Absolute molecular optical Kerr effect …

1 Absolute molecular optical Kerr effectspectroscopy of dilute organicsolutions and neat organic liquidsSteven R. Vigil*and Mark G. Kuzyk Department of Physics, Washington State University, Pullman, Washington 99164-2814 Received October 13, 2000; revised manuscript received December 1, 2000We report the results of pump probe optical Kerr effect (OKE) experiments performed on neat solutions ofcarbon tetrachloride, nitrobenzene, methyl methacrylate monomer, binary solutions of the squaraine dye in-dole squarylium, and the phthalocyanine dye silicon phthalocyanine-monomethacrylate, respectively, in car-bon tetrachloride, and solid solutions of indole squarylium and phthalocyanine-monomethacrylate inpoly(methyl methacrylate). Dispersion measurements of the dye solutions were performed in the visible one-photon resonant region of the dyes defined by their linear-absorption spectra. The dyes third-order molecularsusceptibility responsegxxxx(2v2;v1,2v1,v2) in this spectral region is markedly different, withR$gISQ%.

2 0 andR$gSiPc%,0. Analysis of the dyes OKE response requires the inclusion of high-lying two-photonstates and suggests that a purely electronic mechanism dominates their OKE response. The results are usedto calculate the dyes off-resonant third-order molecular susceptibilities, which are well within the limits pre-dicted by the Thomas Reiche Kuhn sum rule [M. G. Kuzyk, Opt. , 1183 1185 (2000)]. 2001 Op-tical Society of AmericaOCIS , , , INTRODUCTIONIt has long been known that conjugated molecules ( ,molecules with alternating single and double bonds) havevery strong absorption bands in the visible and ultravioletregions of the conjugation strongly af-fects the molecular polarizabilitya, which determines themolecular-absorption moleculesalso have appreciable nonlinear- optical (NLO) suscepti-bilities. Because of their large nonlinear response andease of incorporation into polymer waveguides, organicdyes have been extensively studied as NLO dopants inpolymer optical 4 The NLO response of thesematerials is due to their relatively large transition dipolemoments and strong, narrow absorption features.

3 Thereis a vast literature of linear and nonlinear studies of or-ganic dyes, much of it concerned with the structure-property relationships necessary to optimize the molecu-lar NLO response. The relative ease with which organicmolecules can be tailored to a particular environment po-tentially gives them a great advantage as NLO materials,once the factors affecting their nonlinearity are well un-derstood, allowing them, for instance, to be chemicallytailored to a particular environment while their nonlinearoptical response is not affected. In this paper we reportthe results of resonant pump probe optical Kerr effect (OKE) experiments performed on neat organic liquids andorganic liquids and solids doped with squaraine andphthalocyanine dyes. While their strong absorption pre-cludes the use of devices made with these dyes in theirone-photon resonant regime, we show that the study oftheir OKE spectra in the resonant regime yields informa-tion about their higher-lying electronic excited states, theknowledge of which is necessary to accurately predict themolecular NLO response at nonresonant THEORYA.

4 optical Kerr effect TheoryThe optical Kerr effect describes an optically induced bi-refringence wherein a strong optical field (the pump field)in a medium induces a change in the medium s zero-fielddielectric tensor. (Unless otherwise noted in the follow-ing discussion, we will assume an initially isotropic me-dium, , a medium whose zero-field dielectric responsecan be described by a scalar and a linearly polarizedpump field.) The induced birefringence is characterizedby the difference between the refractive indices paralleland perpendicular to the pump field s polarization a pump probe experiment the refractive-index differ-ence induced by the strong pump field is probed by a sepa-rate, weak optical field having polarization componentsparallel and perpendicular to the birefringence-inducingfield. For example, a linearly polarized plane-wave probefield having components parallel and perpendicular to thepump-field polarization will, upon passing through a bire-fringent medium of lengthL, in general be elliptically po-larized with a phase difference between orthogonal com-ponentsdf52pl~dni2dn'!

5 L,(1)wherelis the vacuum wavelength of the probe field, anddnianddn'are the optically induced refractive-indexchanges parallel and perpendicular to the pump-field po-S. R. Vigil and M. G. KuzykVol. 18, No. 5 / May 2001 / J. Opt. Soc. Am. B6790740-3224/2001/050679-13$ 2001 optical Society of Americalarization, respectively. The changed polarization stateof the probe field can be measured, for example, by plac-ing the birefringent sample between crossed the OKE the refractive-index difference in Eq. (1) isfield dependent and expressed asDn5dni2dn'512n2 BuEu2,(2)wheren2 Bis the optical Kerr coefficient5,6andEis theamplitude of the pump electric field. It is the mecha-nisms contributing to the optical Kerr coefficientn2 Binwhich we are a pump probe OKE arrangement the total fieldEincident upon the Kerr sample can be writtenE5E11E2,(3)whereE1is the strong pump field andE2is the compara-tively weak probe field. We assume both the pump andthe probe fields are linearly polarized plane waves travel-ing in thezdirection, described @id~z!

6 #cosux 1sinuy % ),(5)wheref15k1z2v1t1f~z!,(6)f25k2z2v2t, (7)and (k1,v1) and (k2,v2) are the vacuum wave vectorsand the angular frequencies of the pump and probe fields,respectively. In Eq. (5),d(z) is the phase shift inducedin the probe field by the pump-induced birefringence, anduis the angle between the polarization vectors of thepump and the probe fields at the entrance to the Kerrsample (z50).In Eq. (4),f(z) is the intensity-dependent self-induced phase shift of the is assumed weak enough that it induces nointensity-dependent phase change in the pump or a probe wave that is initially linearly polarized@d(z<0)50#the solution of the nonlinear wave equa-tion for the probe field7,8yields a probe phase change,d~z!53k2puA1u2ze0~v2!x~3!~2v2;v1, 2v1,v2!,(8)wheree0(v2) is the dielectric constant of the Kerrmediumattheprobewavelength,andx(3)(2 v2;v1,2v1,v2) is the third-order NLO suscepti-bility for the pump probe interaction.

7 Equations (5) and(8) can be used to calculate the intensity output from theKerr shutter:Itrans~v2;t!5h2~t!exp~2a2Lc!3F24 p3Ll2n0~v2!h1~t!G2sin2~2u2!3uxxyyx~3!~2v 2;v1,2v1,v2!1xxyxy~3!~2v2;v1,2v1,v2!u2,( 9)wherehi5 Iimaxpi~t!,(10)Iimaxis the maximum intensity attained by pulseiin thesample,pi(t) is the temporal intensity profile of pulseinormalized to unit maximum,a2is the linear-absorptioncoefficient at the probe wavelength (and we assume neg-ligible absorption at the pump wavelength),n0(v2) is therefractive index of the sample at the probe frequency,Lcis the length of the Kerr sample, andLis the pump probe overlap distance in the sample. Figures 1 and 2show typical experimental results of angular- andintensity-dependence measurements, respectively, andtheir agreement with Eq. (9).For all experimentsFig. 1. Dependence of the measured optical Kerr intensity onthe angleubetween the pump and the probe polarization vectors.

8 (Statistical error bars are smaller than marker size.)Fig. 2. Quadratic intensity dependence of the optical Kerr effectsignal of nitrobenzene. The solid curve is a fit of the functionIOKE/Iprobe5aIpump2to the Opt. Soc. Am. B / Vol. 18, No. 5 / May 2001S. R. Vigil and M. G. Kuzykreported here the angle between the pump and the probepolarizations was kept at 45 for maximum note in Eq. (9) the timetappearing on the left-handside and in the pump and the probe intensities on theright-hand omission from the susceptibilityterms implies an instantaneous susceptibility response tothe pump field. If the third-order susceptibility responseof the material is not instantaneous on the pump or theprobe pulse s time scale, the result is a convolution of thepulse profiles and the temporal response function of ,10 Since the;2-ps11reorientational re-sponse time of the CCl4solvent is short compared withthe 35-ps pump and 24-ps probe pulses, we assume an in-stantaneous response from the solvent.

9 As we will seelater, the response of the dyes in solution is well modeledby a purely electronic ( , instantaneous) response de-scribed by the third-order molecular susceptibility12where$i,j,k,l%5$x,y,z%,e is the electronic charge,xis the position operator,Vmgis the (angular) transitionfrequency between statemand the ground state,vais anincident-field frequency, and^xj&lm5^xj&lm2^xj& prime in both summation terms indicates the sum-mation is only over the excited states$m,n,n%( , theground state is excluded). Equation (11) clearly shows adependence on those states accessible directly from theground state (double summation) and those that passthrough an intermediate state to reach the final excitedstate from the ground state (triple summation).Equation (11) is calculated in the dipole approximationby applying the method of averages13,14to the time-dependent perturbation solution of the Schro dinger expression also allows for the inclusion ofdamping phenomena in a phenomenological manner byallowing the transition frequenciesVmgto be the case of homogeneous Lorentzian broadening thetransition frequency is given byVmg5 Vmg02iGm,(12)whereVmg0is the real transition frequency between theground level,g, and the excited level,m, andGmis thelinewidth of the transition.

10 It is important to note thatthe choice of the negative sign in the definition of the com-plex transition frequency is not arbitrary. The sign isbound by causality to be , in or-der to compare the molecular quantitygijkl, whose Car-tesian indices in Eq. (11) refer to a molecule-fixed frame,to bulk measurements described byxIJKL(3), it is trans-formed to the lab frame by an orientational average fromwhich a bulk response can be calculated by applying theappropriate local-field EXPERIMENTA. ApparatusFigure 3 shows a detailed schematic of the apparatus weuse to perform our OKE experiments. The laser provid-ing the pump pulse is a Continuum PY61-series active passive mode-locked system producing 30-mJ, 35-ps(FWHM) pulses at a rate of 10 Hz from Nd:YAG lasingmedia. The lasing wavelength is 1064 nm. The probepulse is provided by an optical parametric generator/amplifier (Continuum Mirage OPG-OPA) based on a de-sign and analysis reported by Zhanget OPG-OPA output is tunable from 440 nm to 2000 nm.