzene side-chain chromophore were linked to apoly(methacrylate) backbone with either a methyl or a do-decyl group as the linear optical side group. No reductionof the apparent first hyperpolarizability per chromophorewas observed for chromophore loadings up to almost 80 %of the repeat unit.[25] This means that no unfavorable inter-action takes place, but, off course, also that no enhance-ment is to be expected. Hence, these polymers are not ex-amples of our strategy. They will not be discussed furtherhere.

A particularly nice example of the successful applicationof the simple vector model is the story of the binaphthylethers (see Fig. 6, with n = 1, 2, 3, 4).[36] All conditions forthe applicability are fulfilled: the individual chromophoricmoieties of the binaphthyl ethers are in a fixed geometry;the second-order nonlinear optical properties of the mono-mer can be adequately described by a single hyperpolariz-ability tensor component; and the two nonlinear moietiesdo not show electronic ground-state interaction, althoughthe absorption spectra of different binaphthyl ethers doshow different wavelengths of maximal absorption for thecharge-transfer band for different numbers of methyleneunits between the two oxygens. In this specific case, thishas very nicely been explained in terms of varying elec-tron-donating capabilities of these oxygens. Therefore, notjust one, but two monomer model compounds have beenmeasured for comparison, one with the electron-donating




methoxy group present, 2-methoxy-6-nitronaphthalene,and one with this group absent, 2-nitronaphthalene. Thewavelengths of maximal charge-transfer absorption areblue shifted and identical (306 nm) for the nitronaphtha-lene and the n = 1 ether 1a. They are also identical but redshifted (336 nm) for the methoxynitronaphthalene, the n =4 ether 1d, and additionally, the binaphthyl ether with twomethoxy groups instead of the ring, 1e. At this point al-ready, the linear optical properties can be explained by thering strain and related to the value of the dihedral angle be-tween the two naphthalene moieties. This angle, as calcu-lated with AM1 semi-empirical calculations, evolves from44� for n = 1 (1a), with strong ring strain and no electron-donating capabilities, and, hence, a blue shift, to 90� for then = 4 (1d) and the open (1e) ether, with no ring strain, gooddonating properties, and a red shift.

The mesoscopic second-order nonlinear polarizabilitytensor for the binaphthyls, bIJK,B, has been analyzed interms of only two independent non-zero components,

which are a function of this dihedral angle and the micro-scopic value of the single hyperpolarizability tensor compo-nent of the monomer, bmono (see Eqs. 15 and 16).

bZZZ,B = 2 cosy2

� �3

bmono (15)

bZXX,B = bXZX,B = bXXZ,B = 2 siny2

� �2

cosy2

� �bmono (16)

Referring to Equation 7, it is clear that independentlyfrom EFISHG and independently from HRS, an experi-mental value for the microscopic monomeric first hyperpo-larizability can be retrieved. These values can then be com-pared with the values for the model compounds, but, moreinterestingly, the values resulting from EFISHG can becompared with the ones from HRS. Good agreement overall the values is then a powerful indication of the validity ofthe vectorial approach. All relevant parameters are sum-marized in Table 1.

The values for the microscopic first hyperpolarizabilityof the individual moiety bmono range from 10 ´ 10±30 esu forthe n = 1 ether 1a (in good agreement with the value of 8 ´10±30 esu for the nitronaphthalene) to 27 ´ 10±30 esu for then = 4 ether 1d (in turn in good agreement with 26 ´10±30 esu for the methoxynitronaphthalene and the openether 1e). Note the excellent continuity in the derived mi-croscopic monomeric first hyperpolarizability bmono ingoing from the nitronaphthalene model or from the n = 1ether 1a to the methoxynitronaphthalene, the n = 4 ether1d, or the open ring binaphthyl ether 1e.

This exceptionally good agreement of the resulting val-ues for the individual nonlinear optical moieties with thecorresponding monomeric model compounds shows in avery convincing way the applicability of the model. Thesame model has already been applied to another set of bi-naphthol derivatives, with the same good agreement, bothbetween HRS and EFISHG experimental results and be-tween model compounds and open structures.[37]

It may be important to point out that a change in spec-troscopic properties, as observed here, is not necessarily an


Table 1. Calculated dihedral angle y and experimental wavelength of maximal absorption lmax, dipole momentm, hyperpolarizability tensor components bIJK obtained both from EFISHG and from HRS, and derived mono-mer hyperpolarizability bmono, again both from EFISHG and from HRS, for the binaphthyl ethers and modelcompounds (all measurements in CHCl3, 25 �C; * denotes multiphoton fluorescence, precluding the incoherentHRS measurement; na: not applicable).

Fig. 6. Molecular structure of the binaphthyl ethers and corresponding ge-ometry. The arrows represent the vector part of the first hyperpolarizabilitytensor of the monomeric chromophore.

indication of electronic ground-state interaction. As shownwith these binaphthyl ethers, it can also be a result of achange in the electronic properties of the individual moiety.This is then also evidenced in the resulting microscopic firsthyperpolarizability of this moiety. This is a nice example ofa situation where bmono is not necessarily equal to bzzz ofthe monomeric model compounds. However, combinationwith the linear absorption data indicates that the bmono ofthe constituent monomers should differ from bzzz.

5. Failure of the Vector Analysis

The intrinsic boundary conditions for the applicability ofthe vector model were given in the introduction. Wheneverone of these is not fulfilled, the vector analysis fails.

When the individual chromophores do show appreciableelectronic interaction, it is no longer possible to univocallyrelate the mesoscopic second-order nonlinear polarizabilitytensor to the value for the single tensor component for thechromophore. The charge-transfer contribution to the firsthyperpolarizability in electron donor±acceptor charge-transfer complexes is, in fact, already a good example. Bythe simple vector model proposed here, the first hyperpo-larizability of 4-4¢ asymmetrically substituted stilbenesshould be the vector sum of the individually substitutedbenzenes. That this is not the case, was one of the first con-clusions of the search for structure±property relations insecond-order nonlinear optics. Evidence of the electronicinteraction is utterly clear from the charge-transfer absorp-tion band in the UV-vis spectrum.

It should be clear that only ground-state interactionshave to be considered. For excited-state electronic interac-tions to become important, appreciable population of a realenergy level with a certain lifetime should be achieved.This can only be realized through effective absorption ofthe fundamental (or a harmonic). That this is to be pre-vented, is self-explanatory. The electronic interaction in theground-state, if present, can inherently not be avoided.

Population of an excited state can, however, be anotherstrategy to enhance the nonlinear response. It has beendemonstrated in the field of third-order nonlinear optics,[38]

in the case where the excited state has a larger second hyper-polarizability than the ground state. This is, in fact, a generalobservation that fits very well to the bond-length alterna-tion model. A ground state with preferentially aromaticcharacter will have an excited state with largely quinoidcharacter. This loss of aromaticity results in a small hyper-polarizability, with the reverse true for the excited state.

In the case where the hyperpolarizability tensor compo-nent cannot be described by a single tensor component, thevector analysis model may still be viable, but it will cer-tainly be very laborious. At this time, no literature report isknown where such an effort has been put into explainingthe second-order nonlinear optical response of a super-structure. Small deviations from values predicted on the

basis of the vector model for chromophores with an as-sumed single tensor component, however, have been as-signed to the presence of a small off-axis contribution.

Also in the case where the hyperpolarizability tensor ofthe mesoscopic superstructure has a very low symmetry, itmay become extremely tedious not only to elaborate therelations between all the non-zero and independent meso-scopic tensor components and the single microscopic tensorcomponent (if this is the case, see above) but even more soto measure this number of tensor components.[22]

Finally, even if a single molecular tensor component canreadily be assumed, for example, on the basis of a depolari-zation ratio approaching five, and even if ground-state elec-tronic interaction is absent, as deduced from identical ab-sorption spectra for monomer and superstructure, it maybe impossible to apply the simple vector model. The lastcondition is the requirement for a fixed relative position ofthe constituting monomers in the mesoscopic structure.This is the equivalent of the lattice structure in crystals, andof the oriented-gas model in bulk structures where the non-centrosymmetry, necessary for second-order nonlinear op-tics, has been induced in an averaged way.

Only spatial averaging can be tolerated here. This spatialaveraging relates the bulk susceptibility with the monomo-lecular tensor component through an averaged angular pa-rameter, such as the orientation factor. Temporal averagingdoes not work, since then different conformations with dif-ferent symmetry, with different contributions from differ-ent monomers, have to be considered. Molecular dynamicscalculations can come to the rescue, but this brings us farfrom the simple, static, vector model. An example of thefailure of the vector model, partly owing to the low symme-try of the superstructure, partly owing to the dynamics ofthe conformers, is the case of the calixarenes. Calixarenesare very attractive in the field of second-order nonlinearoptics. They have been incorporated in neat films withlarge susceptibility and exceptional stability,[39] and are,therefore, interesting for application. The possibility of sub-stituting the calyx with one, two, three, or four groups alsopromised them to be good candidates for a thorough vectoranalysis of the hyperpolarizability of the calixarene super-structure. However, the NLO chromophores in the calix-structure do not adopt identical configurations for the ca-lix[4]arene with one, two, three, or four chromophores at-tached. For the disubstituted calix[4]arene, there are differ-ent isomers (1,2- and 1,3-disubstitution). For all there aredifferent conformers, for example, for the tetra-substitutedcalix[4]arene, there is the cone conformation, the partialcone conformation, and the 1,2- and 1,3 alternate confor-mation, for the different possible directions the chromo-phores point up or down the calix-ring. Figure 7 gives asnap-shot of the dynamic geometry of the cone conforma-tion of a tetrapropoxytetranitrocalix[4]arene. Energy-mini-mized structures (molecular dynamics calculations inchloroform using the CHARMm force field) indicate twodifferent tilt angles for the two juxtaposed chromophores,



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and also considerable dynamics of this conformation.[40]

For all these reasons, the application of the simple vectoraddition model, which assumes a constant relative positionof the monomeric chromophore with respect to the macro-scopic structure, here the calyx, is not valid. An additionaldifficulty proved to be the multiphoton-fluorescence con-tribution to the HRS signal.[41]

6. Conclusions: Guidelines and Perspectives forMesomolecular Engineering

From the experimentally observed enhancements in sec-ond-order nonlinear optical response for mesoscopic super-structures of electronically independent chromophoricmoieties, pre-packaged with a fixed relative orientation,and from the demonstrated applicability of the simple vec-tor model, a number of pertinent conclusions can bedrawn:

i) Any effort on the level of the single-molecule optimi-zation of the microscopic hyperpolarizability of the mono-meric chromophore is bound to bear fruit on the meso-scopic level also. Since no nonlinear interactions are to beinvoked in our model, the individual molecular propertiesare retained.

ii) The relative orientation of the microscopic chromo-phores in the mesoscopic superstructure should be opti-mized so as to allow addition of the microscopic hyperpo-larizability, resulting in an enlarged mesoscopic second-order nonlinear polarizability. The examples presentedhere prove the applicability of vector addition of the vec-torial part of the third-rank second-order first hyperpolar-izability tensor. The important conclusion is that the opti-mal orientation of the chromophores is parallel, resultingin a pure dipolar arrangement, both for the hyperpolariz-ability and the dipole moment. No cancellation and onlyaddition occurs. The same enhancement factor (ncosáyñ =n) then holds for both the dipole moment and the vectorialhyperpolarizability. The enhancement factor per chromo-phore is then still equal to n. A vectorial addition, resultingin an octopolar mesoscopic structure is also possible. No re-sulting vectorial properties are present (no dipole momentand no vector part of the first hyperpolarizability). In prin-

ciple, the octopolar addition of an octopolar monomericchromophore may also prove valuable.

iii) The vector model has the intrinsic advantage that thedipole moment vector can also be included in the analysis.Also based on the relative positions of the monomeric di-pole moments, a mesoscopic dipole moment can be calcu-lated. For charge-transfer molecules with high symmetry,the dipole moment vector and the vector part of the firsthyperpolarizability tensor are likely to be parallel. A largevalue for the mesoscopic dipole moment then results, col-laterally with a large second-order nonlinear polarizability.This has already been seen in the first demonstration of en-hancement of nonlinear optical properties in the polypep-tide. Since non-centrosymmetry is also a prerequisite at thebulk level, advantage is often taken of the dipole momentto induce a non-centrosymmetric orientation throughapplication of an orienting field. A larger dipole momentresults in a better orientation, a higher value for the orderparameter, and eventually, a larger bulk susceptibility.

iv) All the achievements in the field of temporal stabilityof induced bulk susceptibility should also be applicable.Due to the larger volume of the mesomer, the orientationalrelaxation may intrinsically be slowed down already.

v) When elaborating on the octopolar addition of the oc-topolar part of the hyperpolarizability tensor, all-opticalpoling of the octopolar mesoscopic superstructure may alsoresult in an overall non-centrosymmetric bulk. This ap-proach may prove valuable in the development of polariza-tion-insensitive materials. When a material with a verylarge dipole moment is oriented in a field, Langevin satura-tion and a very strong anisotropy may be achieved.

Received: September 19, 1997Final version: December 1, 1997

±[1] S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J.-L.

BrØdas, B. M. Pierce, Science 1994, 265, 632.[2] For an overview of recent advances in chromophore design, see: T.

Verbiest, S. Houbrechts, M. Kauranen, K. Clays, A. Persoons, J. Mater.Chem. 1997, 7, 2175.

[3] W. E. Moerner, S. M. Silence, Chem. Rev. 1994, 94, 127.[4] S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford

University Press, Oxford 1995.[5] C. B. Gorman, S. R. Marder, Proc. Natl. Acad. Sci. USA 1993, 90,

11 297.[6] S. R. Marder, W. Torruellas, M. Blanchard-Desce, V. Ricci, G. I. Stege-

man, S. Gilmour, J.-L. BrØdas, J. Li, G. U. Bublitz, S. G. Boxer, Science1997, 276, 1233.

[7] T. Verbiest, D. M. Burland, M. C. Jurich, V. Y. Lee, R. D. Miller, W.Volksen, Science 1995, 268, 1604.

[8] X.-M. Duan, S. Okada, H. Nakanishi, A. Watanabe, M. Matsuda, K.Clays, A. Persoons, Proc. Soc. Photo-Opt. Instrum. Eng. 1994, 2143,41.

[9] J. Zyss, D. S. Chemla, in Nonlinear Optical Properties of OrganicMolecules and Crystals (Eds: D. S. Chemla, J. Zyss), Academic Press,New York 1987, p. 23.

[10] R. W. Terhune, P. D. Maker, C. M. Savage, Phys. Rev. Lett. 1965, 14,681.

[11] G. Mayer, C. R. Seances Acad. Sci., Ser. B 1968, 267, 5457.[12] B. F. Levine, C. G. Bethea, J. Chem. Phys. 1975, 63, 2666.[13] K. D. Singer, A. F. Garito, J. Chem. Phys. 1981, 75, 3572.[14] G. R. Meredith, Rev. Sci. Instrum. 1982, 53, 48.[15] J. Jerphagnon, Phys. Rev. B 1970, 2, 1091.


Fig. 7. Snap-shot of the dynamic geometry of the cone conformer of the tet-ranitrotetrapropoxycalix[4]arene, showing the two different tilt angles forjuxtaposed monomers.

[16] D. A. Kleinman, Phys. Rev. 1962, 126, 1977.[17] K. Clays, A. Persoons, Phys. Rev. Lett. 1991, 66, 2980.[18] K. Clays, A. Persoons, Rev. Sci. Instrum. 1992, 63, 3285.[19] K. Clays, A. Persoons, L. De Maeyer, in Modern Nonlinear Optics,

Part 3 (Eds: M. Evans S. Kielich), Wiley, New York 1994, p. 455.[20] S. J. Cyvin, J. E. Rauch, J. C. Decius, J. Chem. Phys. 1965, 43, 4083.[21] R. Bersohn, Y.-H. Pao, H. L. Frisch, J. Chem. Phys. 1966, 45, 3184.[22] M. Kauranen, A. Persoons, J. Chem. Phys. 1996, 104, 3445.[23] G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, B. Bölger, Phys.

Rev. Lett. 1993, 71, 999.[24] E. Hendrickx, A. Vinckier, K. Clays, A. Persoons, J. Phys. Chem. 1996,

100, 19 672.[25] E. J. H. Put, K. Clays, A. Persoons, H. A. M. Biemans, J. F. G. A. Jan-

sen, R. Kurvers, C. P. M. Luijkx, E. W. Meijer, Proc. Soc. Photo-Opt.Instrum. Eng. 1996, 2852, 122.

[26] J. J. Wolff, D. Längle, D. Hillenbrand, R. Wortmann, R. Matschiner, C.Glania, P. Krämer, Adv. Mater. 1997, 9, 138.

[27] B. F. Levine, C. G. Bethea, J. Chem. Phys. 1976, 65, 1989.[28] T. Verbiest, C. Samyn, C. Boutton, S. Houbrechts, M. Kauranen, A.

Persoons, Adv. Mater. 1996, 8, 756.[29] P. N. Prasad, D. J. Williams, Introduction to Nonlinear Optical Effects

in Molecules and Polymers, Wiley, New York 1991.

[30] K. Clays, E. Hendrickx, S. Houbrechts, M. Triest, T. Verbiest, A. Per-soons, Proc. Soc. Photo-Opt. Instrum. Eng. 1993, 2025, 182.

[31] K. Clays, E. Hendrickx, M. Triest, T. Verbiest, A. Persoons, C. Dehu,J.-L. BrØdas, Science 1993, 262, 1419.

[32] M. Kauranen, T. Verbiest, C. Boutton, M. N. Teerenstra, K. Clays,A. J. Schouten, R. J. M. Nolte, A. Persoons, Science 1995, 270, 966.

[33] C. J. M. Huige, A. M. F. Hezemans, R. J. M. Nolte, W. Drenth, Recl.Trav. Chim. Pays-Bas 1993, 112, 33.

[34] E. J. H. Put, K. Clays, A. Persoons, H. A. M. Biemans, C. P. M. Luijkx,E. W. Meijer, Chem. Phys. Lett. 1996, 260, 136.

[35] C. Willand, D. J. Williams, Ber. Bunsenges. Phys. Chem. 1987, 91, 1304.[36] E. Hendrickx, C. Boutton, K. Clays, A. Persoons, S. Van Es, T. Bie-

mans, B. Meijer, Chem. Phys. Lett. 1997, 270, 241.[37] H.-J. Deussen, E. Hendrickx, C. Boutton, D. Krog, K. Clays, K.

Bechgaard, A. Persoons, T. Bjornholm, J. Am. Chem. Soc. 1996, 118,6841.

[38] D. C. Rodenberger, J. R. Heflin, A. F. Garito, Nature 1992, 359, 309.[39] E. Kelderman, G. J. T. Heesink, L. Derhaeg, T. Verbiest, P. T. A.

Klaase, W. Verboom, J. F. J. Engbersen, N. F. van Hulst, K. Clays, A.Persoons, D. N. Reinhoudt, Adv. Mater. 1993, 5, 925.

[40] P. J. A. Kenis, Ph.D. Thesis, University of Twente 1997.[41] O. F. J. Noordman, N. F. van Hulst, Chem. Phys. Lett. 1996, 253, 145.



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Nonlinear Optical Properties of Correlated Chromophores in Organic Mesoscopic Superstructures

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