Nonlinear-optical processes in lower-dimensional ...qmmrc.net › webhard › publications › Resonant-NLO-josab-6-4-707.pdf · X(jk(-C4; W1, 2, c), nonlinear-optical susceptibilities,

Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 707

Nonlinear-optical processes in lower-dimensionalconjugated structures

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, 0. Zamani-Khamiri, and A. F. Garito

Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396

P. Kalyanaraman and J. Sounik

Hoechst Celanese Corporation, 86 Morris Avenue, Summit, New Jersey 07901

Received October 5, 1988; accepted January 3, 1989

Reduced dimensionality and quantum confinement in conjugated organic and polymer structures enhance theeffects of electron correlation on virtual electronic excitation processes and nonlinear-optical responses. A micro-scopic many-electron description of the third-order susceptibilities Yijkl(-W4; w1, 2, c3) of conjugated structures isreviewed for one-dimensional chains and extended to two-dimensional conjugated cyclic structures. Electroncorrelation effects in effectively reduced dimensions result in highly correlated 7-electron virtual excitations thatlead to large, ultrafast nonresonant nonlinear-optical responses. The increase of dimensionality from linear tocyclic chains is found to reduce the nonresonant isotropic third-order susceptibility yg. Resonant experimentalstudies of saturable absorption and optical bistability in ultrathin films of quasi-two-dimensional naphthalocyanineoligomers are also presented. In the saturable-absorption studies, the resonant nonlinear refractive index n wasmeasured to be 1 X 10-4 cm2/kW in the wavelength range of operating laser diodes. Based on this result, electronicabsorptive optical bistability is observed on a nanosecond time scale in a nonlinear Fabry-Perot interferometeremploying the saturably absorbing naphthalocyanine film as the nonlinear-optical medium.

1. INTRODUCTION

Conjugated 7-electron organic and polymer structures arenow well known to exhibit unusually large nonresonant mac-roscopic second-order, x (2)(-w3; )1, w 2 ), and third-order,X(jk(-C4; W1, 2, c), nonlinear-optical susceptibilities,' andtheir microscopic origin and mechanism can be successfullydescribed by the quantum field theory of many-electronsystems in one and two dimensions.2-1 1 In this description,as the spatial dimensionality of the many-electron system iseffectively lowered, the motion among the many electronsbecomes highly correlated.' 2 Electron correlation plays amajor role in determining x (2) and X(t321 in conjugated 7r-electron systems, and, as we shall review, its effects cannotbe neglected in properly accounting for the nonlinear-opti-cal properties of conjugated structures.

Reduced dimensionality and quantum confinement occurin material structures having effective confinement lengthscales L of less than one to several tens of nanometers. Theopposite limit occurs in regular three-dimensional bulkstructures, where L > 100 nm, and the electrons behave as aFermi gas of weakly interacting particles. In this case, theelectron motions are usually weakly correlated and well de-scribed by single-particle theory in the effective-mass ap-proximation.

Conjugated 7-electron organic and polymer structures areviewed as lower-dimensional systems in which quantumconfinement effects are important. For instance, in conju-gated linear chains the many-electron system is confined in

two dimensions, with L < 0.5 nm transverse to the linearchain axis, and thus the 7-electrons are delocalized in theirmotion only in one dimension, along the longitudinal chainaxis. As a result, the repulsive Coulomb interactions amongelectrons are strong, and electron motion becomes highlycorrelated, wherein the motion of any single electron de-pends on all the other remaining many electrons. The ori-gin of the nonresonant y(3) for these and related polymerstructures then appears to reside in strong correlation be-havior in virtual two-photon r-electron states.9 -11 This mi-croscopic many-electron correlation description of nonlin-ear-optical properties of conjugated structures is describedin Section 2. First we review the nonlinear-optical proper-ties of linear polyenes as a function of both conformationand length as prototype one-dimensional conjugated chains.The nonresonant microscopic nonlinear-optical susceptibil-ity is a strong function of the length of the polyene chain andis not significantly dependent on structural conformation.

The role of dimensionality in nonlinear-optical propertiesis further examined by a theoretical study of a two-dimen-sional conjugated cyclic structure with L < 0.5 nm perpen-dicular to the molecular plane. Through comparison withthe linear chain results, the microscopic origin of the nonlin-ear-optical properties is shown to be similar for the twocases. A remarkable effect of increased dimensionality,however, is the decrease of the isotropically averaged third-order susceptibility owing to an actual reduction in the effec-tive length available for the 7 electrons to respond to anapplied optical electric field.

0740-3224/89/040707-14$02.00 © 1989 Optical Society of America

Wu etal.

708 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989

In Section 3 we present experimental measurements of theresonant nonlinear-optical properties of thin films formed oflarge, two-dimensional conjugated cyclic structures. Satu-rable absorption is observed in spin-coated thin films of anaphthalocyanine derivative having an exceptionally largeQ-band 7r-electron absorption (a of 1 X 105 cm-') centered at810 nm. No unsaturable-absorption background is ob-served. For laser frequencies near 810 nm, we find an inten-sity-dependent refractive index (n 2 ) of 1 X 10-4 cm2 /kW.Based on the results of the saturable-absorption studies, wethen demonstrate electronic absorptive optical bistability ina thin-film Fabry-Perot 6talon at nanosecond time scales.

2. MICROSCOPIC DESCRIPTION OFNONRESONANT Yijkl(-W4; Wl, C02, W3) FOR ONE-AND TWO-DIMENSIONAL STRUCTURES

The macroscopic nonlinear-optical properties of organicmolecular and polymer structures in condensed states arebest described by starting from the individual responses ofisolated molecular or polymer chain units.' This approach,which clarifies the origin of x, (2) and X (3)t, is, however, notapplicable to other material classes, such as inorganic semi-conductors, for which it is difficult to identify analogousmicroscopic sources of nonlinear polarization. For the mo-ment neglecting intermolecular interactions, if the nonlinearsusceptibility of an isolated molecule is known, then x(2) or

X,(l,, of the macroscopic ensemble of molecules is determinedby the orientational distribution function of the indepen-dent units. Local field factors must also be included toaccount for the effect of the dielectric environment on theelectric field strength at the molecular site. The macroscop-ic frequency-dependent second- and third-order susceptibil-ities x(1^(-03; C0, W2) and X,(i3kJ 4; xl1; C02, C03) can then beexpressed in terms of the molecular susceptibilities 0lijk(-W3;

(01, W2) and Yijkl(-04; Wl; (2, (W3) asl3

X(? (-W3; W91, W2) =

and

X1JR1( W4; Co1,02, Cd,) = N E iM Rs,,Rser,48isol

(2)

where N, is the number of unit cells per unit volume, thesummation is over all molecules in the unit cell, R is arotation matrix describing the orientation of each moleculein the unit cell, and f is the frequency-dependent local fieldfactor. The description of the macroscopic nonlinear-opti-cal response is thus reduced to an understanding of the

microscopic second- and third-order susceptibilities 13ijk and

,Yijkl and knowledge of the orientational distribution of themolecular units in the condensed phase. As special cases,isotropic gases and liquids reduce Eqs. (1) and (2) to simplerforms. For example, for an isotropic ensemble,

X(31)ll(-W)4; (of (W02, W) = N4gfw2r37Yg(-W 4 ; Coll W2, W), (3)

where N is the number density of molecules and 'yg is theisotropically averaged susceptibility defined by

(4)Yg 5 --[z nii + 3 a (7iijj + rijij + yuji) ,L a L1, 3J

where the indices i and j represent the Cartesian coordinatesx,y, andz.

The above formalism is strictly appropriate only for gasessuch that the mean intermolecular distance is large enoughfor the interaction between molecules to be negligible. Incondensed states, some modifications are required for theeffects of intermolecular interactions to be included. Inorder to account for residual interactions with neighboringmolecules, O3ijk(-W3; W1, W2) and 'Yijk1(-o4; °1, W2, W3) can bedressed to extend their applicability beyond isolated molec-ular units. For instance, in dc-induced second-harmonicgeneration (DCSHG) studies of dilute solutions,34 it wasfound that inclusion of dipole-mediated interactions be-tween solvent and solute molecules provided excellentagreement of the theoretical values for an otherwise inde-pendent molecule with experimental measurements made insolution. In a more recent study' 4" 5 of phase-matched sec-ond-harmonic generation in single crystals of 2-methyl-4-nitroaniline (MNA), the existence of closely oriented pairs ofmolecules in the unit cell crystal structure required treat-ment of an MNA-MNA pair as the fundamental source ofsecond-order response. Because of the strong mutual effectof each molecule on the electronic structure of the other,calculation of /3ijk(- 2w; a, w) for an appropriately orientedpair of MNA molecules was necessary in order to obtainagreement with experiment. In any case, the fact that theintramolecular interaction energy is much stronger than theintermolecular interaction energy in organic molecular crys-tals, liquids, solutions, and polymer thin films means thatthe starting point for understanding the macroscopic non-linear optical properties of these various condensed phaseslies in an accurate description of the microscopic responsefrom an isolated molecular unit.

The general theoretical expression for the components ofthe microscopic third-order susceptibility tensor Yijk1(-c4;

Wo1 , c2, co3) is derived from time-dependent, quantum electro-dynamic perturbation theory. In order to avoid seculardivergences that would occur when any subset of the inputfrequencies sums to zero, one employs the Bogoliubov-Mi-tropolsky method of averages.' 6"17 Owing to dispersive ef-fects 'Yijkl(-W4; W1, W2, W3) is dependent on the input andoutput frequencies involved for each of the various possiblenonlinear-optical phenomena. For the particular case ofthird-harmonic generation, for example, one obtains

Wu et al.

M Rjs.,Rs orm3, i,7, Im hS=l

,r2 , (1)X 0sililk'(_W3; W11 '02)rfln k'o

rl fW2 r3 "X 'YSijhT(_-4; -11 W21 Wd jnk'o 1,P


( 3 ) ~~1 ( 4)[ 'YjlkI(-3 wL; co, co), co) = - 3~~

3 * \ / [ 1

Pjk1[rgn3 1n3n2r 2nrng]

{ (Wn3g - 3 w)(con2g - 2 w)(Wn1g - ')

+ Pjkl[rgn3 ?n3 n2 r 2nirn1 g] + Pjk~rgn3 rk r2rn2n$1g + IikLI-gnrn 3 n2rn2nTrnkgJ l

(Wn39 + CO)(Wn2- 2 W)(on 1g - °) (Wn3g + )(n2g + 2w)(Wnig - a) (-n3g + CO)( (n2g + 2 wo)(nlg + 3w)J

Pk)rgn21+n2grgnlrnlg] Pjkl[rg n r2gr gnr n1g]

n (n2g 3))(Wn29 - )(Conig - (cWn29 Co)(wnig + co)(Wnlg w)

+ 2+jkt[rgn2rkglgn1r2 g] + P jkl[rgn22rkgrgnlrn1g](Wn2g + 3( c)(Wn2 + c) (Wn1g + ) (Wn2g + W)(n 1g - )G(cOng +) j (5)

where r is the matrix element (nlriln 2) (ri = ri - (ri)gg),hwng is the excitation energy of state n, the prime on thesummation indicates that the ground state is omitted, andPjkl denotes the sum over all permutations of those threeindices. We will be concerned here with the case when allthe optical frequencies are above the molecular vibrationaland rotational modes but below the electronic excitationenergies so that the nonlinear-optical response is strictlyelectronic in origin. In addition, for conjugated organicstructures, -y is dominated by the delocalized 7r-electron con-tributions, which in general have both larger transition di-pole moments and lower transition energies than the a-electron excitations. Thus, with an accurate description ofboth the excitation energies and the transition moments ofthe 7-electron manifold, one can calculate the frequencydependence of each of the different third-order nonlinear-optical processes by using expressions such as Eq. (5).

The theoretical method employed to achieve a properdescription of the 7r-electron manifold of conjugated organicmolecular structures for calculation of Yijkl(-°4; (W1, 2, O3 )was described previously.1 0 It consists of a multiply excitedconfiguration interaction calculation (SCF-MO-SDCI) per-formed on a molecular orbital basis obtained through self-consistent field theory in the rigid lattice CNDO/S approxi-mation. This method, which was previously proved success-ful in calculations of ijk(-c3; W, Co2) for a variety ofconjugated structures, will not be discussed here other thanto reemphasize the many-electron nature of the generalproblem. Because of the reduced dimensionality, Coulombinteractions among 7r electrons result in marked electroncorrelation effects that render independent particle theoriesincomplete for the description of nonlinear-optical proper-ties. This has already been demonstrated in the comparisonof experimental and theoretical determinations of Oijk

(-2w; 'a, ), for which calculations involving both single- anddouble-excited configuration interactions result in goodagreement with experiment, whereas calculations with onlysingle-excited configuration interactions differ by as muchas 50%. In the case of z'ijkl for the linear polyenes discussedbelow, independent particle models fare even worse, result-ing not only in different magnitudes but also in opposite signfrom single- and double-excited configuration interactioncalculations and existing experimental data. Because inde-

pendent particle results are not only quantitatively incorrectbut also miss some important qualitative features of t3ijk and,ijkl, it is essential to take account of electron correlationsthrough multiply excited configuration interactions in de-scriptions of nonlinear-optical processes.

A. One Dimension: Conjugated Linear ChainsWe briefly review here the origin of the microscopic third-order susceptibility Yijkl(-°4; '1, Wa2, cv3) in prototype conju-gated linear chains as revealed by the theoretical methoddescribed above.9-1 In particular, we consider the linearpolyenes, which are hydrocarbon chains in which eachcarbon site is covalently bonded to a hydrogen and its twonearest-neighbor carbons. The remaining valence electronof each carbon atom contributes to a delocalized, stronglycorrelated 7r-electron distribution along the carbon chain.The ground state of this system is a spin-singlet, broken-symmetry state in which the carbon lattice possesses a sin-gle-bond/double-bond alternation. We have performed cal-culations on polyenes ranging in length from four to sixteencarbon sites (N = 4 to 16) in both the all-trans and cis-transoid conformations.

Although the self-consistent field calculation of theground state includes all the valence shell electrons for eachatom in the molecule, configuration interaction theory needsonly to consider 7r-electron orbitals since the low-lying exci-tations are 7r - 7r* transitions and for conjugated systemsthe 7r-electron contributions to -Yijkl(-c4; Wb, 2, W3) domi-nate those from a electrons. Because the polyenes are mem-bers of the C2h symmetry group, all the 7r-electron statesmust possess either Ag or Bu symmetry. Within the centro-symmetric C2h group, these two symmetries are of oppositeparity, leading to optical dipole selection rules. The groundstate is always Ag, and therefore the 'B, states are one-photon-allowed transitions observable in the linear absorp-tion spectrum. The excited Ag states, on the other hand,are one-photon forbidden but two-photon allowed. Experi-mental and theoretical studies'8 -24 of one-photon and two-photon resonant processes in finite polyenes have shownthat below the first optically allowed, dominant 1 'B, state islocated a strongly electron correlated two-photon 2 'Agstate.

Because the r-electron distribution is easily deformable

Wu etal.


(a )

X

( b )

Fig. 1. Schematic diagrams of the molecular structures for (a) all-trans and (b) cis-transoid polyenes.

Table 1. Symmetries, Energies, and SelectedTransition Dipole Moments of the Calculated Low-

Lying States of Trans-OT

Symmetry Energy (eV) u', (D) /'X,1 (D)

2 'Ag 4.15 0.00 2.821 Bu 4.42 7.81 0.002 'Bu 4.79 0.86 0.003 'A5 5.19 0.00 0.074 'Ag 6.00 0.00 2.845 'A, 6.07 0.00 1.113 'Bu 6.47 0.01 0.004 'B, 7.01 1.11 0.006 'A, 7.16 0.00 13.245 'Bu 7.30 1.14 0.00

along the conjugation axis by a perturbing optical electricfield but is strictly confined in the two transverse directions,it is to be expected that the dominant tensor component of-Yijkl will be Yxxx, for which all the electric fields are along theaxis of conjugation. We define the x axis as the directionalong the chain and the y axis as the perpendicular directionwithin the molecular plane. In all our calculations of vary-ing chain length and conformation of linear polyenes, theYxxxX component was indeed found to be far larger than anyof the others. As an example, for the specific case of trans-octatetraene (trans-OT) [Figure 1(a)] consisting of eightcarbon sites (N = 8), the independent, nonvanishing tensorcomponents of the third-harmonic susceptibility -Yijkl(-3w; w, w, w) at a nonresonant fundamental photon energyof 0.65 eV (A = 1.907 ,m) are yxxx = 15.5, yxyyx = 0.6, yixy =0.5, and -yyyy = 0.2 X 10-36 esu. All components involvingthe z component necessarily vanish because of the symmetryconstraints of the 7r-electron orbitals.

The symmetries, energies, and relevant transition dipolemoments of the ten lowest calculated excited states of trans-OT are listed in Table 1. All 153 of the calculated states areincluded in the calculation of Yijkl, but Table 1 serves toillustrate the important points. The columns ng and iu1Brefer to the x components of the transition dipole moment ofeach state with the ground state and with the 1 'B,1 state,respectively. The optical selection rules are observed in thevanishing transition moments Axg for all the Ag states anduXn,1B for all the 'B,1 states. It is also seen that the 1 B, statehas by far the largest ,g and the 6 Ag state has the largestA'n,1B. As a result, these two are the primary contributors toyxxxx, as will be described below.

It is instructive to consider the individual terms in thesum-over-states perturbation expansion. Based on Eq. (5)and the symmetry selection rules described above, it is evi-dent that the 7r-electron states in a third-order process mustbe connected in the series g - Bu -> Ag - 'Bu - g. Forcentrosymmetric structures, third-order processes necessar-ily involve virtual transitions to both one-photon and two-photon states. For trans-OT, there are (153)3 terms in-volved in the summation of Eq. (5). However, two of theseterms are an order of magnitude larger than all the othersand constitute 70% of x The remaining terms to a largeextent cancel one another, resulting in a much smaller netcontribution. In both of the dominant terms, the only 'Bustate involved is the dominant low-lying one-photon 1 'Bu 7r-electron excited state. In addition to its low excitation ener-gy, this state is important because its 7.8 D transition dipolemoment with the ground state is more than three timeslarger than any other ground-state transition moment. Oneof the two major terms comes from the double sum of Eq. (5),with both of the intermediate states being the 1 'B,1. In thecase of the double sum, the middle intermediate state isalways the ground state. This term makes a negative contri-bution to 7yxxxx below resonance, since both the numeratorand the denominator are positive but the double sum has anoverall negative contribution. The other major term is fromthe triple sum with the 6 Ag state as the middle intermedi-ate. This state, calculated at 7.2 eV, has a large transitionmoment with 1 'Bu of 13.2 D. This term makes a positivecontribution to y and is larger than the first, leading to anoverall positive value for xxx. Importantly, the 6 'Ag con-sists of 60% double-excited configurations, indicating that itis highly correlated. Single-excited configuration interac-tion calculations obtain a negative value for yxxxx becausethey do not adequately describe this state and thereforeomit its large contribution.

Figure 2 displays the calculated dispersion curve foryxxxx(- 3co; co, w, ) of trans-OT as a function of the inputphoton energy. The first resonance, located at 1.47 eV (X =0.84 gm) and indicated by the vertical dashed lines, is due tothe 3w resonance of the 1 'Bu state. The second singularity,located at 2.08 eV (A = 0.6 m), is from the 2w resonance of

100.0 -

80.0-

60.0 -

40.0a- 20.0-

3 0 .0 ....... .

3 -20.0

-40.0 -..

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

ENERGY (eV)

Fig. 2. Calculated dispersion of yxxxx(-3 w; co, c, ) for trans-OT(solid curves). The vertical dashed lines locate the 3 resonance tothe 1 B,1 state and the 2w resonance to the 2 'Ag state. The dottedcurves show the analogous calculated dispersion for cis-OT.

Wu et al.


(a) (b)

(c) (d)

Fig. 3. Transition density matrix diagrams for (a) cis-OT and (b) trans-OT ground states with the 1 lB,, state and (c) cis-OT and (d) trans-OT6 lAg states with the 1 'lB state. In both cases these are the most important virtual transitions for Yxxxx(-c4; Wl, w2, 3). The corresponding xcomponents of the transition dipole moments are 7.9, 7.8, 12.0, and 13.2 D, respectively."

the 2 1Ag state. As can be seen from Eq. (5), the 'B, stateswill have both 3w and co resonances in third-harmonic gener-ation, whereas the Ag states will have only 2w resonances.Other third-order processes have different resonance selec-tion rules. For example, in dc-induced second-harmonicgeneration both the 'B, and Ag states (or, more generally,both one-photon and two-photon states) have 2 and Xresonances, while there are no 3w resonances. It should alsobe noted that in real systems natural broadening of electron-ic states will prevent divergence at the resonances. This isaccounted for theoretically by making the excitation ener-gies in Eq. (5) complex with the inclusion of an imaginarydamping term. Unfortunately, damping constants cannotbe reliably calculated, and one must therefore use empiricalvalues.

In order to determine the influence of structural geometryon nonlinear-optical properties, we have also calculated 'ijklfor the cis-transoid(cis) conformation of polyenes [Fig. 1(b)]over the same range of chain lengths. The results for the cisconformations are in direct analogy to those for trans, indi-cating that geometry is not a predominant factor. For therange of chain lengths that we have considered, we find thatthe transition energies of the 1 B, and 2 'Ag states of the cisconformation are just slightly red shifted from the values fortrans by 0.02-0.10 eV. For example, for trans-OT the 1 B,state is calculated at 4.42 eV and the 2 'Ag at 4.16 eV, whilefor cis-OT the values are 4.37 and 4.11 eV, respectively.Furthermore, just as for trans, the dominant tensor compo-nent of Yijkl(-W4; W, W2 , W3 ) is 7XXXXx and the most significantvirtual transitions and the dispersion are essentially thesame as discussed above. The mechanism for Yijl(-W4; WI,

w2 , W3 ) is still a symmetry-dictated virtual excitation processinvolving strongly correlated r-electron states. The calcu-lated dispersion of yxxxx(- 3w; w, w, w) for cis-OT is comparedwith that of trans-OT in Fig. 2. The two curves are similar,and the most significant difference is the smaller nonreso-nant value in the case of cis-OT. Because of the nearlyequal excitation energies, the first two resonances occur nearthe same energies for the two different structural conforma-tions.

The similarity between the two conformations is furtheremphasized in the transition density matrix contour dia-grams that graphically illustrate the electron redistributionon virtual excitation. The transition density matrix p, isdefined through the expression

= -e f rpnn,(r)dr, (6)

with

pnn=(rl) J | n*(rl, r2 ... rM)ln,(rl, r2 ,... rM)dr2 ... drM,

(7)

where M is the number of valence electrons included in themolecular wave function . Contour diagrams for Pnn' of theground and 6 'Ag states with the 1 B,, state for both cis-OTand trans-OT are compared in Fig. 3, where solid anddashed lines correspond to increased and decreased chargedensity. The contour cut is taken 0.4 A above the molecularplane since yr orbitals vanish on the atoms. The antisym-metry of Pnn" is a requirement for a one-photon transition,and for a large transition dipole moment nn' the contoursshould have well-separated increased and decreased densi-ties with particularly large magnitudes toward the ends. Ofcourse, the actual charge density of any state, given by Pnn,must be symmetric because of the centrosymmetry of themolecule so that all states will have vanishing dipole mo-ments. In Fig. 3 the cis [Fig. 3(a)] and the trans [Fig. 3(b)]virtual g -1 'B, transition results in a somewhat modulatedredistribution of charge with transition moment x compo-nents of 7.9 and 7.8 D, respectively. For the 1 B - 6 A 5transition, however, there results a highly separated chargedistribution in the cis [Fig. 3(c)] and trans [Fig. 3(d)] confor-mations. The corresponding transition moments are 12.0and 13.2 D for the cis and trans cases, respectively.

There are few experimental data available for Yijkl(-W4;

W, 2, W3) of finite polyenes. Our calculations comparequite well with the experimental values that have been re-ported 2 5 for two of the shortest polyenes. Accounting forthe proper fundamental photon energy, isotropic orienta-

Ia$ .I

r

Wu et al.

, . z,I .:.,. �


tional averaging, and the small estimated a-electron contri-bution, our results are in good agreements with the gas-phase dc-induced second-harmonic generation measure-ments of butadiene (N = 4) and hexatriene (N = 6) by Wardand Elliott.2 5 Comparison of calculated results with experi-mental measurement of both the sign and magnitude of y isobviously an important test of the validity of a theoreticalmethod, but it has all too often been neglected in recentliterature.

Analysis of the chain-length dependence of Yxxxx for thetrans and cis conformations shows that the two are furtherunified by a common power-law dependence of yxxxx on L,defined as the distance in the x direction between the twoend carbon sites. The power-law exponent was found to be4.6 + 0.2, with several common features leading to this rapidgrowth of yxxxx with chain length. First, the excitation ener-gies decrease with increased chain length. Second, the mag-nitudes of transition dipole moments along the chain axisincrease steadily with chain length. Third, while for octa-tetraene and the shorter chains the nonlinear susceptibilityis almost entirely composed of the contributions from only afew states, longer chains have significant contributions froman increasingly larger number of both 'B,, and 'Ag states.

B. Two Dimensions: Conjugated Cyclic ChainsIn this subsection we extend the microscopic description of'Yijkl for one dimension to two dimensions and consider aspecific example within the class of conjugated cyclic struc-tures known as annulenes. As a major case, we consider theplanar structure of cyclo-octatetraene (COT), the cyclic ana-log to octatetraene with N = 8, illustrated schematically inFig. 4. Although the geometrically relaxed ground state ofCOT is known to be a nonplanar, bent structure, we willexamine only the planar structure of COT here. The pur-pose is to explore the effect of dimensionality on the micro-scopic features of 'Yijkl(-w4; W1 , W2, W3 ). Because the inclu-sion of the geometrically relaxed distortions of the physical-ly observed COT structure unnecessarily complicatescomparison of cyclic structure results with those describedabove for linear chains, we consider only the planar struc-ture. Analogies and contrasts between linear and cyclicstructures are clearest when the only distinction is the in-crease in dimensionality from one to two, so that one neednot be concerned with decoupling dimensionality from non-planarity effects.

For linear chains, since the x component of the transitiondipole moments is much larger than the y and z components,the isotropically averaged susceptibility yg is effectively de-termined by the yxxxx component, while all components in-

y

Fig. 4. Schematic diagram of the molecular structure of planarCOT.

volving transverse fields make negligible contributicThis reduces Eq. (4) to

)ns.

p9 t' ' xxxx. (8)But for cyclic structures, since the in-plane x and y direc-tions are equivalent, yxxx and yyyyy should be of equal mag-nitude. Furthermore, components such as xxy will also besignificant since they involve these two directions as well.The corresponding nonnegligible terms of Eq. (4) are-- [xxxx + YYYY + -('YXYY + lXYX + XYYX

+ Yyyxx + Yyxyx + Yzxxy)] (9)

It seems, therefore, that one might be able to enhance g bymoving from linear to cyclic conjugated structures and open-ing pathways for new components of the Yijkl tensor to con-tribute. We shall demonstrate below, however, a most strik-ing, opposite finding. We show that, because of the relevantlength scales involved in the two problems, the conjugatedcyclic structure will necessarily have a smaller -yg than thecorresponding conjugated linear chain with an equal numberof carbon sites.

Our planar model of COT is a member of the dihedral D4h

symmetry group, which is non-Abelian and, hence, has two-dimensional irreducible representations denoted as E class-es. The allowed-state symmetries for 7r-electron excitationsare Alg, A2g, Bg, B2g, and E,. Of these, only states of 'E,,symmetry are one-photon-allowed excitations from the A 5ground state. The 'E,, states are doubly degenerate, withthe two representations related by a 7r/2 rotation about the zaxis perpendicular to the molecular plane. All the remain-ing symmetries listed above describe nondegenerate, two-photon states. A typical feature of conjugated cyclic mole-cules, including phthalocyanines and porphyrins, is the exis-tence of a relatively low-frequency absorption in the visibleor near ultraviolet and a higher-frequency absorption deeperin the ultraviolet. 2 6 This feature appears in our model COTwith the weak low-frequency 1 'E,, state at 4.4 eV and themuch stronger, higher-frequency 2 'I, state at 6.5 eV. Inthe case of phthalocyanines, however, it is always the low-frequency band that is stronger.

In Table 2 we list the symmetries, energies, and relevanttransition dipole moments for the eight lowest calculatedexcited states of COT. Again, a total of 153 states arecalculated. The third and fourth columns list the x and ycomponents, respectively, of the transition moment betweena given state and the ground state, while the column labeled/ln,2E lists the x component of the transition moments of thatstate with the two degenerate representations of the 2 'E,,state; the y components are given in the yu2E column. Al-though the x and y directions are equivalent in COT, it isseen from Table 2 that these components of the transitionmoments are not always equal, and this is a direct result ofthe double degeneracy of the E,, states. Transition mo-ments involving any degenerate pair of 'E,, states with a two-photon state are clearly related by a r/2 rotation or x - y, y

-x. Thus the appearance of negative signs in some of thetransition moments merely reflects the choice of basis inHilbert space and has no absolute physical meaning. Bychoosing an appropriate basis for the degenerate pair, the

Wu etal.


Table 2. Symmetries, Energies, and Selected Transition Dipole Moments of the Calculated Low-Lying States ofCOT

Symmetry Energy (eV) jug (D) AY, (D) Mn,2E (D) ,2E (D)

1 A2g 2.24 0.00 0.00 -1.60, 2.40 -2.40, -1.602 'Al, 3.19 0.00 0.00 0.14, 0.09 -0.09, 0.141 'Eu 4.41 0.05 -0.03 0.00, 0.00 0.00, 0.001 E 4.41 0.03 0.05 0.00, 0.00 0.00, 0.001 B2g 5.21 0.00 0.00 -0.33, 0.50 0.50, 0.331 B1, 5.94 0.00 0.00 1.03, 0.68 0.68, -1.032 'Eu 6.48 4.58 -3.04 0.00, 0.00 0.00, 0.002 E, 6.48 3.04 4.58 0.00, 0.00 0.00, 0.00

(a)

(b)

Fig. 5. Transition density matrix diagrams for the ground state ofCOT with each of the two representations of the doubly degenerate2 'E,, state. The yr/2 rotational relationship between the two repre-sentations is clear. In this basis for the 2 'E,, degenerate pair, the xand y components of the transition dipole moments are 4.6 and -3.0D for (a) and 3.0 and 4.6 D for (b). Other choices for the 2 'E,, basiswill result in different values for the individual components of thetransition dipole moments, but the magnitude of the transitiondipole moment vector must remain invariant.

magnitudes of the x and y components can be made equal,although this is not necessary, as is illustrated in Table 2.

The first one-photon doubly degenerate 1 'E,, state hassmall transition moments with the ground state and a corre-spondingly small oscillator strength. The 2 'E,, doubly de-generate state, on the other hand, has a maximum transitionmoment of 4.6 D in this x-y basis and is a large oscillatorstrength one-photon state, in analogy to the 'B,, state ofoctatetraene. Thus the transition moments of the two-pho-ton states with the 2 E,, state determine their importancefor Yiyjk1(-w4; w1, W 2 , W3) and are also listed in Table 2 for thelowest-lying states.

Analysis of the various terms in the summations of Eq. (5)for COT reveals much similarity to the linear chain analog.

As for octatetraene, there is one dominant term in the dou-ble summation that is due to the state with the largestoscillator strength, in this case the 2 'Eu state. The domi-nant contributions from the triple sum also all involve the2 'Eu state, but rather than just one term, there are severalsignificant contributions for COT. Each one is smaller thanthe dominant negative term from the 2 E, state, but togeth-er they again lead to positive values for the nonresonanttensor components Yijkl. The significant contribution fromseveral terms involving different intermediate two-photonstates is similar to what was found for the linear polyeneslonger than octatetraene.

In Fig. 5 the transition density matrix p,,' is shown for theground state with the two representations of the 2 'E,, state.The 7r/2 rotational relationship of the two representations of2 'E,, is also clear here, as in Table 2. The charge redistribu-tion for this transition is fairly modulated, as it is for thelinear chains. In the particular basis shown for therepresentation of the doubly degenerate 2 E,, state, thetransition moments along the x and y directions are compa-rable, as can be seen from the figure.

The calculated dispersion of the isotropic third-order sus-ceptibility -yg(-3o,; co, w, w) is given in Fig. 6. The nonreso-nant value is quite small compared with those of the linearchains. Sharp resonances occur at 1.47 eV because of a 3wresonance to 1 'E,, and 1.60 eV owing to a 2w resonance with2 'Alg. Since both of these states have small transition mo-ments (Table 2), they make significant contributions only

50.0

'0

3-3

.3,3,

al

25.0-

0.0-

-25.0 -

-50.0).5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.

ENERGY (eV)

Fig. 6. Calculated dispersion of the isotropically averaged third-order susceptibility yg(-3 w; w, c, c) for COT.

.

I , R. .. .. A. 4. .--- -- --- -- --- --

) I I , . , . I

Wu et al.


directly on resonance. Calculations including imaginarydamping terms to account for the finite width of the elec-tronic excitations show that these resonances become com-pletely washed out and the dispersion remains flat in thispart of the spectrum. Experimental dispersion measure-ments, therefore, likely would not give evidence of signifi-cant resonant enhancement until the 3 resonance to the2 'E,, state, which occurs at 2.16 eV.

The calculated values of Yijkl(-3w; a, a, o) for COT at the

nonresonant fundamental photon energy of 0.65 eV are xxx= 0.75 and zyxyy = 0.21 X 10-36 esu. Because of the D4h

symmetry, Yxxxx = yyyyy and -yxyy is equal to all other compo-nents that involve two x-component fields and two y-compo-nent fields. This equivalence between the x and y directionsis in contrast to the linear polyene case, in which the yxxxxcomponent dominates all others. Furthermore, the yxxxxcomponent of octatetraene (15.5 X 10-36 esu) is far largerthan any of the components of COT. However, since COThas significant components in both the x and y directions, itis more reasonable to compare values of the isotropicallyaveraged susceptibility. For COT, yg = 0.38 X 10-36 esu,compared with 3.4 X 10-36 esu for trans-OT. As in the caseof comparing values for the trans and cis conformations oflinear polyenes, here also we must consider the actual lengthscale involved in the problem.

The important length for nonlinear-optical responses isthe largest length over which charge can be separated be-cause of the presence of an optical electric field. For thelinear polyenes, that length is the distance along the conju-gation axis separating the end carbons. For COT, the equiv-alent length is between two points on either end of a diame-ter of the ring. Additionally, since 7r-electron motion isconstrained along the carbon lattice, the relevant length isone half of the circumference of the molecular structure.This distance is 5.3 A for COT. For comparison, for trans-hexatriene (N = 6), yg = 0.75 X 10-36 esu at hw = 0.65 eV, andthe end-to-end length L is 6 A. Thus, for these two quitedifferent structures in which the relevant lengths are nearlyequal, we find that the calculated values of yg are also com-parable. In the case of cyclic structures, the length thatdetermines the magnitude of yg appears to be one half of thecircumference; this is a general finding in calculations thatwe have performed for other sizes of rings and will be report-ed in a later publication.

3. RESONANT X(3) MEASUREMENTS IN QUASI-TWO-DIMENSIONAL RING STRUCTURES:SATURABLE ABSORPTION AND OPTICALBISTABILITYWe showed in Section 2 that increased dimensionality fromlinear to cyclic chains leads to a decrease in the isotropicsusceptibility yg rather than to an enhancement, as onemight first expect. This is due to an effective reduction inthe length available for the r electrons to respond to anapplied optical electric field. There are, however, othercompelling reasons to investigate conjugated cyclic struc-tures for their nonlinear-optical properties. Primary amongthese is the presence of optically intense low- and high-frequency bands in the visible and ultraviolet generally ob-served in large diverse classes of related ring structures that,in addition, exhibit important secondary material propertiessuch as thermal and chemical stability and ease of fabrica-

tion and processing. Among such classes are the well-known, large ring porphyrin and phthalocyanine structures,which exhibit well-defined intense Q and Soret bands in thevisible and near ultraviolet, respectively. Free-base por-phyrin, for example, has long been identified as an analog of18-annulene, which possesses nine double bonds.2 7 Al-though, in general, we expect the nonresonant x (3) 1 of ringstructures not to be large, porphyrinlike structures providemany attractive features for studying resonant Xt(~j process-es.

Optical bistability in saturable absorbers has long beenunder intense study,2 8 first, to enhance understanding ofbistable phenomena and their relationships to the mediatingintensity-dependent refractive index n2 and, second, to aidin developing thin-film nonlinear-optical devices. Based onthe microscopic descriptions discussed in Section 2, we haveselected phthalocyanine structures29 3 0 in order to conductsaturable-absorption and optical-bistability studies in qua-si-two-dimensional conjugated ring structures. We havesucceeded in designing ultrathin naphthalocyanine filmspossessing large resonant n 2 values and in implementingwide-aperture Fabry-Perot thin-film 6talons for optical-bi-stability studies. In addition to primary nonlinear-opticalproperties, the design of the thin film talons incorporatedimportant secondary material properties: (i) large satura-ble absorption with zero unsaturable background, (ii) satu-rable absorption centered in the spectral range of operatinglaser diodes, (iii) thin-film formation, (iv) spin-coatablefilms and high-throughput fabrication, and (v) photolitho-graphic properties for micrometer-sized pattern features.

A first major example of this type of film is the siliconnaphthalocyanine oligomer (SINC) with the molecularstructure shown in Fig. 7. Both pure-SINC and SINC solid-solution ultrathin films were directly fabricated by spin-coating techniques. The films were homogeneous and ofhigh optical quality with typical thicknesses of 80 and 420nm for pure dye and solid solution, respectively. Figure 8shows the linear absorption spectra of the pure-SINC film(solid curve) and a solid-solution film of SINC in polymethylmethacrylate (dashed curve). The optical spectrum exhib-its an intense Q band centered in the near infrared at 810 nm(1.53 eV) for the pure dye and 774 nm (1.60 eV) for the solidsolution, with a linewidth (FWHM) of 0.1 eV and a linearabsorption coefficient a of 1 X 105 cm-1. The molecularsymmetry of SINC is D4h, and the doubly degenerate Q bandis analogous to the 1 'Alg - 1 E,, 7r-electron transition ofCOT described in Section 2.

We first present a physical model for the optical excita-tions of the thin film and then present saturable-absorptionstudies. A Maxwell-Bloch two-level model is used for thedependence of the saturation threshold power on pulse du-ration, and the experimental results support this simplepicture. For laser frequencies near the absorption maxi-mum, we find an effective n 2 of 1 X 10-4 cm2/kW. Based onthe saturable-absorption behavior, electronic absorptive op-tical bistability at nanosecond time scales is then observed inthin-film Fabry-Perot talons. Bistability behavior is stud-ied as a function of longer pulse duration purposely to distin-guish thermally induced bistable effects.

A. Glassy Polymer Dye Model and Saturable AbsorptionIn this subsection we present a physical model for opticalexcitations in the SINC ultrathin films. The films obtained

Wu etal.


N S I N 1i 11

/ N N (OS I MeO(CH2 )3 NH C CH2 )8CNH(CH 2 )3 OH) 2

N

Fig. 7. Schematic diagram of the molecular structure of SINC.

1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3I I I . I . I I I . I . I I I

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4

Energy (eV)

4. nism. The linewidth of the homogeneous broadening inamorphous media can be accounted for31'32 by using the two-

o level-system (TLS) glass models3 3 introduced by Andersonet al. that have been fairly successful in accounting for many

-o of the physical properties (e.g., specific heat, thermal con-ductivity, ultrasonic absorption) of disordered systems suchas glasses and polymerlike matrices. The Hamiltonian ofthe glassy polymer dye thin film on a substrate can be writ-

-o ten as34

(lOa)H = Ho + H12 + H23,

Ho = e0 0tqI0 + e1Ilt 1 + 2 Ea

+ h(nq + 2)2

H12 = 2 vtotto + E' Vlq~qla2 , 2 ,a a

H23 = - E fa-ea,

(lOb)

(lOc)

(lOd)

Fig. 8. Linear absorption spectra of pure-SINC (solid curve) andSINC solid-solution (dashed curve) thin films. The large oscillatorstrength Q-band absorption peaks at 1.53 eV (810 nm) in pure-SINCfilm and 1.60 eV (774 nm) in SINC solid-solution film.

by spin coating do not possess either positional or orienta-tional long-range order. Because of this random distribu-tion of SINC molecules in the films, the excitations arestrictly on-site r-electron transitions, which have a typicalabsorption coefficient a of 105 cm-'. The on-site 7r-electronoptical excitations in an isolated molecule have an intrinsic,temperature-independent natural linewidth of the order of0.1 to 1 GHz with a corresponding radiative decay lifetime of1 to 10 nsec.

The large linewidth of the Q band observed in Fig. 8 isprimarily due to inhomogeneous broadening. This sitebroadening in the thin film has a Gaussian shape, which is aconsequence of the statistical distribution of resonance fre-quencies of the optical centers owing to a variation in localenvironment in the polymer matrix. Within the inhomo-geneously broadened Gaussian- envelope of the Q band is aseries of narrow homogeneously broadened resonances forwhich the characteristic temperature dependence of thelinewidth depends on the microscopic broadening mecha-

where Ho is the noninteracting Hamiltonian of the molecule(the difference e - Eo corresponding to the Q-band absorp-tion), the TLS, and the phonons; H12 is the electrostaticdipole interaction between the molecule and the TLS; andH23 is the interaction between the TLS and the phonons, i.e.,the strain field e is coupled to the TLS.

Each homogeneous line under the Gaussian envelope isapproximated by a Lorentzian function, and the width isrelated to the temperature-dependent population and phaserelaxation rate of the excited state by Fourier transforma-tion. The amorphous material surrounding an optical sitecan be considered an ensemble of noninteracting TLS flip-flopping between two eigenstates as they emit or absorbacoustic phonons. The homogeneous line broadening inamorphous media comes from the dipole coupling of theoptical sites with the TLS's, and the line width can be ex-pressed in terms of TLS lifetime (or flip-flopping rate), thetemperature dependence of which is determined from thecoupling between the TLS and the strain field manifested asacoustic phonons. In this way, the line width of optical sitesin the amorphous media is predicted to have T1+6 (O < 6 < 1)dependence, and the absolute magnitude can be obtainedonce all the physical parameters for the TLS are known.

14

5-0-

(AzLXQ q

:C- t05 -0

1.4 1.5 1.6

- l i

o , | l | l , ,--------------- o

Wu etal.

:1

II

I: I

IIIII III I , ,11 -, , "I -, ,

_O

-O

-O!

-o!


0 0

6~~~~~~~~~~~~~~O O~~~~~~~~~~~~~~~d

10 10 10S 104 10l 10 10 10 10POWER IN (WATT/CM*CM)

Fig. 9. Saturable-absorption data and least-squares fit to Eq. (11).Squares are data for pure-SINC film at pulse width rp = 10 nsec;circles, pure-SINC film at i-p = 30 psec; and triangles, SINC solid-solution film at Tp = 30 psec. aL is reflection calibrated, and thelow-intensity limit is aL = 1.40.

For various organic molecules in different polymeric matri-ces, the theoretically predicted temperature dependence ofthe homogeneous linewidth is in good agreement with spec-tral hole-burning data.35 36 According to photochemicalhole-burning data on porphyrins and phthalocyanines invarious glasses and polymeric matrices, 3 7 the homogeneouslinewidth of the naphthalocyanine oligomer at room tem-perature is estimated to be between 10 and 100 GHz. ForSINC films, comparison of the homogeneous linewidth (100GHz) with the inhomogeneous width (0.1 eV) shows that theGaussian envelope contains of the order of ten thousandLorentzian-broadened resonances. 38 39

Saturable-absorption behavior within the Q band of thepure-SINC and SINC solid-solution thin film was investi-gated as a function of pulse duration and wavelength of theincident beam. A methane Raman cell pumped by funda-mental or doubled Nd:YAG output was used to produceStokes radiation near the peak maximum of the Q band at813 nm for a pure-SINC thin film and at 770 nm for a SINCsolid-solution thin film. The methane Raman cell pumpedby a Quantel Nd:YAG picosecond laser system provided 30-GHz-bandwidth, 30-psec pulses of 200 J per pulse thatwere easily focused to give light intensities exceeding 50MW/cm2. Nanosecond pulses of 30-GHz bandwidth withan energy of 20 J per pulse were obtained in the same wayby using a Quanta-Ray DCR Nd:YAG laser system to pro-vide an incident intensity of 500 kW/cm2. Figure 9 showsthe incident intensity dependence of the absorption aL for30-psec (circles, pure-SINC; triangles, SINC solid-solution)and 10-nsec (squares, pure-SINC dye) pulses, respectively.The change in the absorption was reproducible throughmany cycles of increased and decreased incident light inten-sity. Data points for 10 nsec are more scattered owing sim-ply to power fluctuations in the Nd:YAG pump laser. In the

case of the pure-SINC film, if the light intensity was in-creased more than the maximum of the data points, i.e., 30MW/cm2 for 30-psec pulses and 200 kW/cm2 for 10-nsecpulses, an irreversible, simple melt phase change was ob-served in the film. But, for the solid-solution film, no irre-versible change was observed up to an incident intensity of 4GW/cm2, and, furthermore, the saturation behavior was al-most identical to that of the pure-SINC film.

The solid curves in Fig. 9 are least-squares curves to aBloch-type saturable absorption:

= oL1 + I/Is (11)

where IO is the threshold power for the saturation, a0L givesthe low-intensity linear absorption, and aBL is the unsatura-ble background absorption. Importantly, aBL was found tobe zero for both the pure-SINC and solid-solution films. Inthe case of the pure-SINC films, the threshold powers forsaturation were 100 MW/cm 2 and 440 kW/cm2 for 30-psecand 10-nsec pulses, respectively. The threshold power forthe 10-nsec pulse is lower than that for the 30-psec pulse, butthis trend saturates at or near the 10-,usec scale. Important-ly, for the SINC solid-solution thin film, the threshold powerfor the 30-psec pulse was also 100 MW/cm 2 , the same valueas that of the pure-SINC film. The fact that the saturable-absorption behavior is identical for both pure-SINC andsolid-solution film is quite striking and can be accounted forby the absence of any positional and orientational orderbetween molecular sites in the thin-film phase; thus there isno phase coherence between optical sites. From this we canconclude that the on-site r-electron excitations of the Qband in individual molecular sites are responsible for thelarge resonant nonlinear-optical response.

The pulse-duration dependence of the saturation-absorp-tion threshold power is well explained in terms of a two-leveloptical system interacting with the resonant incidentlight.4 04 ' The dynamic transmission can be described bytwo coupled rate equations:

an(x, t) = _I(x, t)ajn(x, t) - [No - n(x, t)]-n(x, at

(12)

x = -I(x, t)al [N0 - n(x, t)]} - n(x, t),ax

(13)

where No is the total number of molecules per unit volume,n(x, t) is the number of molecules in the excited state atdepth x and time t, a is the absorption cross section permolecule, and -r is the radiative decay time of the excitedstate. Now let the incident pulse shape f(t) be normalizedby the incident light intensity,

1(0, t) = Iof(t). (14)

As the light pulse passes through the absorbing molecule,the pulse is distorted as well as attenuated. The change inthe pulse shape can be expressed in terms of a transmissionfunction T(x, t) at depth x and time t, defined as

I(x, t) = Iof(t)T(x, t). (15)

The two equations (12) and (13) can be reduced to oneequation for the transmission T(x, t):

Wu etal.


1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.72,,i ' I . I . I ' I ' I I ' I . . I . I . I , . ._ l

. 1 . . . 4 . I . 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58

Energy (eV)

\ a\,776 nm

~~~~~~~~~~ \

1n

ro!

I=O

1.60 1.62 1.64 1.66 1.68 1.70

Fig. 10. Dispersion of saturable absorption between 1.45 and 1.55eV measured with a 10-Asec pulse. The solid curve is the linearabsorption curve. The dashed curve is the Gaussian function least-squares-fit curve of the linear absorption, and the dotted curve is asimilar least-squares fit of the nonlinear absorption. The curveswith maxima occurring at X = 776 nm correspond to the real parts ofthe refractive indices obtained from the Kramers-Kronig relations.

al n T(x, t) + n T(x, t) = 2ar Io f(t) [1 - T(x, t)] + n To,

(16)

where Io is the incident light intensity, To is the low-intensi-ty transmission, and f(t) is the incident light pulse profile.From numerical simulation of Eq. (16), the saturationthreshold intensity Is can be obtained for a given pulse widthand excited-state lifetime r,. Furthermore, the ratio of sat-uration threshold for two given pulse widths can be used todetermine r, uniquely. Using 230 as the ratio of thresholdpowers at 30 psec and 10 nsec as determined from our experi-ment, we find the excited-state lifetime to be 5 nsec, in goodagreement with previous independent relaxation measure-ments on related structures.30'4 2

From the saturable-absorption measurement2 8 we canalso estimate the nonlinear refractive index n2. The nonlin-ear-optical susceptibility x(X) for a Bloch-type system isgiven by

x() = (a,0 c ( + \ (17)

where ao is the linear absorption coefficient, A is the detun-ing ( - cO)/P, and I, is the saturation power. The nonlinearrefractive index n2 is the derivative of the intensity-depen-dent refractive index n with respect to the intensity I, so forthis model

2 3 (4w)X = (4r)[i +A22] (18)From this expression, we obtain a value of n2 for the pure-SINC thin film of 1 X 10-4 cm2/kW.

To characterize fully the nonlinear absorption propertiesof the pure-SINC film, we measured the dispersion of the Q-band nonlinear absorption. A Spectra-Physics 380B cwring dye laser using LDS 821 dye and tunable between 790and 860 nm was used as the light source with typical peakpowers of 150 mW. The cw dye output of 5-MHz bandwidthwas chopped by an acousto-optic modulator, so that 10-,usecpulses were produced at a low duty cycle (10-4) to eliminateany heating effects. A light intensity of approximately 80kW/cm2 was obtained by focusing the laser output directlyonto the sample with a microscope objective lens.

The dispersion of the nonlinear absorption of the thin filmis compared in Fig. 10 with the linear absorption spectrum.It is clear that the change in absorption is maximum onresonance and decreases moving away from the peak. Thedashed curves are a least-squares fit to a Gaussian envelopemodel for the linear absorption, and the dispersion was de-rived from the Kramers-Kronig relations. The dottedcurves are the fitted curves for the nonlinear absorption anddispersion. We can see that the maximum change of refrac-tive index as obtained from Eq. (18) occurs at 776 nm, andthe maximum n2 at 776 nm results from a linear superposi-tion of the refractive-index changes of each homogeneouslybroadened resonance within the inhomogeneously broad-ened envelope.

B. Optical BistabilitySINC thin films can be employed as the nonlinear mediumin Fabry-Perot talons for optical-bistability studies. The6talon was formed by spin coating a wide-area (2-5 cm indiameter) thin film of approximately 80-nm thickness ontothe front mirror of two highly reflecting dielectric mirrors ofa Burleigh RC-110 Fabry-Perot interferometer. The freespectral range of the cavity was adjustable and set at 12.5GHz. Initial cavity detuning was adjusted by varying thehigh voltage applied to a piezoelectric transducer (PZT)annular ring that held the output mirror (the PZT had totalmotion of 2.21 m/100 0 V), and when this output mirror wasscanned, a Fabry-Perot interference pattern with a finesseof 2 was obtained with the sample in the cavity.

The optical-bistability experimental layout (Fig. 11) wasbasically the same as the arrangement used for measuringthe dispersion of saturable absorption. The laser outputwas partially reflected by a pellicle beam splitter to a refer-ence silicon detector, and the transmitted beam was tightlyfocused upon the thin film, which had been spin coateddirectly onto the front mirror. The output fringes werecollimated and passed through a 500-,um pinhole, and asample silicon detector monitored the intensity at the cen-tral part of the bull's-eye interference fringe. Silicon P-I-Nphotodiodes were used for reference and sample arms, andthe output intensity versus input intensity was directly dis-played on a 1-GHz oscilloscope operating in the x-y modeand externally triggered. At nanosecond time scales, initialmeasurements were attempted at 813 nm, using the outputfrom the Nd:YAG-pumped methane Raman cell as the lasersource; but later, more stable and smooth pulses at 799 nmfrom a single-mode pulsed Ti:A 203 laser pumped by a fre-quency-doubled Nd:YAG laser were used. Figure 12 showsthe bistable hysteresis behavior observed when 40-nsecpulses with intensity 160 kW/cm2 at 799 nm were incidentupon the nonlinear Fabry-Perot interferometer. We found

807 nm

<0-

't -

li]

I!

S-

a:

CL , 6

w A _, . . . . . . . . . . . . . . . . . .

Wu etal.

I :II

II

I


FunctionGenerator

OscilloscopeFig. 11. Schematic diagram of optical-bistability experiment for the pulse widths 10-6 to 2.0 sec: AOM, acousto-optic modulator; PH,pinhole; PD's, photodiodes. For nanosecond pulse-width measurements, a single-mode Ti:Al2O3 laser replaced the Ar+ laser, the ring dyelaser, and the AOM configuration.

that for zero cavity detuning (0 = 0.0) the bistable behaviorwas the largest, while when the cavity was detuned ( = yr)

the shape of the hysteresis curve changed and the effectbecame much smaller. In each case, the data were repro-ducible through many cycles of increased and decreasedincident light intensity. Further, the data were also repro-ducible by focusing at different areas of each film sample.This kind of initial cavity detuning dependence is typical ofabsorptive optical bistability, which results from saturableabsorption and a subsequent change in the loss of the inter-ferometer cavity, permitting higher transmission than ispossible at low light levels. However, the greatly reducedeffects observed for nonzero cavity detuning indicate only asmall dispersive contribution.

The incident laser wavelength was moved to 780 nm, cor-responding to near optimum conditions for possible disper-sive contributions to the bistability. The same measure-ments were repeated, and under all conditions no bistablebehavior was observed (Fig. 13). The absence of any bi-stable behavior at 780 nm, where a large dispersive effect isexpected from the Kramers-Kronig relation analysis, meanssimply that the relatively broad Q band is not one singlehomogeneously broadened line but an inhomogeneouslybroadened envelope for many homogeneous lines and sup-ports the microscopic picture of the glassy polymer SINCfilm. Thus, near maximum saturable absorption at 810 nm,naphthalocyanine thin films exhibit primarily absorptiveoptical bistability at nanosecond time scales. The aboveanalysis is based on steady-state conditions for optical bista-bility because of the relevant time. scales (pulse width, 40nsec; relaxation time, 5 nsec; cavity round-trip time, 1 nsec),but transient effects may also play some role in the observed

(a)

.... .... ... .... ... ._ .... 1"..

Al ~~~~+

CL

0) ' -u -

X,~~~+- H- e -

0.

_ I I I I I I I

Input Power

L

Fig. 12. Absorptive optical bistability observed for a polymer dye6talon with pulse width T p = 40 nsec and wavelength X = 799 nm. In(a) the initial cavity detuning 0 is set at 0, and in (b) the initialcavity detuning 0 is set at r.

Wu etal.


importantly, this behavior is distinctly different from thefast-pulse bistability observed at nanosecond time scales.

For both electronic absorptive and thermal dispersive op-tical bistability, the hysteresis loops do not show a completeswitching on and switching off. The reason for this is that,even though the resonant n2 value of the SINC thin film isfairly large, the film thickness (80 nm) is so small that thenonlinear phase shift experienced by the light inside the6talon is not large enough for complete switching to occur.Thicker SINC-containing films have been prepared in ourcontinuing studies.

Input PowerFig. 13. No optical bistability is observed for polymer dye 6talonwith pulse width Tp = 40 nsec and wavelength X = 780 nm for initialcavity detuning 0o set at either 0 or 7r.

L_03)

0a.

03

20W

7,

20W

Input Power

Fig. 14. Thermal dispersive optical bistability observed for poly-mer dye 6talon with pulse width Tp = 2 sec and wavelength X = 810nm. The curve at the lower right is for the initial cavity detuning 00= 0.0, the curve at the left is for 0o =-1.0, and the curve at the upperright is for 00 = 0.75.

hysteresis behavior, which continues to be examined in on-going studies.

Since purely absorptive optical bistability is rarely ob-served, a systematic series of studies of possible thermallyinduced refractive-index changes in the thin films was per-formed as a function of increased pulse duration from 10-6 to2 sec. The laser source used in these studies was theacousto-optic-modulator chopped, Spectra-Physics cw ringdye laser described above. Figure 14 shows an example ofthe optical bistability observed; the pulse width was 2.0 secand the duty cycle 20%. When the cavity was tuned onresonance with the incident light wavelength ( = 0.0; lowerright in Fig. 14), no hysteresis loop was observed, indicatingthe lack of an absorptive bistability effect, and this was trueeven when the dye-laser output frequency was resonant withthe linear absorption peak of the sample. However, for anegative X (-1.0; at left in Fig. 14), bistable hysteresis with acounterclockwise circulation was observed, and for a positive0 (0.75; upper right in Fig. 14), the bistable hysteresis hadclockwise circulation. With the pulse width and the reso-nant wavelength near the linear absorption peak of 810 nm,the bistable behavior is due to a thermally induced disper-sive intensity-dependent refractive-index change. Most

4. CONCLUSION

Electron correlation effects markedly determine the virtualelectronic excitation processes and nonlinear-optical prop-erties of the low-dimensional structures of conjugated linearand cyclic chains. Microscopic understanding of the originof the large, ultrafast nonresonant x (2 (-w3; W1, W2) andX(kl(-W4; 1, 2, 3) of these materials is obtained throughmany-electron calculations of the molecular susceptibilitiesI3 iJk(-(J3; W.1, W2) and 'Yijk(-W4; W1, C2, c 3) and direct compari-son with available experimental results. Details of themechanism for Yijki(-cv4; W1, 2, W3 ) of one-dimensional con-jugated linear chains have been explained in terms of virtualtransitions among highly correlated r-electron states, andcontour diagrams of transition density matrices Pnn' provid-ed direct illustration of the most significant virtual transi-tions. The dependences of 'ijkl(-cz4; c)1, 2, W3) on chainlength and structural conformation have been examined,and conformation was found to be significant only inasmuchas it affects the actual physical length of the chain. Resultsfor the all-trans and cis-transoid conformations of polyenesare unified by a power-law dependence of the dominanttensor component yxxxx(-3 w; , c, w) on the chain length Lwith an exponent of 4.6 + 0.2.

A theoretical study of 'ijkl(-W4; 1, W2, W3) in a two-dimen-sional conjugated cyclic structure permitted examination ofthe role of dimensionality in the nonlinear-optical proper-ties of conjugated systems. The origin of Yijkl(-W4; W-1, 2,

(03) in this case was found to be similar to that for the one-dimensional case, but the magnitudes of the various compo-nents of Yijkl are all smaller than the YXXXX component of theone-dimensional chain with an equal number of carbons.More important, the isotropically averaged third-order sus-ceptibility yg is also much less for the two-dimensional struc-ture compared with the one-dimensional chain. Our analy-sis shows that this is a result of a reduction in the effectivelength over which r electrons can respond to an appliedoptical electric field. For two-dimensional cyclic structures,this length is one half of the circumference of the ring com-pared with the full end-to-end chain length in one-dimen-sional structures. As a general rule, two-dimensional conju-gated cyclic structures are therefore expected to have small-er nonresonant X(]31(-C4; W1, 2, 3) values than their one-dimensional analogs.

The presence of large oscillator strength 7r-electron bandsin the visible and near ultraviolet characteristic of conjugat-ed quasi-two-dimensional structures provides attractiveconditions for studying resonant X(3) processes, especially inphthalocyanine-related structures that also possess out-standing secondary material properties. We have demon-

L0)

00L

0.

0

. ~ ~ ~ .. . .)

. . . . . . . .

Wu etal.

I I l


strated that such two-dimensional structures can be de-signed as wide-area, spin-coatable nonlinear-optical filmsand that these can be represented as a microscopic compos-ite system of molecular optical sites in a TLS glass randommedium. The resonant nonlinear-optical properties of ho-mogeneously broadened lines contained in the inhomogen-eously broadened Gaussian envelope were directly investi-gated by standard saturable-absorption measurements.These results showed for the SINC films that saturableabsorption occurs at the peak maximum of the low-frequen-cy Q band near 810 nm with essentially zero unsaturable-absorption background and that on-site r-electron excita-tions of the Q band in individual molecular sites are respon-sible for the large resonant nonlinear-optical response n2 of1 X 10-4 cm 2/kW at 810 nm.

A careful study of optical bistability in thin-film 6talonsdemonstrated that, near the peak maximum of the saturableQ band centered at 810 nm, SINC thin films exhibit primari-ly electronic absorptive optical bistability at fast time scales(nanoseconds). At long time scales (seconds), thermallyinduced dispersive bistability occurs, which is entirely dif-ferent and distinct from the observed fast time behavior.

The present results represent a first report on studiescentering on conjugated quasi-two-dimensional structures.Further theoretical and experimental studies of larger ringstructures and micrometer-thick films of naphthalocyaninesfor their resonant and nonresonant X(3) behavior have beencompleted and will be reported in a later publication.

ACKNOWLEDGMENTS

This research was generously supported by the U.S. AirForce Office of Scientific Research and the U.S. DefenseAdvanced Research Projects Agency (grant F49620-85-C-0105) and the National Science Foundation/Materials Re-search Laboratories Program (grant DMR-85-19059). Thecalculations were performed on the Cray X-MP computer ofthe Pittsburgh Supercomputing Center. We gratefully ac-knowledge the contributions of Q. Zhou and C. Yan, scientif-ic interactions with A. Baylis and J. Stamatoff of HoechstCelanese and R. Lytel and G. F. Lipscomb of Lockheed, andespecially the collaboration with K. Aron of Lockheed con-cerning Ti:sapphire laser measurements.

REFERENCES,

1. See, for example, D. J. Williams, ed., Nonlinear Optical Proper-ties of Organic and Polymeric Materials ACS Symp. Ser. 233(American Chemical Society, Washington, D.C. 1983).

2. S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).3. K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).4. C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983);

Phys. Rev. B 28, 6766 (1983).5. A. F. Garito, K. D. Singer, and C. C. Teng, in Nonlinear Optical

Properties of Organic and Polymeric Materials, D. J. Williams,ed., ACS Symp. Ser. 233 (American Chemical Society, Washing-ton, D.C., 1983), Chap. 1.

6. A. F. Garito, C. C. Teng, K. Y. Wong, and 0. Zamani-Khamiri,Mol. Cryst. Liq. Cryst. 106, 219 (1984).

7. A. F. Garito, Y. M. Cai, H. T. Man, and 0. Zamani-Khamiri, inCrystallographically Ordered Polymers, D. J. Sandman, ed.,ACS Symp. Ser. 337 (American Chemical Society, Washington,D.C., 1987), Chap. 14.

8. A. F. Garito, K. Y. Wong, and 0. Zamani-Khamiri, in NonlinearOptical and Electroactive Polymers, D. Ulrich and P. Prasad,eds. (Plenum, New York, 1987).

9. J. R. Heflin, K. Y. Wong, 0. Zamani-Khamiri, and A. F. Garito,J. Opt. Soc. Am. B 4, P136 (1987).

10. J. R. Heflin, K. Y. Wong, 0. Zamani-Khamiri, and A. F. Garito,Phys. Rev. B 38, 1573 (1988).

11. A. F. Garito, J. R. Heflin, K. Y. Wong, and 0. Zamani-Khamiri,in Nonlinear Optical Properties of Polymers, A. J. Heeger, D.Ulrich, and J. Orenstein, eds., Proc. Mater. Res. Soc. 109, 91(1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988).

12. See, for example, J. Solyom, Adv. Phys. 28, 201 (1979), andreferences therein.

13. A. F. Garito and K. Y. Wong, Polymer J. 19, 51 (1987).14. C. H. Grossman, Ph.D. dissertation (University of Pennsylva-

nia, Philadelphia, Pa., 1987).15. C. H. Grossman, J. R. Heflin, K. Y. Wong, 0. Zamani-Khamiri,

and A. F. Garito, in Nonlinear Optical Effects in Organic Poly-mers, F. Kajzar and J. Messier, eds. (NATO ASI, Brussels, to bepublished).

16. N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic Methodsin the Theory of Nonlinear Oscillations (Gordon & Breach,London, 1961); translated from Russian.

17. B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).18. B. S. Hudson and B. E. Kohler, J. Chem. Phys. 59, 4984 (1973).19. See, for example, B. S. Hudson, B. E. Kohler, and K. Schulten,

in Excited States, E. C. Lim, ed. (Academic, New York, 1982),Vol. 6, p. 1, and references therein.

20. A. A. Ovchinnikov, I. I. Ukrainski, and G. V. Kuentsel, Sov.Phys. Usp. 15, 575 (1973), and references therein.

21. K. Schulten, I. Ohmine, and M. Karplus, J. Chem. Phys. 64,4422 (1976).

22. K. Schulten, U. Dinur, and B. Honig, J. Chem. Phys. 73, 3927(1980).

23. Z. G. Soos and S. Ramasesha, Phys. Rev. B 29, 5410 (1984).24. P. Tavan and K. Schulten, Phys. Rev. B 36, 4337 (1987).25. J. F. Ward and D. S. Elliott, J. Chem. Phys. 69, 5438 (1978).26. R. P. Linstead, J. Am. Chem. Soc. 75, 2873 (1953).27. M. Gouterman, J. Mol. Spectrosc. 6, 138 (1961).28. See, for example, H. M. Gibbs, Optical Bistability: Controlling

Light with Light (Academic, Orlando, Fla., 1985).29. J. A. Armstrong, J. Appl. Phys. 36, 471 (1965).30. W. F. Kosonocky and S. E. Harrison, J. Appl. Phys. 37, 4789

(1966).31. A. G. Redfield, Adv. Magn. Res. 1, 1 (1968).32. See, for example, K. E. Jones and A. H. Zewali, in Advances in

Laser Chemistry, Vol. 3 of Springer Series in Chemical Physics,A. Zewail, ed. (Springer, New York, 1978).

33. P. W. Anderson, B. I. Halperin, and C. Varma, Philos. Mag. 25, 1(1972).

34. S. K. Lyo and R. Orbach, Phys. Rev. 22, 4223 (1980).35. A. Gutierrez, G. Castro, G. Schulte, and D. Haarer, in Organic

Molecular Aggregates, P. Reineker, H. Haken, and H. C. Wolf,eds. (Springer, New York, 1983).

36. R. M. Macfarlane and R. M. Shelby, J. Lumin. 36, 179 (1987).37. S. Volker and R. M. Macfarlane, IBM J. Res. Dev. 23, 547

(1979).38. A. M. Stoneham, Rev. Mod. Phys. 41, 82 (1969).39. M. Romagnoli, W. E. Moerner, F. M. Schellenberg, M. D. Le-

venson, and G. C. Bjorklund, J. Opt. Soc. Am. B 1, 341 (1984).40. P. Gires and F. Combaud, J. Phys. (Paris) 26, 325 (1965).41. A. C. Seldon, Br. J. Appl. Phys. 18, 743 (1967).42. J. McVie, R. S. Sinclair, and T. G. Truscott, J. Chem. Soc.

Faraday Trans. 2 74, 1870 (1978).

Wu etal.

Documents

Nonlinear-optical processes in lower-dimensional ...qmmrc.net › webhard › publications › Resonant-NLO-josab-6-4-707.pdf · X(jk(-C4; W1, 2, c), nonlinear-optical susceptibilities,