Study of domain formation and relaxation in thin polymeric films by femtosecond hyper-Rayleigh scattering

Olbrechts et al. Vol. 15, No. 1 /January 1998 /J. Opt. Soc. Am. B 369

Study of domain formation and relaxationin thin polymeric films by

femtosecond hyper-Rayleigh scattering

Geert Olbrechts, Erik J. H. Put, David Van Steenwinckel, and Koen Clays

Laboratory of Chemical and Biological Dynamics, Center for Research in Molecular Electronics and Photonics,Department of Chemistry, University of Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium

Andre Persoons

Laboratory of Chemical and Biological Dynamics, Center for Research in Molecular Electronics and Photonics,Department of Chemistry, University of Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium,

and Optical Sciences Center, University of Arizona, Tucson, Arizona 85721

Celest Samyn

Laboratory of Macromolecular and Physical Organic Chemistry, Department of Chemistry, University of Leuven,Celestijnenlaan 200F, B-3001 Leuven, Belgium

Naoki Matsuda

Department of Analytical Chemistry, National Institute of Materials and Chemical Research,Ministry of International Trade and Industry, Agency of Industrial Science and Technology,

Tsukuba, Ibaraki 305, Japan

Received February 28, 1997; revised manuscript received July 15, 1997

Femtosecond hyper-Rayleigh scattering has been used to probe the spatial orientational fluctuations betweennonlinear optical chromophores as dopants in spin-coated polymer films. The fluctuation in the second-orderincoherently scattered light intensity on microtranslation of the solid sample is indicative of the degree of spa-tial correlation between the individual chromophores. The decay of the autocorrelation function of this fluc-tuating signal is characterized by a spatial correlation length. Electric-field poling of dipolar chromophores isshown to increase this correlation length. The temporal characteristics of the correlation length have beenstudied and compared with thermal relaxation times obtained with coherent second-harmonic generation.The correlation length decays much faster than the second-harmonic intensity. Possible implications of thisfast relaxation are addressed. © 1998 Optical Society of America [S0740-3224(98)02901-4]

OCIS codes: 190.0190, 190.4710, 290.5870, 320.2250.

1. INTRODUCTIONThe importance of organic materials as nonlinear optical(NLO) active media1 is intrinsically situated in the fast,purely electronic, contribution to the NLO response. Ininorganic crystals a large contribution to this responsecomes from slow displacement of nuclei, whereas only asmall part of the response is purely electronic in nature.A second advantage, which is inherent in organic materi-als, is that a virtually infinite number of organic mol-ecules can be synthesized. After the relevant structure–property relationships have been established, newmolecules can be designed by modeling techniques andsynthesized in the laboratory. The NLO properties canbe theoretically calculated and experimentally measuredto verify the validity of the modeling assumptions.Clearly, this feedback loop can start either with a concept,e.g., large electronic polarizabilities require loosely boundelectrons, or with experiments on existing molecules. Byvirtue of the loop structure, a technique should be avail-

0740-3224/98/010369-10$10.00 ©

able for the experimental determination of the relevantproperty without any limitation whatsoever. This rel-evant molecular property for second-order NLO is thesecond-order molecular polarizability or the first hyperpo-larizability, b. The observation of such an even-ordernonlinear molecular effect is, however, complicated bysymmetry restrictions: even-order NLO effects are ob-served only if the individual chromophores are arrangedin a noncentrosymmetric bulk ensemble. This require-ment used to make the determination of the molecularhyperpolarizability troublesome and time consuming.Each chromophore that was expected to be highly NLOactive first had to be noncentrosymmetrically imple-mented in a medium before any characterization couldtake place. Such a macroscopic noncentrosymmetry canbe obtained in crystals, Langmuir–Blodgett (LB) films,self-assembled films, and poled polymers.1 Another tech-nique, electric-field-induced second-harmonic gener-ation (SHG),2–4 results in a more direct way to study the

1998 Optical Society of America

370 J. Opt. Soc. Am. B/Vol. 15, No. 1 /January 1998 Olbrechts et al.

first hyperpolarizability in solution. Applying a staticelectric field over the solution under study reduces itssymmetry and makes the measurement of the first hyper-polarizability possible. Nevertheless, it makes dataanalysis more complicated, because a third-order nonlin-earity arises from the coupling of the optical fields withthe orienting field. Therefore, extracting the first hyper-polarizability b requires knowledge of the value of the di-pole moment, the third-order hyperpolarizability, and theadditional local-field correction factor at zero frequency.Apart from these data-retrieval complications, the use ofan orienting field in electric-field-induced SHG does notpermit the measurement of ionic species or of octopolarmolecules. A new technique, hyper-Rayleigh scattering(HRS), which circumvents these problems, has beendeveloped.5,6 The HRS technique is based on the mea-surement of the incoherent second-order scattering inten-sity caused by intense laser light impinging upon noncen-trosymmetric molecules in an isotropic solution. Insolution, a combination of spatial and temporal fluctua-tions within the volume and time window of the measure-ment causes the instantaneous and local deviation frommacroscopic centrosymmetry that is necessary for obser-vation of a second-order HRS signal.7 These fluctuationsare also probed in the linear light-scattering techniquesin which fluctuations in position can be translated intodensity or refractive-index fluctuations. The temporalcharacteristics of the fluctuation can be related to thetranslational diffusion coefficient and hydrodynamic vol-ume of the solute molecule. Fluctuations play the sameessential role in second-order nonlinear light scattering.However, because of the symmetry requirements for aneven-order effect, not the translational fluctuations butthe rotational fluctuations cause the scattering here. Ro-tational fluctuations destroy the average isotropy in a so-lution. Because HRS makes no use of an electric field toorient the molecules, not only dipolar but also octopolarmolecules8–10 and ionic species11,12 can be measured. Be-cause second-order nonlinear effects are forbidden in iso-tropic media in the dipole approximation, the efficiencyfor HRS is fairly low. Moreover, the scattering is not inone specific direction. As a result, nanosecond high-power injection-seeded Q-switched Nd:YAG lasers werefirst used to detect the weak HRS intensities.6 The tem-poral characteristics of the typical Q-switched laser sys-tem are low repetition frequency (10–100 Hz at most) andnanosecond pulses (approximately 10 ns). Recently, highpeak power became available from another generic lasertype. The mode-locked femtosecond titanium:sapphirelaser with a typical average power of 1 W, an 80-MHz rep-etition frequency, and a pulse duration of 100 fs delivers12.5 nJ of energy per pulse, resulting in a peak power of0.125 MW. Such high peak power permits the retrievalof values for the first hyperpolarizability by femtosecondHRS.13 The use of femtosecond HRS has some major ad-vantages. First, the temporal resolution can be used toresolve HRS from multiphoton fluorescence in the timedomain, permitting the determination of the first hyper-polarizability of fluorescent chromophores.14 Second, theshort pulse duration combines high peak power to allow

NLO effects to be observed with low total energy in thepulse to avoid optical damage to the solid samples. It isthis feature that has made femtosecond HRS attractivefor use in the characterization of polymeric thin films.

As we have already pointed out, the macroscopic NLOsusceptibility is determined not only by the molecularfirst hyperpolarizability but also by the way in which theNLO active molecules are implemented in a bulk en-semble. Achieving maximum nonlinear efficiencies re-quires that the bulk ensemble be ordered as uniformly aspossible. Applications such as phase matching in poly-meric thin films depend greatly on the uniformity of theorientation of the chromophores in such a film. Whereassingle crystals exhibit high phase-matching efficienciesover the whole physical length, in artificially ordered sys-tems these lengths are much more restricted by thelength over which the molecular order is constant. Inthis paper we describe a method to probe this uniformityby means of the orientational correlation between succes-sive chromophores. The obtained correlation length is ameasure of the average domain size, which gives an ideaof the constancy of order in the macroscopic bulk struc-ture.

The ability to obtain values for the first hyperpolariz-ability with femtosecond HRS in solution is demonstratedin Section 2. The ability to retrieve relevant structuralinformation from typical ensembles by means of femtosec-ond HRS is discussed in Section 3. The correlations be-tween dipolar chromophores are studied in Section 4.The results of a relaxation study are shown in Section 5.Possible implications of the findings are presented in Sec-tion 6.

2. FEMTOSECOND HYPER-RAYLEIGHSCATTERING IN SOLUTIONBecause in HRS, i.e., incoherently scattered second-harmonic (SH) radiation, the conversion efficiency is ex-tremely low, it is essential to have high peak power in thefundamental laser pulse. The classical way to obtainthis high peak power is to Q switch a laser with a gainmedium with a relatively long lifetime for the excitedstate. The best known example is probably the Nd31 ionsin a YAG matrix with a luminescence lifetime of 230 ms.Recently, high peak power has become available at muchhigher repetition rates in the titanium:sapphire laser sys-tem. Titanium-doped sapphire has emerged as a versa-tile new laser medium with an extremely broad tuningrange, ideally suited to replace the infrared dye solutions.The shorter excited-state lifetime of 3.2 ms of Ti31 in asapphire matrix allows for the higher pulse repetitionrate (determined by the length of the laser cavity) butprecludes Q switching to obtain high peak power. Thebroad tuning range of titanium-doped sapphire results ina laser pulse with potentially femtosecond duration.However, the small absorption cross section requires asapphire rod length of typically 2 cm, which in turn, en-larges the positive group-velocity dispersion (GVD) in thecavity. The incorporation of prism pairs with negativeGVD to compensate for the positive dispersion in the tita-nium:sapphire rod in the self-mode-locked laser systemallows for the generation of femtosecond pulses with the


same average power as the picosecond pulses.13 Systemspecifications (Spectra-Physics Model 3960, Tsunami) aretypically 1 W of average power for an 80-MHz-repetition-rate train of 80-fs pulses and results in 140-kW peakpower. Although this amount of power is still at thelower end of the fundamental power normally used in aHRS experiment—and for a second-order process resultsin 2 orders of magnitude less signal per pulse—nonlinearsecond-order light scattering from a self-mode-lockedTi:sapphire laser system has been observed.15–17 For allpractical purposes in an HRS experiment this 80 MHzpulse train can be considered quasi-continuous; hence theself-mode-locked Ti:sapphire laser system can be thoughtof as a continuous source of high peak power at the fun-damental wavelength. The high repetition rate is alsoadvantageous in increasing the signal-to-noise ratio of thescattering experiment.

When one is using femtosecond pulses, care has to betaken not to distort the pulse by passing it through opti-cal elements with nonzero GVD. The GVD of most ma-terials (including the Ti:sapphire laser rod) is positive inthe near infrared, which means that an ultrashort pulsewill be broadened simply by passage of the pulse throughthis material. The amount of broadening is determinedby the value of the GVD, b9(v), by the path length in thematerial z, and by the input pulse width t0 . For initiallytransform-limited Gaussian pulses with FWHM t0 , thepulse width t after broadening will be18

t 5 t0@1 1 ~4 ln 2b9~v!z/t02!#1/2. (1)

One can either minimize the problem by limiting thelength z of material that the pulse has to transverse oreliminate it by using femtosecond optics, designed to havezero GVD b9(v) at a specified wavelength v.

The HRS measurement consists of measuring the in-tensity of the second-order scattered light as a function offundamental light intensity. For a second-order effectthis dependence is quadratic. The quadratic coefficientas a function of concentration is a linear relation for non-absorbing molecules. For solvent and solute moleculeswith the same symmetry, e.g., C2v , the coefficients fromaveraging over the products of the direction cosines areidentical.19 Direct comparison of the intercept and theslope of the quadratic coefficient as a function of concen-tration is then possible. This is the basis for the internalreference method, in which the hyperpolarizability of thesolute molecule is calculated with the value for the hyper-polarizability of the solvent as the reference or vice versa.When the molecules partially absorb at the SH wave-length, a Lambert–Beer correction is applied.20 For mol-ecules that have different symmetries, other hyperpolar-izability tensor components contribute with differentweights to the susceptibility. This contribution then hasto be accounted for, both when the internal referencemethod is used and when a reference solute molecule isbeing used for purposes of comparison of hyperpolariz-abilities. Depolarization measurements also permit thedetermination of a number of hyperpolarizability tensorcomponents.21,22

The variation of the fundamental light intensityneeded for determining the quadratic dependence of ascattered harmonic on incident fundamental intensity in

HRS is controlled by a rotating half-wave plate in front ofa polarizer. The thickness of the wave plate is smallenough to avoid appreciable broadening of an 80-fs pulse.The high-power polarizer used in the nanosecond HRSsetup has the centimeter dimensions of a material withnonzero GVD. This optical element has been replaced bya femtosecond polarizer with zero GVD at 800 nm. Athin glass sheet is used to sample the fundamental inten-sity with a slow, integrating photodiode. The main laserbeam is then focused in a classical linear light-scatteringcell. At the end of the optical line a femtosecond autocor-relator can be placed for monitoring the mode locking ofthe laser, minimizing the pulse width, and checking thepulse broadening that results from the insertion of opticalelements.

Because of the high repetition rate of the femtosecondTi:sapphire laser, the gated (10-ns) detection electronicsassociated with low-repetition-rate Nd:YAG lasers be-come obsolete and can be replaced by much simpler andcheaper phase-sensitive detection. Hence the laser beamis chopped (1 kHz) just before focusing in the light-scattering cell. The photon collection and detection sys-tem is essentially the same as in the nanosecond HRSsetup. The output of the photomultiplier is connected tothe high-impedance input (10 MV) of a lock-in detector.The high impedance raises the sensitivity of the measure-ment, while the dark current and other background sig-nals are eliminated by the proper action of phase-sensitive detection. The in-phase output of the lock-indetector is then recorded as a function of the signal fromthe photodiode used to monitor the varying fundamentallight intensity. Figure 1 shows schematically the experi-mental setup for femtosecond HRS in solution. The mea-surement procedure is analogous to that for the nanosec-ond version and is also completely automated.

The possibility of retrieving accurate values for the firsthyperpolarizability b of NLO molecules was demon-strated by the determination of b for Crystal Violet chlo-rides, an octopolar molecule. Figure 2 shows the quad-

Fig. 1. Schematic of the experimental setup for femtosecondHRS: AC, femtosecond autocorrelator; ASL, aspheric lens; B,beam sampler; C, chopper (1 kHz); H, half-wave plate; HV, high-voltage supply; INT, interference filter; LPF, low-wavelength-pass filter; M’s, mirrors; ND, neutral-density filter; P, femtosec-ond polarizer; PC, personal computer; PCL’s, plano-convexlenses; PD, photodiode; PMT, photomultiplier tube; PSD, phase-sensitive detector; REF, reference frequency; SIG, signal; X, x in-put (fundamental light intensity); Y, y input (HRS signal).


ratic dependence obtained by plotting the fundamentalintensity against the incoherent SH intensity. A valuefor b of Crystal Violet chloride, determined with nanosec-ond HRS, was reported previously. From the quadraticcoefficients obtained for the different number densitiesshown in Fig. 3, a b value of (450 6 100) 3 10230 esu at800 nm for 2.2 3 1024 to 2.6 3 1023 mol/L has been de-duced with femtosecond HRS. This value agrees verywell with the reported value [(433 6 130) 3 10230 esu at872 nm for the same concentration range]. The low peakpower of femtosecond pulses, still 1 order of magnitudelower than that of the nanosecond pulses from theQ-switched YAG lasers, is offset by the higher signal-to-noise ratio of the phase-sensitive detection. This fact hasbeen further demonstrated by the recording of relativelysmooth quadratic curves for neat methanol.13 There is

Fig. 2. HRS signal for Crystal Violet in methanol at 293 K atdifferent number densities in units of 1018 cm23: a, 1.57; b,1.33; c, 0.37; d, 0.25; e, 0.14; f, 0.13. The solid curves are fittedcurves.

Fig. 3. Quadratic coefficient obtained from the curves shown inFig. 2 versus number density of Crystal Violet in methanol at293 K.

some controversy about the b value of Crystal Violet at1064 nm.23 From the dispersion of the first hyperpolar-izability, we have been able to show that our reported val-ues are in agreement with two-photon resonanceenhancement.13

Apart from the experimental simplicity associated witha continuous-wave laser source and phase-sensitive detec-tion as compared with the wideband, gated detection for aQ-switched laser source, the broad wavelength tunabilityof the Ti:sapphire laser is another important advantage.Dispersion data become easily accessible, especially withthe advent of the (femtosecond, synchronously pumped)parametric oscillator.

3. SPATIAL ORIENTATIONALCORRELATIONS OF MODEL ENSEMBLESWITH FEMTOSECOND HYPER-RAYLEIGHSCATTERINGThe available peak power has led to the exciting possibil-ity of applying HRS to solid samples. The peak power inlaser pulses with total energy low enough to preclude op-tical damage is high enough to permit observation of in-coherent second-order NLO effects. Point defects or re-sidual absorption had resulted in damage to the sample,optically induced by nanosecond pulses, rather than inuseful second-order scattering. However, it is now pos-sible to obtain HRS signals from solid samples with theuse of nanojoule, femtosecond pulses, even in LB filmsthat show microcrystallization and in spin-coated poly-mer films.

Whereas one can use HRS in solution to deduce a valuefor the first hyperpolarizability by varying the fundamen-tal intensity, an average value of the domain sizes in amacroscopic sample can be obtained by microtranslatingthe sample while keeping the fundamental intensity con-stant. Because of the symmetry restrictions for a second-order NLO process, HRS is sensitive to the orientation ofthe NLO chromophores in the solid matrix. Any fluctua-tion in centrosymmetry of the spatial arrangement of theNLO chromophores will show up as a fluctuation in HRSsignal. So measurement of the HRS signal as a functionof position reveals a fluctuating signal. The autocorrela-tion (AC) function of the fluctuating signal I2v is used toanalyze these fluctuating signals. The deduced correla-tion length is taken as a measure for the average domainsize.

To obtain information about the spatial orientationalalignment of the chromophores instead of the measure-ment of the first hyperpolarizability, we had to makesome changes in the femtosecond setup. Whereas a vary-ing fundamental intensity is needed for measurement ofthe first hyperpolarizability, a varying sample position isneeded for recording fluctuating HRS intensities as afunction of sample position. So, instead of rotating thehalf-wave plate in front of the polarizer, we microtrans-late the sample, together with the detector and the con-densing system, perpendicular to the beam (Fig. 4) with aresolution of 3 mm. This sample geometry is chosen tominimize the amount of coherent SH generated. For out-of-plane poling, a minimum of coherent SH is generatedfor a zero-incidence angle.15 Then a minimal amount of


linearly scattered SH is collected. The condensing sys-tem, consisting of a concave reflector, an aspheric lens, alow-wavelength-pass filter, and a plano-convex lens, isused to maximize the amount of incoherent scatteredlight detected by the photomultiplier tube. The spatialresolution of the measurement depends on the resolutionof microtranslation as well as on the optical resolution de-termined by the focal distance of the lens, the divergenceof the beam, and the beam diameter. A beam waist di-ameter of 5 mm and a Rayleigh length of 50 mm can easilybe obtained with a 20-mm focal-length lens and a beamdiameter of 4 mm. The second-order nature of the signalwas checked by the quadratic dependence on fundamen-tal intensity and by spectral discrimination.

To illustrate the possibility of making domain-sizemeasurements by the use of femtosecond HRS, we ini-tially compared three typical bulk ensembles with pre-dictable orientational correlation: (a) a commercialfrequency-doubling crystal [potassium titanyl phosphate(KTP)] that is expected to have a high degree of orienta-

Fig. 4. Schematic of the essential change in the experimentalsetup to yield the femtosecond HRS setup: ASL, aspheric lens;CR, concave reflector; INT, interference filter; LPF, low-wavelength-pass filter; PCL’s, plano-convex lenses; PMT, photo-multiplier tube; ref, reference frequency; 2v, beam-waist diam-eter; f, focal length; PSD, phase-sensitive detection.

Fig. 5. Intensity of the HRS signal as a function of position x fora, KTP crystal; b, DCANP LB film; c, pNA in PMMA.

tional order, (b) a thin 10-layer LB film of 2-docosylamino-5-nitropyridine (DCANP) that shows microdomainformation,24 and (c) a sample with para-nitroaniline(pNA) dispersed in a solid poly(methyl methacrylate)(PMMA) film that is expected to show no orientationalcorrelation.25

The primary experiment is the measurement of the in-coherently second-order scattered light as a function ofsample position. Figure 5 shows the spatial fluctuationsof the HRS signal for these three types of macroscopic en-semble. The three curves are plotted on the same scalebut are offset for greater clarity. One can evaluate theprimary data evaluated by calculating the AC function ofthe primary data. The AC function is defined as follows:

AC@I2v~j!# 5 Î2v~x !I2v~x 1 j!&, (2)

where x is the spatial distance and j is the distance be-tween two measurement points to be multiplied duringthe calculation of the correlation function (correlation orsample distance). The AC function decays from Î2v

2&,with maximum correlation between identical positions, toÎ2v&2, with minimum correlation for infinite separation.To make the interpretation easier, the normalized auto-correlation (NAC) function can be calculated. Even sim-pler is the NAC function of the fluctuations near the av-erage value (dI2v 5 I2v 2 Î2v&):

NAC@dI2v~j!# 5^dI2v~x !dI2v~x 1 j!&

^dI2v~x !2&

5Î2v~x !I2v~x 1 j!& 2 Î2v&2

Î2v~x !2& 2 Î2v&2 . (3)

This last function decays from 1 to 0. The parameterof interest of such a correlation function is the correlationlength. One can derive the length by assuming a singleexponential decay. In theory, such single exponential de-cay corresponds to a change in a single parameter (e.g.,only a single correlation phenomenon). Multiple expo-nential decays must be taken into account when the ma-terial exhibits multiple variable parameters (e.g., a fastfluctuation superimposed upon a slow variation). More-over, a single exponential decay can be obtained only ifthe total measurement distance L is long compared withthe correlation length. We did not undertake a detailedstudy of the best analytical form for the AC function. Wetook the correlation length as that distance for which theAC had dropped to exp(21) of its original value; this cor-responds to assuming a single exponential decay.

The NAC curves that correspond to the three en-sembles of Fig. 5 are shown in Fig. 6. The left-hand axiscorresponds to the NAC function of the fluctuating signalI2v . The value for Î2v&2/Î2v

2& of 0.9847 is indicated bythe thick line. This value is derived from 771 for Î2v&and from 603,680 for Î2v

2& from curve b (DCANP LBfilm) of Fig. 5. The respective values for the pNA-in-PMMA sample (from curve c, shifted in Fig. 5) are 430 forÎ2v& and 187,730 for Î2v

2&, resulting in a value forÎ2v&2/Î2v

2& of 0.9849. The stationary value for the KTPcrystal was not obtained within 1-mm displacement; inother words, correlation is still evident over more than500 mm. The right-hand axis indicates the degree of


NAC for the deviation dI2v from the stationary value.The difference in degree of spatial correlation is clearlyevident.

The approximately constant intensity of the scatteredSH from the single crystal and the resulting long spatialcorrelation is unquestionably due to the great uniformitythat is characteristic of single crystals. However, a ran-dom orientation of chromophores is observed in an un-poled polymeric thin film. This random orientationaldistribution results in a correlation length of almost 0.All correlation is lost within the spatial resolution of thesetup. A much longer spatial correlation has been ob-served for LB film. In LB deposition, the amphiphilicproperties of the molecules are used to induce molecularorder. Domain formation is a well-known process in LBfilms. The value for the calculated correlation length isshown in Fig. 6 and is approximately 280 mm. Given thenonideal functional form of the decay and the fact thatthe total measurement distance L is of the same order ofmagnitude as the correlation length jcoh , a conservativeestimate for jcoh would be (300 6 100) mm. This valueis in good agreement with previously reported domainsizes of 500 mm measured by coherent SHG in transmis-sion with a beam waist of 60 mm.26 This value is deducedonly from the curves of SHG as a function of sample po-sition, not from a decaying AC function of the SHGintensity.26

4. STUDIES OF DIPOLAR CHROMOPHORESDISPERSED IN SPIN-COATED THINPOLYMERIC FILMSAs we showed in Section 3, domain-size measurementspermit the retrieval of information about the persistenceof orientational alignment of the chromophores in a mac-roscopic arrangement. The use of spin-coated polymericthin films in NLO applications is totally based on this ori-entational alignment. After heating the film above theTg of the polymer matrix, we apply a dc electric field toorient the chromophores in a noncentrosymmetric way.By leaving the dc field on while cooling down the film, wefreeze the orientational alignment of the chromophoresinto the polymer matrix. The degree of orientational

Fig. 6. NAC function of the HRS intensity fluctuations as afunction of displacement j for a, KTP crystal; b, DCANP LB film;c, pNA in PMMA.

alignment is thus affected by the applied dc field. In thelimit for infinite dc field strength, all chromophores areoriented in the same direction along the dc field and arethus perfectly correlated. The obtained correlationlength will be determined by the physical dimensions ofthe film. At the lower limit, for no applied dc field, nocorrelation exists and the measurement results in a ran-domly fluctuating signal, corresponding to the randomlyoriented chromophores in the polymer film. Virtually nocoherent SHG signal will be generated for an unpoledfilm.

To study the effect of poling on the domain sizes wecompound polymer films corona poled at different polingvoltages (different effective field strengths).27 The co-rona poling was performed with a two-wire configurationto ensure poling uniformity. The samples consisted ofthe 4-methoxy-48-nitrostilbene (MONS) molecule in aPMMA matrix (dye loading of 4.3 wt. % after spin coatingfrom a chloroform solution to a film thickness of 1 mm).Figure 7 shows the measured fluctuation of the second-order scattered light intensity as a function of position forunpoled films (zero field strength), after intermediate pol-ing at 8 kV (intermediate field strength), and after fullpoling at 9 kV (high field strength). Figure 8 shows the

Fig. 7. HRS intensities as a function of position for spin-coatedpolymer films (4.3 wt. % MONS in PMMA) after corona poling ata, 9 kV (high field strength); b, 8 kV (intermediate field strength);c, 0 kV (zero field strength).

Fig. 8. NAC functions of the fluctuating HRS intensities forspin-coated polymer films (4.3 wt. % MONS in PMMA) at indi-cated corona voltages: a, 9 kV (high orienting field strength); b,8 kV (intermediate orienting field strength); c, 0 kV (zero orient-ing field strength).


Fig. 9. Reproducibility test and correlation between two consecutive measurements of a LB film of DCANP. The inset shows the con-secutive primary data of the fluctuating intensities as a function of position.

NAC’s calculated from the data presented in Fig. 7.From these figures it is clear that poling increases thecorrelation length. The crossing of the curves is causedby a different baseline; this is indicative of different long-distance correlation.

Reproducibility tests as a function of position were per-formed to prove that the fluctuations in intensity are re-lated to the fluctuations in orientation of the chro-mophores only. Figure 9 shows reproducible runs (inset)and the correlation between two consecutive measure-ments of a LB film of DCANP. The lower correlation be-tween runs on polymer films is believed to be due to localheating and relaxation.

A correlation function decaying to zero within the spa-tial resolution of the experiment (5 mm) is observed forthe unpoled polymer film, and correlation lengths of 20and 121 mm are obtained for the 8- and 9-kV poled poly-mer films, respectively. The value of the correlationlength of the fully poled polymer film (121 mm) corre-sponds well to values for the interaction length deducedfrom experimental phase-matching curves (6200mm).28,29 Although the poled polymeric waveguides arequasi-phase matched over their complete physical length,efficient interaction occurs only over a fraction of thislength.

We suggest that the observed discrepancy between thetheoretically infinite coherence length for phase-matchedstructures and the limited effective interaction length forfrequency doubling is due to the limited length over whichorientational correlation between the NLO chromophoresexists. The degree of phase matching is determined bythe refractive indices at the fundamental and the SHwavelengths. In the field of linear optics, not the symme-try of the molecules but only the density of polarizableelectrons is important. However, symmetry does play arole in frequency doubling, which is a second-order NLOeffect. As an example of the importance of symmetry, pe-riodic poling has been used in non-phase-matchedwaveguides.28 Alternatively, successive deposition of LB

layers with inverted symmetry of the nonlinear suscepti-bility has been used to comply with the symmetry re-quirement for second-order NLO effects.29 Therefore theefficiency of frequency doubling in phase-matched struc-tures is also determined by the length over which a cor-relation in orientation can be maintained. It follows im-mediately that the relaxation of the SH efficiency isadditionally determined by the decay of the AC length.Previously, only the relaxation of the electric field hadbeen taken into account. Because temporal and thermalstability studies of poled polymers are often conducted byfollowing the coherent SH intensity generated in trans-mission as a function of time and temperature, we havecompared the relaxation times obtained from the twotechniques.

5. RELAXATION STUDY OF THECORRELATION LENGTHThe samples used for the study of relaxation of the corre-lation length were identical to those used in the polingstudy (4.3 wt. % MONS in PMMA). To investigate thetemporal relaxation of the orientational alignment in-duced by poling we took primary data at different mo-ments after poling. The computed correlation functionscorresponding to the primary data are shown in Fig. 10.The NAC functions of the fluctuations dI2v are plottedagainst the correlation distance for a set of measure-ments. We can deduce the relaxation of the correlationlength at room temperature by plotting the value of thenormalized correlation length against the time intervalbetween poling and measurement (Fig. 11). The ob-served relaxation time at room temperature from correla-tion measurements with femtosecond HRS, tHRS , is 3.46 0.6 days.30

Normally the relaxation behavior of poled polymericthin films is studied by coherent SHG.31,32 The SHG in-tensity is recorded as a function of time at different tem-peratures to yield a relaxation time, tSHG , of poled poly-


mer films. The square root of the normalized SHGintensity as a function of time can be fitted to a stretchedexponential (Kohlrausch–Williams–Watts) function.The physically correct form to use is still a matter ofdebate.33 For the analysis of our second-order nonlinear-ity decay curves, a Kohlrausch–Williams–Watts functionwas used only as an empirical relationship. Based on therelaxation time tSHG as a function of temperature (50, 60,70, and 80 °C), the Arrhenius activation energy for relax-ation of 155 6 15 kJ mol21 and an entropy factor(ln tSHG,0) of 245 6 5 can be derived. The values ob-tained are in good agreement with the results from otherpolymer systems. Extrapolation to room temperatureyields a relaxation time tSHG,RT of 540 days.30

Thus a big difference between the two nonlinearity re-laxation times is observed. Although tSHG,RT has a rea-sonable value, that of tHRS seems to be extremely short.Possible artifacts in the incoherent measurement tech-nique have been identified and excluded.30 Additionally,the temporal relaxation in another guest–host system hasbeen studied. This system, 2-(5-piperidinyl-2-furyl)

Fig. 10. NAC function of the fluctuation of the HRS intensity fora spin-coated film (4.3 wt. % MONS in PMMA) after corona pol-ing at 9 kV at different times after poling: a, 0 days; b, 4 days;c, 5 days.

Fig. 11. Temporal decay of the normalized correlation lengthjcorr(t)/jcorr(0). Different symbols are used for differentsamples. The sizes of the symbols indicate the relative esti-mated statistical uncertainty in correlation length and system-atic uncertainty in measurement time owing to the number ofdata points to be acquired.

ethylene-1,1-dicarbonitrile in PMMA at a loading of 3.9wt. %, was chosen because of its lower absorbance at 400nm and its larger polarizability owing to the furan moi-ety. This system showed a similar decay in time, char-acterized by a relaxation time tHRS of 3.5 6 0.6 days atroom temperature. The system was also used for a studyof the possible influence of the surface roughness on thecorrelation length and on the relaxation time: A thicklayer of poly(vinyl alcohol) (PVA) was spun upon thePMMA layer. After the film was dried for 24 h in avacuum oven, it was corona poled at 9 kV. The role ofPVA is to prevent surface damage from the corona dis-charge that can easily be seen by the naked eye or withthe aid of a microscope. After corona poling, the PVAlayer is removed with pure water, yielding a muchsmoother surface. Although the thickness of the film isincreased by coverage with the PVA layer, the effectiveelectric-field strength experienced by the chromophores isnot affected. The charges that generate the effectivefield over the film migrate through the conductive PVAlayer, allowing a layer of ions to be formed on top of thePMMA matrix. Hence, poling at the same voltage (9 kV)yields identical effective electric-field strengths, ensuringsimilar poling circumstances. The ground electrode is anindium tin oxide layer upon the glass substrate. No sig-nificant difference could be observed in correlation lengthor in relaxation time as a result of the additional coverageof the PMMA layer with PVA. Thus the correlation timeis not determined by possible surface roughness of thesame spatial dimensions, nor would its relaxation be asurface degradation artifact.

From the large difference between tHRS (3.4 days) andtSHG (540 days), we must conclude that the two measure-ment techniques probe fundamentally different proper-ties of a thin film. The SHG measurements reveal themagnitude of an optical field, whereas the HRS measure-ments yield statistical information about the correlationlength. We speculate that the SHG measurement is sen-sitive only to global relaxation of the induced polar orderfrom the C`v symmetry to isotropy. The HRS measure-ment, however, is locally sensitive to domain formation.

6. CONCLUSIONS AND PERSPECTIVESWe have illustrated the possibility of using femtosecondHRS as a measurement technique for determination ofdomain sizes in different kinds of macroscopic bulk en-semble. By microtranslating the sample relative to thelaser beam, fluctuating HRS signals are obtained. Thesefluctuating signals, because of different interactions be-tween the fundamental light intensity and the chro-mophores, represent changes in orientational alignmentof the chromophores. The correlation function calculatedfrom the fluctuating signals is characterized by a correla-tion length. This correlation length is representative ofthe average domain size, the length over which the chro-mophores are equally oriented.

Measurements of spin-coated polymeric thin filmsshowed that corona poling affects the observed domainsize. Corona poling at increasing voltages induces an in-crease in this correlation length that is indicative of ahigher degree of spatial orientational correlation between


the chromophores. The correlation length obtained for afully poled polymer film corresponds well to the effectiveinteraction length in a polymer nonlinear waveguide.Taking into account symmetry considerations can explainthe difference between the theoretically infinite coherencelength and the observed limited effective interactionlength.

Another aspect of spin-coated polymer films is theirtypical relaxation behavior. From the measurement ofthe correlation length as a function of the poling voltage ithas been deduced that higher poling voltages not only in-duce larger order parameters but also favor domain en-largement. Conversely, the phenomenological descrip-tion of relaxation should also include breaking up insmaller domains, an aspect that hitherto has been ne-glected. This domain formation might be especially im-portant in dispersed polymer systems in which the mono-meric NLO chromophore can act as a plasticizer andinduce phase separation.

Because efficiencies for second-order NLO effects inwaveguides are, as we have already shown, determinednot only by the global orientation of the chromophores inthe film but also largely by the microscopic orientationalcorrelation between chromophores, i.e., by microscopic do-main sizes, the overall relaxation time t of the effect maybe much shorter than predicted from the SHG measure-ment only. The intensity of SHG in a waveguide,ISHG,waveguide(t), as a function of time, t, can be writtenas30

ISHG,waveguide~t ! 5 cE2v2L2 5 c$E2v,0 exp@2~t/tSHG!b#%2

3 $L0 exp@2~t/tHRS!#%2, (4)

where c is a constant that contains time-independent fac-tors (e.g., the magnitude of the overlap integral betweenthe matched modes). The magnitude of the optical fieldE2v at the SH wavelength is determined by the funda-mental intensity and the effective nonlinearity. In spin-coated polymer films the initial nonlinearity E2v,0 is in-duced by poling and is largely dependent on the polingvoltage. The length L, however, is also an important pa-rameter. We have shown that the initial length L0 isalso positively affected by large poling voltages. How-ever, if the length over which effective interaction for fre-quency doubling in the waveguide format takes place ischaracterized by a short relaxation time tHRS , the overallrelaxation time t that corresponds to the global time de-pendence of Eq. (4) can be approximated by the shorttHRS . One needs to compare the optical nonlinearity re-laxation time from SHG in waveguide format with the re-laxation times from SHG in transmission and from HRSto determine the importance of the breaking up in smallerdomains in waveguides.

From the statistical nature of this approach, it is essen-tial to calculate the autocorrelation for a large sample. Acomparison with dynamic light scattering (quasi-elasticlight scattering, photon correlation spectroscopy) isinstructive.34 In this technique the typical temporal in-terval is 1 ms for a total measurement time of at least 1 s.It is evident that obtaining the corresponding statisticalquality requires a large number of data points to be col-lected. At this point, spatial autocorrelation functions

are calculated off line for as many as 5000 data points.We are currently looking into implementing fast scanningof the thin film with real-time buildup of the autocorrela-tion function with a hardware correlator. Then the highrepetition rate of the femtosecond continuous-wave lasernow available over a wide wavelength range through fem-tosecond optical parametric oscillation would again be anindispensable advantage in this process.

ACKNOWLEDGMENTSWe thank Yves Van Rompaey for providing some of theDCANP LB films. G. Olbrechts is a research assistant,and K. Clays is a senior research associate, with the Fundfor Scientific Research—Flanders (FWO-V). E. J. H. Putacknowledges financial support from the Flemish Insti-tute for the Advancement of Scientific and TechnologicalResearch in Industry. This work was supported by re-search grants from the FWO-V (G.0308.96), the Belgiangovernment (IUAP P4/11, ‘‘Supramolecular Chemistryand Supramolecular Catalysis’’), and the University ofLeuven (GOA/95/01).

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Study of domain formation and relaxation in thin polymeric films by femtosecond hyper-Rayleigh scattering