J. Phys. Chem. 1996, 100, 11863-11869
11863
Resonantly Enhanced, Degenerate Four-Wave Mixing Measurement of the Cubic Molecular Hyperpolarizability of Squaraine Dyes at 700 nm† Kim Tran and Gary W. Scott* Department of Chemistry, UniVersity of CaliforniasRiVerside, RiVerside, California 92521
David J. Funk and David S. Moore Photochemistry and Photophysics, CST-10, Chemical Science and Technology DiVision, Mailstop J565, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ReceiVed: February 13, 1996X
We report the results of resonantly enhanced, degenerate four-wave mixing (DFWM) measurements of the cubic molecular hyperpolarizability coefficient (γ) of four squaraine dyes. Different determinations of γ were performed at 696 and 710 nm with both ultrashort (210 fs) and somewhat longer (3 ps) duration laser pulses using the forward wave geometry. Bis[4-(dimethylamino)phenyl]squaraine (H-Sq), bis[4-(dimethylamino)-2-hydroxyphenyl]squaraine (HO-Sq), bis(2,4,6-trihydroxyphenyl)squaraine (3HO-Sq), and diazulenylsquaraine (Az-Sq) were investigated as a function of concentration in liquid solutions and polymer blends, enabling the calculation of γ from the measured values of the third-order nonlinear susceptibilities, χ(3), of these samples. All values of γ for these squaraines were found to be negative with large absolute magnitudes, up to ∼8 × 10-32 in esu “units” [9.9 × 10-57 C m4 V-3 (SI units)] for the real part of γ for Az-Sq at 696 nm. [We discuss the conversion of esu units to SI units for the quadratic (β) and cubic hyperpolarizability coefficients (γ) in the Appendix of this paper, reporting our results throughout in both systems of units.] Significant imaginary contributions to γ were also observed for Az-Sq, but not for the other squaraines as expected from differences in absorption at these wavelengths. The DFWM signals exhibited the expected cubic intensity dependence, polarization dependence, and instantaneous time response, effectively ruling out any contributions to the measured values of γ from experimental artifacts.
1. Introduction During the last 20 years, the unique photophysical properties of squaraines-squarylium dyes-have caught the attention of investigators interested in potential applications in the fields of electrophotography and xerography,1-6 photovoltaics,7-11 and optical recording and storage.12-14 Numerous studies on the linear spectroscopy of the squaraines in liquid solutions15-23 and in polymer matrices24 have also been reported. In terms of molecular structure, as shown in Figure 1, squaraines consist of a C4O2 electron-withdrawing group centered between two electron-donating moieties. This donoracceptor-donor (DAD) configuration suggests that a high degree of intramolecular charge-transfer character should be expected in these molecules. In support of this model, the results of MNDO calculations with ground-state geometry optimization of bis(4-dimethylaminophenyl)squaraine indicated that this dye possesses a distinctive alternate “polyene”-like framework.25 These molecular structure features suggest that squaraines should exhibit relatively large optical nonlinearities, and thus considerable effort has been focused on the investigation of the nonlinear optical behavior of these molecules. The third-order optical nonlinearity of some squaraines has been measured by using various techniques, including the quadratic electrooptic effect (QEO),26-28 Sagnac pump-probe measurement,28,29 electric-field-induced second-harmonic generation (EFISH),28,30 third-harmonic generation (THG),30-32 and quadratic electro* Author for correspondence. † Submitted in honor of Professor Robin M. Hochstrasser on the occasion of his 65th birthday. X Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0022-3654(96)00447-9 CCC: $12.00
Figure 1. Molecular structures of the squaraine dyes investigated.
absorption spectroscopy.33 Relatively large magnitudes of the cubic molecular hyperpolarizability coefficient, γ, have been reported for these dyes. For example, values up to γ ) 2.33 × 10-32 esu units [2.88 × 10-57 C m4 V-3] were reported for a squaraine dye, as measured by the wave guide Sagnac pumpprobe technique.28,29 In addition, the sign of γ for these molecules was found to be negative in determinations by EFISH and THG methods.28,30 The large magnitudes of γ measured for these dyes have been attributed to contributions of a twophoton resonance between the lowest one-photon excited singlet state and higher energy, two-photon excited states in squaraines.35 Molecules, such as squaraines, with a relatively large nonlinear response may provide the basis of materials for devices in optical signal processing applications. Herein we report the results of degenerate four-wave mixing (DFWM) studies to measure the values of γ for some squaraine dyes. A preliminary report of these results has already been published.35 These results confirm that the squaraines exhibit a large, cubic, © 1996 American Chemical Society
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nonlinear response. A detailed report of the nonlinear optical behavior of these squaraine dyes, including new results, is part of the present paper. The structures of the four squaraines studied are presented in Figure 1. The investigations were carried out for the dyes both dissolved in liquid solutions and doped into solid polystyrene matrices. Concentration-dependent DFWM experiments were conducted on these dyes using both 200-fs- and 3-psduration pulses. In addition, the power dependence of the DFWM signals was also studied. Throughout the present paper we report values of γ in both esu units and SI units, with the latter being given in square brackets in each case. Literature values have generally been given in the past in esu units, whereas SI units make clear comparisons between γ and χ(3). As indicated in the abstract, conversions between the two systems of units are discussed in the Appendix. 2. Experimental Section Ultrashort laser pulses at two different wavelengths, 696 and 710 nm, were generated as described previously.35 In these experiments, the 1064-nm fundamental pulses derived from an actively mode-locked Nd3+:YAG laser (Coherent Antares) were frequency-doubled by using an LBO super doubler (Coherent) to 532 nm, and the output (∼5 W) was stabilized in amplitude and space by an active feedback system consisting of an acoustooptic modulator and piezoelectric positioners located on the rear high reflector (Coherent). The frequency-doubled green pulse train was then focused into a folded, hybridly mode-locked dye laser with pyridine 1 (Exciton) in methanol (C ∼ 10-3 M) as the gain medium and DDI (Exciton) in methanol (C ∼ 10-5 M) as the saturable absorber. The output wavelength was tunable from 690 to 710 nm with a single-plate birefringent filter and was set to either 710 or 696 nm for these experiments. The wavelengths at which the DFWM experiments were conducted were measured by using a calibrated spectrometer (Tektronix Model J20) and a storage oscilloscope (Tektronix Model 7834). The average dye laser output power was 200 mW with a pulse duration of ∼250 fs (FWHM). To improve long-term stability, the laser was adjusted to produce pulse durations between 300 and 500 fs. This output was focused onto a ∼10-12-in.-long optical fiber using a microscope objective, where it was chirped through nonlinear interaction with the quartz. The laser beam then passed through a delay line before entering a four-stage amplifier operating on LDS 698 (Exciton). The amplifier was pumped with the frequencydoubled output of a home-built regenerative amplifier operated at 50 Hz with the seed pulse obtained from the Nd3+:YAG laser described earlier. Finally, the amplified pulses (λ ) 710 or 696 nm, with an average pulse energy of approximately 100 µJ) were recompressed in the femtosecond DFWM experiments to about 210 fs by using an SF-10 prism compressor. For the picosecond DFWM experiments, the final amplified pulses had a width of ∼3 ps (FWHM). Pulse durations were determined in an SHG autocorrelation experiment. The output laser pulses were passed through a broadband polarization rotator (Newport Model PR-950) to produce a vertically polarized pulse train that was split into three parts: two pumps and one probe. The intensities of each of the three pulse trains were about 40%, 40%, and 20% of the total pulse train, respectively. The three trains, after appropriate delays, were then focused onto the sample to a spot size of ∼0.2 mm2 in a forward-wave arrangement. In this configuration, the angle between any two of the train paths was about 2°. The timeresolved DFWM signal intensity was obtained while varying
Figure 2. Room temperature absorption spectra of H-Sq in CH2Cl2 (s), HO-Sq in CH2Cl2 (‚‚‚), 3HO-Sq in ethyl acetate (- - -), and AzSq in CH2Cl2 (-‚-‚). The arrows at 696 (λ1) and 710 nm (λ2) indicate the wavelengths at which DFWM experiments were performed.
the delay of the probe relative to the pump pulses using a Klinger 1.0-µm resolution translation stage controlled by a Macintosh IICI equipped with a GPIB board and running Labview software (National Instruments). The voltage output from the signal photomultiplier was monitored with a gated integrator (Stanford Research Systems Model 250). The output of the integrator was fed into a A/D board (Stanford Research Systems Model 245) and transferred to the microprocessor through the GPIB. In most of the experiments the three pulse trains were all vertically polarized. In one experiment, however, the probe pulse train polarization was rotated to horizontal while maintaining both pump pulse trains with vertical polarization. Squaraines and their samples were prepared as previously described.24 3. Results The absorption spectra of liquid solutions of the squaraines studied are shown in Figure 2. In this figure, the arrows indicate the wavelengths at which the DFWM experiments were conducted. Some representative femtosecond time-resolved DFWM signals obtained for the squaraine-doped samples studied are shown in Figure 3. As shown in this figure, these systems exhibit a symmetric temporal response, and the widths of their corresponding DFWM profiles essentially follow the laser pulses used. The third-order nonlinear susceptibilities, χs(3), of the squarainedoped samples were obtained by comparing the peaks of the temporal DFWM profiles with that obtained for CCl4 under the same experimental conditions and input energy. From the reported value of γ ) +2.29 × 10-36 esu units [2.84 × 10-61 C m4 V-3] for neat liquid CCl4,36 the effective values of χs(3) of the squaraine samples were determined from the following expression:37
( ) ( ) ( ){
χs(3) ) χr(3)
Is Ir
0.5
ns nr
2
Ls Lr
ln T(λ)
}
xT(λ)[1 - T(λ)]
(1)
where I denotes the maximum DFWM signal intensity in the time-resolved profile, n is the refractive index of the medium, L is the sample length, and subscripts s and r refer to the sample (squaraine solution) and the reference (neat CCl4), respectively.
Cubic Molecular Hyperpolarizability of Squaraines
J. Phys. Chem., Vol. 100, No. 29, 1996 11865
Figure 3. Room temperature time-resolved DFWM signals at 710 nm for (a) a solution of HO-Sq in CH2Cl2 and (b) a thin film of Az-Sq in polystyrene using 200-fs laser pulses.
The quantity inside the curly brackets corrects for the sample absorption in terms of its transmittance, T(λ). For each sample studied, the effective χs(3), as obtained from the preceding equation, is the sum of the contributions made by both the solute and the solvent. For a noninteracting, ideal mixture of solvent and solute, χs(3) can be expressed in esu units as36
χs(3) )
(
)
n2 + 2 4 [(Nsolγsol + Nxγx)2 + (Nxγxi)2]0.5 3
Figure 4. Concentration dependence of the effective χs(3), measured by a DFWM technique at 696 nm, of (a) solutions of H-Sq in CHCl3 and (b) solutions of Az-Sq in CH2Cl2 using 3-ps laser pulses. The smooth curves result from a nonlinear least-squares fit of eq 2 to the displayed data.
TABLE 1: Cubic Molecular Hyperpolarizability Coefficients, γ, for Squaraine Dyes in Room Temperature Solutions at Wavelengths of 696 and 710 nm Obtained with Laser Pulses of 200-fs Pulse Widtha γ(×1032 esu)[×10-57 C m4 V-3]
(2)
where n is the refractive index of the solution, γx and γxi denote the real and the imaginary components, respectively, of the orientationally averaged, cubic molecular hyperpolarizability of the solute molecules, γsol is the cubic molecular hyperpolarizability coefficient of the solvent (assumed to have only a real component), and Nsol and Nx are the molecular densities (number of molecules per cubic centimeter) of the solute and the solvent, respectively. Nx is related to the molar concentration of the solution given by Nx ) NACs/103, where NA is Avogadro’s number. Some representative plots of the concentration dependence of χs(3) are shown in Figures 4 and 5. The cubic hyperpolarizability coefficients, γ, of the squaraines studied, obtained in room temperature solutions at wavelengths of 696 and 710 nm and the laser pulses of 0.2- and 3-ps pulse widths, are presented in Tables 1 and 2, respectively. The values reported in Tables 1 and 2 were obtained with the pump and probe pulses all vertically polarized. An additional DFWM experiment was performed on a 6.1 × 10-4 M solution of H-Sq in chloroform utilizing a horizontally polarized probe pulse train with vertical pump pulse train polarization. This experiment resulted in a measured χs(3) magnitude of (2.1 ( 0.8) × 10-15 in esu units. By using all vertically polarized pulses, the same sample yielded a magnitude of χs(3) of (5.7 ( 1.3) × 10-15 in esu units. For the DFWM process, the frequency- and time-dependent intensity of the output signal, IDFWM(ω,t), should be proportional to the intensities of the three input pulse trains, namely, I1(ω,t),
squaraine/host H-Sq/CH2Cl2 H-Sq/polystyrene HO-Sq/CH2Cl2 HO-Sq/polystyrene 3HO-Sq/ CH3CO2C2H5 3HO-Sq/polystyrene Az-Sq/CH2Cl2
λ ) 696 nm
(-8.4 ( 1.4) ( (4.6 ( 0.9)i [(-10.4 ( 1.7) ( (5.7 ( 1.1)i]
Az-Sq/polystyrene a
λ ) 710 nm
-4.2 ( 0.7 [-5.2 ( 0.9] -3.3 ( 0.5 [-4.1 ( 0.6] -2.8 ( 0.6 [-3.5 ( 0.7] -4.5 ( 0.7 [-5.6 ( 0.9] -4.3 ( 0.6 [-5.3 ( 0.7] -4.3 ( 0.9 [-5.3 ( 1.1] -3.2 ( 0.4 [-4.2 ( 0.5] -2.1 ( 0.4 [-2.6 ( 0.5] -1.7 ( 0.4 [-2.1 ( 0.5] (-6.4 ( 1.1) ( (4.4 ( 0.9)i [(-7.9 ( 1.4) ( (5.4 ( 1.1)i] -8.6 ( 1.4 [-10.6 ( 1.7]
SI unit values are in square brackets.
I2(ω,t), and I3(ω,t), as follows:39
IDFWM(ω,t) ) κ(χ(3))2I1(ω,t)I2(ω,t)I3(ω,t)
(3)
where κ is a proportionality constant. In these DFWM experiments, all three input pulse trains were derived from the same source, and the ratios of the intensities of the three incident trains were kept constant. Under these conditions, a third-order dependence of the intensity of the output DFWM signal, IDFWM(ω,t), upon the total intensity of the input beams, Iin, should be observed. As shown in Figure 6 and in Table 3, a cubic dependence of the intensity of the DFWM signals on the total input power was observed for all of the squaraines studied. For Az-Sq, however, deviation from the third-order dependence was
11866 J. Phys. Chem., Vol. 100, No. 29, 1996
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TABLE 2: Cubic Molecular Hyperpolarizability Coefficients, γ, for Squaraine Dyes in Room Temperature Solutions at Wavelengths of 696 and 710 nm Obtained with Laser Pulses of 3-ps Pulse Widtha γ (×1032 esu) [×1057 C m4 V-3] λ ) 696 nm squaraine/host H-Sq/CHCl3
λ ) 710 nm
real
imaginary
real
imaginary
-4.0 ( 0.5 [-5.0 ( 0.6]
0.05 ( 0.02 [0.06 ( 0.025]
-5.6 ( 0.8 [-6.9 ( 0.9]
0.10 ( 0.03 [0.12 ( 0.04]
-2.4 ( 0.5 [-3.0 ( 0.6]
0.2 ( 0.2 [0.25 ( 0.25]
-3.4 ( 0.6 [-4.2 ( 0.7] -3.7 ( 0.5 [-4.6 ( 0.6] -4.9 ( 0.9 [-6.1 ( 1.1] -3.7 ( 0.6 [-4.6 ( 0.7] -2.3 ( 0.6 [-2.8 ( 0.7] -1.6 ( 0.5 [-2.0 ( 0.6] -8.0 ( 2.4 [-9.9 ( 3.0] -5.3 ( 1.7 [-6.6 ( 2.1]
0.008 ( 0.004 [0.01 ( 0.005] 0.003 ( 0.001 [0.004 ( 0.0013] 0.8 ( 0.3 [1.0 ( 0.4] 0.4 ( 0.2 [0.5 ( 0.25] 0.04 ( 0.02 [0.05 ( 0.024] 0.04 ( 0.03 [0.05 ( 0.04] 3.0 ( 0.6 [3.7 ( 0.7] 3.0 ( 0.7 [3.7 ( 0.8]
H-Sq/polystyrene HO-Sq/CHCl3 HO-Sq/polystyrene 3HO-Sq/CH3CO2C2H5 3HO-Sq/polystyrene Az-Sq/CH2Cl2
-8.6 ( 2.6 [-10.6 ( 3.2]
3.8 ( 0.8 [4.7 ( 1.0]
Az-Sq/polystyrene a
SI unit values are in square brackets.
Figure 6. Power dependence of the peak intensity of the DFWM signal of (a) H-Sq in polystyrene and (b) Az-Sq in polystyrene at 710 nm produced with a 200-fs laser pulse width.
Figure 5. Concentration dependence of the effective χs(3), measured by a DFWM technique at 710 nm, of polystyrene thin films doped with (a) 3HO-Sq and (b) Az-Sq using 3-ps laser pulses. The smooth curves result from a nonlinear least-squares fit of eq 2 to the displayed data.
observed at relatively high input power, presumably due to physical damage to the sample, as observed at power levels g1011 W/cm2. 4. Discussion As shown in Tables 1 and 2, the real components of γ for the squaraines studied were all found to be negative. This is in agreement with results that were previously reported on the cubic hyperpolarizabilities of squaraines using other nonlinear optical techniques.28,30 From Tables 1 and 2, the magnitudes
TABLE 3: Value of the Exponent n Denoting the Power Law (IDFWM r Iinn) of the Peak Intensity of the Degenerate Four-Wave Mixing Signal to the Input Intensity at 710 nm (200-fs Pulse Width) for Various Squaraines Doped into Polystyrene
a
squaraine
n
H-Sq HO-Sq 3HO-Sq Az-Sq
2.95 ( 0.31 2.84 ( 0.48 2.81 ( 0.41 2.85 ( 0.29a
Obtained from low input intensity only.
of the real components of γ measured with the two different pulse durations used in these experiments are the same, within experimental error, indicating an independence of γ for these compounds upon the laser pulse widths at the wavelengths studied. The third-order optical nonlinearity of H-Sq, HO-Sq, and 3HO-Sq likely contains a significant enhancement due to
Cubic Molecular Hyperpolarizability of Squaraines
J. Phys. Chem., Vol. 100, No. 29, 1996 11867
the near-resonance effect. This enhancement, however, is significantly higher for the case of Az-Sq, for which the frequencies at which the DFWM experiments were conducted were within the lowest energy linear absorption band. In most of these DFWM experiments, the three input beams were all vertically polarized. Thus, the corresponding tensor elements of the third-order susceptibility and the cubic molecular hyperpolarizability that were determined are χ(3)1111 and γ1111, respectively. In isotropic medium, χ(3) has three independent components, namely, χ(3)1111, χ(3)1212, and χ(3)1122. Furthermore, χ(3)1111 ) χ(3)1212 + χ(3)1122 + χ(3)1221. For a case with nonresonant electronic nonlinearities, χ(3)1111 ) 3χ(3)1212 ) 3χ(3)1122.40 The tensor component χ(3)1122 can be determined when the probe beam is orthogonally polarized with respect to the two pump beams. The magnitude of χ(3) for the sample of H-Sq in chloroform was found to be (2.1 ( 0.8) × 10-15 in esu units when the polarizations of the pump and probe beams were orthogonal to each other. However, when the polarizations of the pump and probe beams were all vertical, χ(3) of this sample was found to be (5.7 ( 1.3) × 10-15 in esu units. The ratio of these two obtained values of χ(3)eff is close to 3, strongly suggesting that the DFWM signals observed contain no significant contribution arising from the coherent coupling effect.41 For the samples of H-Sq, HO-Sq, and 3HO-Sq, the DFWM measurements made at 696 and 710 nm are just outside any significant one-photon absorption (see Figure 2). The highly symmetric DFWM pulse shape and instantaneous temporal response of the DFWM signals observed (e.g., see Figure 3) indicate that the DFWM signals obtained are not contaminated by excited-state contributions from a population grating. Excitedstate lifetimes for these dyes are considerably longer than the 210-fs time resolution of the present experiment.24 The values of γ obtained also indicate the lack of an absorption contribution. As shown in Table 2, the contributions of imaginary components to γ, which would be due to any absorption in DFWM processes, are quite small compared to the real part of γ for H-Sq, HOSq, and 3HO-Sq. In fact, only for HO-Sq is the imaginary part in excess of experimental error. This observation is consistent with the fact that this squaraine has the lowest energy absorption band of these three dyes and, hence, the greatest linear absorption at the measurement wavelengths (see Figure 2). For DFWM processes at wavelengths near resonance, theoretical models for conjugated π-electron systems predict that χ(3) is related to the energy gap, Ea, and the transition dipole moment, µ01, as follows:42
χ(3)(ω) )
Nµ014 (Ea - hω)3
(4)
in which N is the number of molecules per unit volume and hω is the incident photon energy. Thus, because the radiative decay rate constants of H-Sq, HO-Sq, and 3HO-Sq are essentially identical24 and proportional to the square of µ01, the χ(3) values of these squaraines should scale inversely with the cube of (Ea - hω). The absorption spectra given in Figure 2 and ref 24 show that (Ea - hω) for both 696 and 710 nm decreases in the order 3HO-Sq, H-Sq, and HO-Sq. Therefore, HO-Sq and 3HOSq are correctly predicted to have the highest and lowest measured values of γ, respectively, of these three dyes (see Tables 1 and 2). For Az-Sq, the wavelengths of 696 and 710 nm both lie well within the lowest energy absorption band. Thus, both groundand excited-state molecules may contribute to the observed DFWM signals. Therefore, for Az-Sq, the observed timeresolved DFWM signal might be predicted to contain a “fast”
component due to the coherent third-order susceptibility and a “slow” component resulting from a population grating.43 However, the time-resolved DFWM signals obtained for AzSq (Figure 3b) are highly symmetric and comparable in width to those obtained for the other three squaraines (see, for example, Figure 3a). Thus, one can conclude either that significant contributions to χ(3) could arise from an excited-state population grating only if it is extremely short-lived43 or that such contributions are not significant. Since the excited state of AzSq may be shorter lived than the probe pulse duration, in agreement with the absence of observed fluorescence from the lowest energy excited state of Az-Sq,24 it is not possible to distinguish between these two possibilities. It should be noted, however, that for Az-Sq the wavelengths of 696 and 710 nm are likely absorbed by a state localized on the azulene chromophore and at lower energy than the squaraine CT state (see Figure 2). Thus, we favor an interpretation that excludes significant contributions from an excited-state population grating. Thermal gratings, particularly for resonant processes in which local nonradiative relaxations produce local heating, could give rise to a contribution to the DFWM signal due to thermal nonlinearity.40 This thermal nonlinearity depends on the repetition rate and the pulse width of the incident pulses. The time response of the thermal nonlinearity is quite long, typically on the time scale of nanoseconds or even much longer.40 A contribution of thermal nonlinearity at long time was not observed in the temporal DFWM profiles of these squaraines. For nonlinear processes involving a two-photon absorption (i.e., two-photon-induced population grating), it has been shown that a fifth-order input intensity dependence is observed for the DFWM signal intensity.44 Thus, the third-order power dependence of the observed squaraine DFWM signals demonstrates that there are no two-photon resonant contributions to this thirdorder nonlinear optical response. As shown in Figures 4 and 5, the plots of the concentration dependence of χ(3) of the squaraines studied all exhibit a characteristic minimum at a low concentration. These results dictate that the sign of γx for the squaraine molecules is opposite that of γsol of the solvent molecules. From eq 2, for γx < 0 at relatively low squaraine concentrations, χ(3) should decrease due to the reduction in the magnitude of the term (Nsolγsol + Nxγx)2 as the squaraine concentration increases from zero to some characteristic concentration at which χ(3) becomes a minimum. At this squaraine concentration, χ(3) actually becomes zero if the contributions of Nsolγsol and Nxγx are of equal magnitude but opposite sign, and if there is no resonance contribution (γxi ) 0). For Az-Sq, as shown in Figure 2, the 696- and 710-nm wavelengths are absorbed in a one-photon absorption process. Thus, the minimum value of χ(3) is not zero due to the contribution of the Nxγxi term (see eq 2 and Figures 4b and 5b). In any case, at higher squaraine concentrations, Nxγx becomes larger in magnitude than Nsolγsol. This results in an increase in the overall magnitude of χ(3) as the squaraine concentration continues to increase. The negative sign of γx of some similar squaraines has been previously reported.28,30,45 For centrosymmetric molecules, such as these squaraines, the ground state has g symmetry, but the excited states may be u or g symmetry, corresponding to wave functions that are either odd or even with respect to inversion, respectively. For these molecules, a one-photon transition from the ground state is allowed only if the excited state is one of u symmetry. Two-photon transitions, on the other hand, are only allowed between states of the same parity. In general, at least three states, namely, the ground state, a one-photon-allowed
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Tran et al.
excited state, and a two-photon-allowed excited state, are needed to model the third-order nonlinear optical process.46 Under the formalism developed by Dirk et al.,28 the molecular third-order nonlinear susceptibility, γ, can be expressed as a summation of three different contributions:
γ ≈ γc + γn + γtp
(5)
in which γc ) -µ014D11, γn ) +µ012(∆µ01)2D111, and γtp ) +µ122µ012D121. For centrosymmetric squaraine molecules, no contribution from γn is expected. As a result, γ is governed by the contributions of two terms, γc and γtp. Since these terms have opposite signs, the sign and the magnitude of γ largely depend on the relative magnitudes of the transition moments between the ground state and the first excited state (µ01) and between the first excited state and the two-photon-allowed second excited state (µ12).28 As shown in Tables 1 and 2, the real components of γ of the squaraines studied are all negative relative to the solvent γ values, which, according to the literature, are positive. Furthermore, the γ values for these squaraines have quite large magnitudes. This suggests that the term γc provides a major contribution to the third-order nonlinear process. The less significant contribution of the term γtp is also supported by the results obtained from the power dependence study. As mentioned earlier, the intensities of the DFWM signals follow a third-order dependence upon the total input intensity, indicating the absence of a large contribution to the third-order nonlinear process arising from two-photon absorption. Also, since the squaraines studied are known to absorb strongly in the visible region,24 the relatively large values of γ obtained for these molecules are likely a result of the relatively large magnitudes of their transition dipole moments, µ01. The values of γ for these squaraines are as large as or larger than those reported by other methods.26-30 As noted in the discussion of eq 4, however, the values obtained in the present work are resonantly enhanced due to the proximity of the DFWM wavelengths investigated combined with the strong, one-photon visible absorption. It is interesting to note that second-harmonic generation studies on the squaraine dyes have been recently reported.47 For materials with centrosymmetric structures such as squaraines, no molecular contribution to a second-order optical nonlinearity would normally be expected. However, the second-harmonic generation (SHG) was detected from these molecules packed in monolayer Langmuir-Blodgett films. In these materials, the relatively large SHG was attributed to the intermolecular chargetransfer processes arising from noncentrosymmetric aggregations of the dye molecules. Since the absorption spectra of our samples, as shown in Figure 2, fail to indicate any evidence of aggregate formation of the squaraine dyes studied in either liquid solutions or polystyrene matrices, no significant contribution from a second-harmonic generation process would be expected to the nonlinear response observed for these samples. For the squaraines studied in these experiments, the values of γ, shown in Table 1, are comparable in magnitude to various γ tensor elements of other related squaraines, measured using the nonlinear electrooptical technique.26,48 Our results confirm that squaraines possess some of the highest cubic molecular hyperpolarizability coefficients among organic compounds investigated. Their cubic molecular hyperpolarizabilities are found to be at least an order of magnitude higher than those of similarly sized aromatic molecules. In addition, as shown in Figure 3, the DFWM signals observed essentially contain only an “instantaneous” response due to the coherent third-order susceptibility. These characteristics make them attractive third-
order nonlinear optical materials for ultrafast device applications, such as in optical computing. Acknowledgment. This research was supported by the INCOR grant program of the Center for Nonlinear Studies at Los Alamos National Laboratory and by the Committee on Research of the University of CaliforniasRiverside. D.S.M. gratefully acknowledges the Alexander von Humboldt Stiftung for support during the writing of this paper. Appendix To report the cubic (also called second) molecular hyperpolarizability coefficients in SI units, we make use of the relationships between esu and SI units found in Quantities, Units and Symbols in Physical Chemistry49 and the nonlinear dipole moment equation:
µ ) RE + 1/2βE2 + 1/6γE3 + ... as follows: term
SI unit
esu unit
relation to SI
µ R E
Cm C m2 V-1 V m-1
Fr cm 4π0 cm3 Fr cm-2/4π0
3.335 64 × 10-12 C m 1.112 65 × 10-16 C m2 V-1 2.997 924 58 × 104 V m-1
Note that 1 Franklin centimeter (Fr cm) is equivalent to a dipole moment of 1 D. From this, we can define the units of β and γ and their relations to SI as follows: term β γ
SI unit m3
V-2
C C m4 V-3
esu unit )2
Fr-1
relation to SI cm5
(4π0 (4π0)3 Fr-2 cm7
3.7114 × 10-21 C m3 V-2 1.237 99 × 10-25 C m4 V-3
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