Quadratic Electrooptic Effect in Small Molecules - ACS Symposium

Chapter 47

Quadratic Electrooptic Effect in Small Molecules 1,3

2,4

C. W. Dirk and M. G. Kuzyk 1

AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974 AT&T Bell Laboratories, P.O. Box 900, Princeton, NJ 08540 Downloaded by CORNELL UNIV on October 6, 2016 | http://pubs.acs.org Publication Date: March 11, 1991 | doi: 10.1021/bk-1991-0455.ch047

2

An attempt is made to fit quadratic electrooptic (QEO) results to a two-level model for the microscopic third order susceptibility, γ. The results are to some extent inconclusive and suggest that a two -photonstate may have to be included. Also reported here are some further major improvements in molecular second order nonlinearities of particular importance to poled-polymer electrooptic applications (EO). Thus, it is found that appropriate replacement of benzene moieties with that of thiazole in certain azo dyes results in a factor of three increase in μ·β, the molecular dipole (μ ) projected molecular second order nonlinear optical susceptibility, β. 0

There is great interest in preparing materials which could facilitate the development of electrooptic devices. Such devices could permit broad band optical signal encoding so that telephone, data, television, and even higher frequency transmissions could simultaneously be sent down a single optical fiber. The nonlinear optical process which makes this possible is the linear electrooptic effect (EO). It is based on the first field nonlinearities (Ê ) of the molecular dipole moment, 2

3

~fî = % + oÊ + β ^ + yÊ + · · ·

,

and the macroscopic polarization, ~P,

3

Current address: Department of Chemistry, University of Texas, El Paso, TX 79968 Current address: Department of Physics, Washington State University, Pullman, WA 99164-2814

4

0097-6156/91/0455-O687$O6.00/0 © 1991 American Chemical Society

Marder et al.; Materials for Nonlinear Optics ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

(1)

688

MATERIALS FOR NONLINEAR OPTICS: CHEMICAL PERSPECTIVES

^ =Μ

0 +

χ

( 1

^

+

χ

(

2

^

+

χ

(

3

^

+

· · ·

,

(2)

-(2)

as governed by the second order tensors, β and χ , respectively. The tensor, β, is responsible for the magnitude of the microscopic (molecular) effect, while the bulk macroscopic effect is dictated by χ . The even order tensors are exactly zero when an inversion operation can be applied, so that second order nonlinear optical materials must be noncentrosymmetric. Odd order tensors (i.e. ά, γ) are unaffected by inversion symmetry. For typical laser, or electrical modulation fields there are at least several orders of magnitude difference between the largest

Downloaded by CORNELL UNIV on October 6, 2016 | http://pubs.acs.org Publication Date: March 11, 1991 | doi: 10.1021/bk-1991-0455.ch047

—->2

~(2)—^2

~K3)

second order and third order polarizations, Ρ (β£ or χ Ε ) and Ρ (γ£ or χ ( 3 ) ϊΡ), respectively. Additionally, optimization of the second order process is well understood, while the structure/property relationship for third order nonlinearities has remained more mysterious. Consequently, despite the annoying restriction to noncentrosymmetry, the present incipient electrooptic modulation technology relies on the linear electrooptic effect (mediated by β) rather than the quadratic electrooptic effect (mediated by γ). This chapter explores further significant optimization of EO, then focuses on the problem of QEO. The main goal of the QEO work is to provide a model for γ in terms of simple physicalorganic parameters such as λ^^, integrated absorption (oscillator strength), solvatochromatic behavior, etc.. This would then provide a tool that organic chemists could readily apply to optimize γ, or to at least broaden the class of materials that have relatively large γ. Optimizing χ Nonlinearities for Electrooptics ( 2 )

Understanding second order nonlinearities in terms of simple well known physical-organic parameters requires starting from the standard perturbation theory expressions and then deriving the more limited expressions which can be related to simple physical observables. It is best to approach perturbation theory from a phenomenological direction, since this can ultimately provide a more intuitive understanding of the physics. We start with the second harmonic generation process. Second harmonic generation (SHG) involves the mixing of two photons at frequency ω, and producing one photon at frequency 2ω. This is frequently referred to as a three-wave mixing process. Third order nonlinearities are fourwave mixing processes. Nonlinear optics is a scattering process. As each photon "arrives" or "leaves", it induces a virtual dipole allowed transition (J\|i erfy dx, frequendy abbreviated as ] ί ) between states ( ψ ψ ) . For SHG, the first photon at ω stimulates a transition between the ground state g (or "zero", 0) and some excited state m, the next photon at ω stimulates a transition between state m and state n. The departing photon, 2ω, stimulates a transition from η back to the ground state, g (Figure 1). Thus, this single microscopic event involves the tensor product of v

ι κ

ι?

K

κ


47.

Quadratic Electrooptic Effect in Small Molecules

DIRK AND KUZYK

6ωοι-2ω FRO

(ω) =

2

689

2

(7)

2

(ω§!-ω ) *

Optimization of the two-level model involves either increasing the change in dipole moment (Δμοι=μ -μ^) between the ground state, g (designated "0"), and first excited state e (designated "1"), increasing the transition moment (μοι) between those states, or operating closer to the molecular electronic resonance, Cûoi, with either the fundamental, ω, or second harmonic, 2ω (in the case of SHG). The preferable course is to increase the moments terms, Δμοι and μοιIncreasing the nonlinearity by resonance is easier, and can lead to substantial enhancements, though this is usually accompanied by linear absorption or damping of the second harmonic. Note from Equation (7), that in the case of EO, one has much more latitude in the use of resonance to enhance β. Past increases in β have been accomplished by two main avenues: Increasing the length of the conjugation path between the donor and acceptor, or by increasing the electron donating and accepting abilities of the donor and acceptor. Increasing the molecular length increases the vector, ~r% of the dipole operator, guaranteeing an increase in the excited state dipole moment, \i . The ground state dipole moment μ^, also increases, though since the ground state is far less charge separated than the excited state, the increase is less for μ^, so that there is still a significant increase in Δμοι (Figure 2). One other consequence of increasing the molecular length is an increase in the transition moment, μοι, supplying yet another boost to β. At some point Δμοι and μοι saturate, and an increase in molecular length does not result in useful increases in β. It is considered important to not further increase the molecular length in order to improve β. In addition to saturation of the electronic moments with increasing length, molecules of the size of the commonly used stilbenes and azobenzene dyes(7) seem to be optimal in terms of solubility properties. Further increases in molecular size would probably induce aggregation in poled polymer systems. Katz(8) has shown that β can be further increased by improving the electron accepting ability of the acceptor moiety, and there-by presumably increasing μ . Thus, replacement of nitro with dicyanovinyl greatly improves β without significantly changing the molecular length. He has demonstrated an excellent correlation with Hammett σ constants in explaining this enhancement. Undoubtedly, Hammett constants will provide at least a qualitative guide for further improvements in β (9). In the absence of significantly better donors and acceptors, and keeping in mind the restrictions on molecular size, we have decided to investigate the effect of changing aromaticity in the conjugating group separating the donor and acceptor. Note in Figure 3, the nitroaniline ground state must localize to a cyclohexatriene structure in order to reach the more charge-separated quinoid excited state. The delocalization energy between benzene and cyclohexatriene is quite large, 36Kcal/mole. It might be postulated that replacing a benzene ring with


£

e

€


690


ω

μ

gm

ω

2ω

μ

mn

μ

ng

Figure 1. The optical scattering leading to a single microscopic nonlinear optical event.

O.

0

0


0

Figure 2. Lengthening the molecule increases both Δμοι and the integrated absorption | μ^ | ). 2


47.

DIRK AND KUZYK


691

three dipole transitions, 'vtgnitfmntfng* Since the transition frequencies ((û > (û ) of the states m and η can be arbitrarily different, one must generally weight this term with a product of terms resonant with either ω or 2ω, gm

(ω^-2ω)(ω^ -ω) '

'

η

gn

(ω^-ω)(ω^ ~2ω) ' η

The states \\f and ψ„ could be anv^ state in the molecule, so the full molecular second order SHG polarization, PSHG* represented as the sum of all possible microscopic three-wave scattering events (1): m

m

u

s

t

D e


~$gm$mn$ng $SHG =

\

Σ

Z

m,n=0 ( ω ^ - 2 ω ) ( ω ^ - ω ) η

~\^gmï^mn[^ng

^gm$mn$ng

(ω^+ω)(ω^ +2ω)

(ω^+ωχω^-ω)

η

(4)

This expression, referred to as a sum-over-states (SOS), can be used to calculate molecular β tensors, presuming one has first calculated the transition moments and energies using, for example, a molecular orbital program. Since much of the susceptibility arises from π-electrons, it is frequently sufficient to only include a single ρ-π orbital per atom capable of donating a π-electron. Calculations of this type have been shown to be relatively accurate (2,3). It has been known experimentally(4) that much of the second order susceptibility generally arises from the lowest singlet excited state. For any particular molecule, the recently introduced Missing States Analysis (MSA)(5,6). can show, via calculation, to what extent β is dominated by the first excited state. For instance, the β of p-nitroaniline has been shown by M S A to be heavily dominated by the first excited state, at least with a PPP (Pariser-Pople-Parr) Hamiltonian and standard basis. The result of these findings is that one can often approximate Equation (4) by including only one excited state in the sum, there-by arriving at a two-level model: 2

βτζ, = I μοι I where the SHG dispersion factor

I Δμοι I F

5 / / G

(œ),

is given by(7)

FSHGÎ®)

3cooi 2

2

2(ωδ -ω )(ωδ -4ω ) 1

1

For the linear electrooptic effect (EO), the two-level model only differs in dispersion, with the dispersion factor, F ((ù), given by EO


(5)


692


a heterocycle could result in an improvement in β by allowing easier access to the charge separated excited state. In Table 1 is a comparison of our best azobenzene EO dye with an analogous one incorporating a thiazole moiety (C. W. Dirk, Η. E . Katz, M . L . Schilling, L . A . King, Submitted to / . Am. Chem. Soc.). The increase in μ·β (the appropriate quantity to compare when considering applications using E O dyes in poled-polymers) is substantial. We have found much of this increase to be due to dispersion. However, examination of Figure 4 shows that the thiazole dye has a more narrow transition, so that absorption and damping are relatively constant. Thus, use of this heterocycle has resulted in a useful increase in β. The stability and solubility properties of this dye are not significantly different from the earlier benzene analog, so it should presently be among the best available for EO applications involving poled-polymers.

3

Optimizing χ( ) Nonlinearities for Quadratic Electrooptics In general, the optimization of organic molecules for third order nonlinear optical applications has enjoyed much less success than for second order optical nonlinearities. The major reason for this has been the questionable validity of the two-level model for γ, and the difficult assessment of the contribution of twophoton states for the more acceptable three-level model. Using a syllogistic approach analogous to the earlier construction of the PSHG perturbation summation (Equation 4), we can "derive" the general third order perturbation theory expression(l_),

^glV-lmVmntfng

Y=«7

H J e l A 3

x

/,m^x) ( ω ^ - ω ) ( ω ^ - ω ι - ω 2 ) ( ω ^ - ω ι ) σ

-

Y — m,»x) ( ω ^ / - ω ) ( ω ^ - ω ι ) ( ω ^ + ω 2 )

(8)

σ

where K' is a constant that depends on the optical process (i.e T H G , D F W M , QEO, etc.), ω =ω -Κΰ2+θ)3, /_σ,ι,2,3 is the average of the 48 terms obtained by σ

1

_

N o t e

t n a t

t n e r e

permuting - ω , ω 0)2, 0)3, and, μ" κ=ΐ?ικ Τζ^· are one-photon, ((Ogn-ωχ), two-photon, ( ω ^ - ο ^ - α ^ ) » and three-photon, (ω^/-ω ), resonant denominators, respectively. One- and three-photon states are accessible from the ground state by use of the dipole operator, e ?, and can be the same state (i.e. l=n). Pure two-photon states are not similarly accessible from the ground state, so that m*l,n. Thus, the minimal formal approximation that we can make to Equation (8) is to sum over two excited states, yielding a three-level modelQO), σ

1 }

ν

σ

7


47. DIRK AND KUZYK


693

Ο Ο

ο, ο

Α, Λ +

μ. ο. ο


Ν'

Figure 3. Bond localization necessary to reach quinoid excited state from aromatic ground state.

Table 1. Second-Order Nonlinearities of Thiazole Dyes

Note that these results are local field corrected


or

(10)

>

(H)

where, γ,=-*'μοι0ιι. /

2

γ =ΑΓ μ§ (Δμ ι) /) ι Λ

1

0

11

>

γ =/Γ μ 2μοι^ΐ2ΐ. /

2

Γ Ρ

This approximation may only be true for centrosymmetric molecules where by analogy to the particle-in-a-box, the selection rules are now more strict. As one increases the asymmetry, selection rules begin to break down and it is possible that μο2 will become more allowed. For the same reason, as | μο2 I increases, we might expect | μΐ2 | to decrease, so that in the extreme of large | Δμ | s (i.e. molecules with large second order nonlinearities, β), we might anticipate a small Jrp. Thus, either in the extreme of centrosymmetry with a small transition moment between excited states ( μ ^ ) and/or if D121 is small relative t o D and D , or in the case of large β it would be possible to mathematically impose a two-level model, n

i n

Y = Yc + Yn

,

(12)

on the observed data. Under what circumstances might this be applicable? Since two-photon states are difficult to characterize, it would be difficult to generally ascertain the magnitude of the excited state transition moment, μΐ2. This remains an unknown in the system, thus we must depend on the characteristics of


696


the dispersion terms ( D u , D , £ ) i ) to define a limiting situation leading to Equation (12). The two-photon resonance of D i consists of Ι / ί ω ^ - ω ι - ο ^ ) . To minimize its contribution, we must maximize the magnitude of the denominator. This can be done by setting a>i=G>2=0. If CÛ3=CÛ*0, this restriction defines the process γ(-ω;0,0,ω). This is the QEO process. For the QEO process, in order to maximize the contributions of the D and D terms relative to that of the D i term, it is necessary to operate close (on the low energy side) to the first excited frequency, CUQI, with the QEO probe, ω. As long as the two-photon state frequency, coo is not too close to cooi, and/or I Hoi I ^ I M12 I > the term based on D could possibly be ignored for the QEO process. The general validity of Equation (12) remains in doubt, because of the uncertainty over the magnitude of μ ι , and the unknown frequency difference, I ΰ>υ2~ωοι I · However, these conditions are likely the closest one can get toward imposing a two-level model for γ. If we check the preceding argument against the CNDO and PPP results of Heflin et. alQJ.) and Soos et. al(12), respectively, for the irans-octatetraene molecule, we can judge how good this approximation is for at least one centrosymmetric system. From their transition moments, and transition energies, it is possible to calculate y and y for a hypothetical QEO measurement as proposed above. For this hypothetical measurement, we have set the probe 2000cm" below the lowest excited state. In an actual measurement it is possible to measure JQEO closer to resonance, and even right on resonance, though damping corrections necessary to correct D (for y ) and D i (for y ) become uncertain so that experimental data cannot be easily related to anything. Actual measurements are generally done far enough off resonance (1000cm to 3000cm" , depending on peak width) that effective damping corrections can be made. The values ( x l O " cm C M " ) , as calculated for the hypothetical measurement on irawj-octatetraene are given below in Table 2: m

1 2

1 2

n

n

i

1 2

2


1 2 1

2

c

TP

1

n

c

1 2

TP

_ 1

1

34

7

2

Table 2. Calculated Third-Order Susceptibilities

Re[Yn]

Heflin et. al

Soos et. al

-4.9

-6.6

Ξ0

=0

+10.7

+15.2

For both calculations (based on the M O and V B calculations of Garito or Soos, respectively), the two-photon state of rra/is-octatetraene ( ψ 6 ) is significantly removed (v -v =22000cm" ) from the lowest excited state, ψ ι , so that D i (actually D ; states ψ - ψ 5 appear irrelevant) should be poorly competitive with D . Despite this, | y | is still larger than | y | . Thus, in spite of a best case scenario for a two-level model, we should see a significant two-photon 1

1

6

1 2

1 6 1

n

2

TP

c


47.


DIRK AND KUZYK

697

contribution for a centrosymmetric molecule. This leaves unresolved the case of a molecule possessing a large β, which is experimentally dealt with below.


QEO Measurements Third order N L O measurements are frequently plagued by artifacts. Among the most difficult contributions to eliminate are the slow orientational contributions which mask the smaller fast electronic component. For the QEO process, two major orientational contributions must be dealt with, often referred to as "μβ" and "αα", respectively. The "μβ" component arises from the electric field coupling to the molecular dipole moment, orienting the molecule, permitting a field induced electrooptic effect. The "αα" effect, on the other hand, involves a field induced dipole moment, (oE) via the polarizability tensor, depends on the magnitude of the dipole moment and the dipole projection of β, while the magnitude of the "αα" contribution, γ , depends on the magnitude and anisotropy of the molecular polarizability, α (13,14). These two contributions are of opposite sign, and for molecules with large β, normally the same order of magnitude. The resulting mutual cancellation of γ β and leads to a total orientational contribution, γOR, which is comparable to, or smaller than the electronic QEO susceptibilities measured here (vide infra). μ

α α

μ

In order to limit orientational contributions, we have created a new procedure to measure QEO. This involves dissolving the molecule of interest in a solution containing poly(methylmethacrylate) (PMMA), and spinning a thin (2-3μΜ) film onto an ITO glass electrode, placing two of these films face to face and heating briefly under compression to effect an optical contact between the film surfaces (Figure 5a). One then places the sample into a Mach-Zehnder interferometer, oscillate an electric field (at 4000Hz) across the ITΟ electrodes, monotonically "delay" the signal in the other arm of the interferometer (Figure 5b), and lock-in on the fringes being created at 8000Hz. The fringe magnitude provides the real part of the quadratic electrooptic coefficient, Re[>] , while the imaginary part, I Im[s] I is measured from the offset. Details are provided elsewhere(13,15). The high viscosity of the P M M A damps out orientational contributions so that the QEO that is measured is thought to be =60-90% electronic. This has been ascertained by measuring the electric field induced second harmonic generation (EFISH) below the T of the polymer. From this can be obtained the microscopic elastic constant, which can in turn be used to estimate the magnitude of the two orientational contributions to QEO- Details are provided elsewhere(13,16). g


698


SPIN FILM

a

-GLASS POLYMER / DYE FILM I

>

•


HEAT AND PRESS

Sample Preparation

Figure 5. (a)QEO sample preparation, (b) QEO interferometric measurement.


47.

DIRK AND KUZYK


699

QEO Results The QEO susceptibility results for several molecules (structures shown in Figure 6) are summarized in Table 3 (17). Table 3. QEO Susceptibility Results 1 Re[y 7 ] 1 $


molecule 1

29

Re[y ]§ -6.8

2

7.1

-1.2

3

7.3

-0.5

Z

0

c

4

1.8

-0.2

5

2.8

-0.06

6

6.2

-0.4

7

18

-3.8

8

4.3

-0.6

9

68

-11

Re[y ]+Re[Y ]

Re[yJ§ +45

+38

+9.3

+7.1

=0

-11

M

1

Note that all susceptibilities are xlO cm t ±25%; § γ, ±20%; y ±30-35%

c

n

2

esu .

n

Note that the squarylium dye, 9, has quite a large susceptibility. At 1% in P M M A , the bulk susceptibility is 13xl0~ esw(18). At a hypothetical "100%", this susceptibility is comparable to the T H G and D F W M susceptibilities of some polydiacetylenes, though this comparison must be viewed with some circumspection considering the difficulty in accounting for the differences in dispersion between different processes. 14

Optimizing QEO Materials Is it possible to enhance

QEO?

Answering this question involves an examination of Equation (12). The largest QEO nonlinearities are available when the QEO probe frequency, ω, is close to resonance. This is the restriction that can potentially allow the two-level model to be applicable. Note that the two-level model depends on the competition between and γ , which have opposite sign. It is important to note that under centrosymmetry, y should be the only contribution to YgEo, while the QEO for noncentrosymmetric molecules consists of y +Y . A first order correction to this model will require the additional term yTP. It is important to judge what effect this term may have on this speculation and the potential interpretation. In general, it should be to lower (However, note as in the case of trans-octatetraene, c

η

c

c

n




700


47.


DIRK AND KUZYK

701

the magnitude of γ?ρ is sufficiently large that despite the opposite sign to y , I ΊΟ+ΊΤΡ I > I Yc I ) the expected | JQEO I for centrosymmetric molecules, but increase the susceptibility magnitude expected in noncentrosymmetric molecules. For our measurements, the quantity, D111/Dn approximately equals two. As one operates the QEO probe, ω, closer to resonance (i.e. C o i - ω < 500c/n ), this ratio can increase greatly. If the breadth of the molecular excitation, cuoi, is sufficiently narrow (20x) are possible in y when close to resonance, which could lead to much larger JQEOS- It would then appear that one has two options in increasing JQEO mediated through Equation (12): increase the integrated absorption ( μ§ι Y ) of centrosymmetric molecules, or prepare noncentrosymmetric molecules with large β ( Δμοι °* Yn) d especially narrow electronic absorptions. Transition moments, μο!, to the first excited state can be calculated from the integrated absorption of the linear electronic spectrum. This can be used to calculate -KQIDU, the first term (defined here as y ) of the two-level model. The second term (Κ'μΙΑμΙ ) from Equation (12) (defined here γ ) involves Δμο!, which can be determined directly from solvatochromism(19), or from a two-level analysis of a molecular EFISH measurement of β. Shown in Table 3 are the Re[y ] results(17) along with some preliminary values for Re[Y„] as determined from EFISH. It can be seen that JQEO is well accounted for by Y . For the two results for which we have y data, Y +Y does reasonably well account for JQEO- However, note that for molecule 9, γ Ξ θ in its centrosymmetric conformation, so that JQEO is not well accounted for by I Yc+Yn I · There are several possible explanations for this: (1) There may be significant noncentrosymmetric conformations that exist for 9 in solution leading to γ * 0 . (2) If molecule 9 is indeed dominated by the centrosymmetric conformation, γ β should be small, and may not fully cancel γ . Thus, there could be a much larger total orientational contribution, γ ^ , than is anticipated. (3) Finally, the two-photon contribution, jrp, is unknown. As pointed out earlier, for centrosymmetric systems, frp may be the most significant contributing term to the measured JQEOIf JTP represents a significant contribution to JQEO for molecule 9, then it is curious that it appears to be less important for the two dipolar dyes, 1 and 2. In keeping with the earlier discussion, this could possibly reflect the effect of breaking symmetry so that for dyes with large β, the second excited state is not purely two-photon in nature with μ < μο I · c

-1

_1

n

A S

0 0

c


a n

c

m

η

c

n o t

c

n

c

n

η

η

μ

α α

1 2

Conclusions We report the largest known useful microscopic N L O susceptibilities for the linear and quadratic electrooptic effects. The QEO susceptibility of 9 might be large enough to explore simple primitive QEO modulation experiments, though perhaps is not nearly large enough to be of commercial importance. With the permutation-symmetry-corrected results(17) it appears that we cannot successfully fit our QEO data to a two-level model, at least for centrosymmetric structures. We have only one data point (9) to make this judgement, however, and


702


have not eliminated the problem of an uncompensated "αα" orientational contribution. In the case of molecules with large β, our two results for 1 and 2 indicate a reasonable fit to Equation (12). These results are consistent with the observations of Garito et. al. where they show γ„ to be a dominant contribution in donor-acceptor substituted polyenes(20). If Equation (11) is a more accurate overall representation to cover the extremes between centrosymmetry and large β, it would appear that despite the large value of | RC[JQEO] I f° 9, an attractive route to especially large QEO susceptibilities might be noncentrosymmetric molecules with large β and narrow electronic transitions. Any significant JTP iU only end up supplementing the potentially very large susceptibility offered by y when very close to resonance. While there has been little success (or effort?) at narrowing electronic transitions of molecules with large β, the thiazole dye reported earlier in this chapter is a distinct improvement in this regard over others previously reported. Preliminary QEO measurements indicate this dye to possess a JQEO larger than that of molecule 1. It would appear that optimizing molecules for a large EO effect (via y ) will also optimize them for a large QEO effect. However, compared to EO, obtaining the largest QEO susceptibilities may require operating even closer to resonance with the probe frequency. While it appears that a good deal of the QEO susceptibility may be accounted for by three terms, y , γ , and γτ/>, we do not intend to ignore the potential importance of other terms in Equation (9). The strategy will be to see where a reasonable cut-off of terms of Equation (9) can still lead to an adequate explanation of the structure/property trend. We are presently working on solvatochromatic and EFISH determinations of Δμοι, with the aim to more fully characterize molecules with regard to γ„, and have plans to experimentally determine μΐ2 in order to calculate yjp. There are also efforts underway to more accurately determine orientational contributions. r

w


n

n

c

Λ

Literature Cited 1. Orr, B. J.; Ward, J. F. Mol. Phys. 1971, 20, 513-526. 2. Dirk, C. W.; Twieg, R. J.; Wagniere, G. J. Am. Chem. Soc. 1986, 108, 53873. Li, D.; Ratner, Μ. Α.; Marks, T. J. J. Am. Chem. Soc. 1988, 110, 17074. Oudar, J. L. J. Chem. Phys., 1977, 67, 446-457. 5. Dirk, C. W.; Kuzyk, M. G. Physical Review A, 1989, 39, 1219-1226. 6. Dirk, C. W.; Kuzyk, M. G. SPIE Proceedings 1988, 971, 11-16. 7. Singer, K. D.; Sohn, J. E.; King, L. Α.; Gordon, H. M.; Katz, Η. E.; Dirk, C. W. J. Opt. Soc. B, 1989, 6, 1339-1350. 8. Katz, Η. E.; Singer, K. D.; Sohn, J. E.; Dirk, C. W.; King, L. Α.; Gordon, H. M. J. Am. Chem. Soc., 1987, 109, 6561-


47. DIRK AND KUZYK


9. For some further discussion on the applicability of linear free energy relationships to second order nonlinear optics, see: Ulman, A. J. Phys. Chem. 1988, 92, 2385-2390. 10. Kuzyk, M. G.; Dirk; C. W. Physical Review A, 1990, 41, 5098-5109. 11. Heflin, J. R.; Wong, K. Y.; Zamani-Khamiri, O.; Garito, A. F. Phys. Rev. Β 1988, 38, 1573-. 12. Soos, Z. G.; Ramasesha, S. J. Chem. Phys. 1989, 90, 1067-.


13. Kuzyk, M. G.; Dirk, C. W.; Sohn, J. E. J. Opt. Soc. B, 1990, 7, 842-. 14. Kuzyk, M. G.; Moore, R. C.; Sohn, J. E.; King, L. Α.; Dirk, C. W. SPIE Proceedings, 1989, 1147, 198-209. 15. Kuzyk, M. G.; Dirk, C. W. Appl. Phys. Lett. 1989, 54, 1628-1630. 16. Kuzyk, M. G.; Moore, R. C.; King, L. A. J. Opt. Soc. B, 1990, 7, 64-72. 17. Dirk, C. W.; Kuzyk, M. G. SPIE Proceedings 1989, 1147, 18-25. Note that the Re[γ] in this reference are incorrect (too high by a factor of six) due to an error in properly applying the permutation symmetry operation. c

18. Dirk, C. W.; Kuzyk, M. G. Chem. Materials, 1990, 2, 4-6. 19. Paley, m. S.; Harris, J. M.; Looser, H.; Baumert, J. C.; Bjorklund, G. C. Jundt, D.; Twieg R. J. J. Org. Chem. 1989, 54, 3774-3778. 20. Garito, A. F.; Heflin, J. R.; Wong, Κ. Y.; Zamani-Khamiri, O. SPIE Proceedings 1988, 971, 2-10. RECEIVED

July 10, 1990


Quadratic Electrooptic Effect in Small Molecules - ACS Symposium

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