7307
J. Phys. Chem. 1994,98, 7307-7312
Study of Resonant Third-Order Nonlinear Optical Susceptibilities by the Phase-Tuned Optically Heterodyned Kerr Gate Technique Maciek E. Orczyk, Jacek Swiatkiewicz, Guolin Huang,+ and Paras N. Prasad' Photonics Research Laboratory, State University of New York at Buffalo, Buffalo, New York 14214 Received: January 21, 1994; In Final Form: April 12, 1994"
This paper discusses the investigation of the complex third-order nonlinear optical susceptibilities to obtain spectroscopic information on one- and two-photon resonances. The merits of the new method of phase-tuned optically heterodyned femtosecond Kerr gate relative to the inner reference method are discussed in relation to obtaining the magnitudes and the signs of both the real and the imaginary components of the third-order optical susceptibility. The results presented here show that, as expected, near a one-photon resonance, the saturation effect leads to a negative imaginary component while near a two-photon resonance the sign of the imaginary component is positive.
Introduction The field of nonlinear optics is currently at the forefront of The interest in this field is derived from both the quest for a fundamental understanding as well as its importance for the technology of photonics. Most applications of nonlinear optics utilize a field (electric or optical) dependence of the refractive index (or bulk susceptibility) in a medium to produce effects leading to optical modulation and optical switching for processing of information. Near a resonance the refractive index of a material becomes complex and, therefore, the nonlinear susceptibility is complex. In addition, these resonances lead to an enhancementof the nonlinear optical susceptibility. Therefore, resonant nonlinear optics can provide useful information on the dynamics of one-photon as well as multiphoton resonances. Linear spectroscopy probes resonancesof a medium by directly investigating damping of an optical wave propagating in it. It, therefore, probes the imaginary component of the linear refractive index (or bulk susceptibility) which provides a part of the contribution to nonlinear optical processes. Therefore, if one uses a nonlinear optical technique whereby contributions of the real and the imaginary components of susceptibility can be separated, one can get valuable spectroscopic information regarding resonances and associated dynamics. As we discuss in this paper, the sign of the imaginary part of the nonlinear optical susceptibility also contains information on the nature of a resonance. In this paper, we provide a unified theoretical discussion of nonlinear optics and spectroscopy. We then focus on the thirdorder nonlinear optical processes, particularly those described by the nonlinear susceptibility x(3)(-w;w,-w,w) where all the input frequencies as well as the output frequency of optical waves are the same. This susceptibility describes the intensity dependence of the refractive index. This nonlinear susceptibility becomes complex and shows resonance enhancement both at one-photon and two-photon resonances. We discuss the experimental methods of concentration dependence of ~ ( 3 and ) our new technique of phase-tuned optically heterodyned femtosecond Kerr gate which can be used to separate the real and the imaginary parts of the susceptibility, ~ ( 3 ) . We compare their relative merits and show that the phase-sensitive optically heterodyned Kerr gate method has the advantage of being more reliable in evaluating the imaginary of x@). Furthermore, this method also yields the sign of the imaginary part t Present address: Department of Physics, Memphis State University, Memphis, TN 38152. Abstract published in Advance ACS Absrracrs, July 1, 1994.
0022-3654/94/2098-7307$04.50/0
of x ( ~which ) directly relates to the nature and the dynamics of electronic resonances. As an example, we investigate and discuss the influence of saturable one-photon and two-photon resonances on the sign of the imaginary part of third-order susceptibility. Experimental results are presented on a series of selected organic dyes. Nonlinear Optics and Spectroscopy: Theoretical Considerations Nonlinear optical effects are often described by a power expansion of the bulk polarization involving products of higher order nonlinear susceptibilities (hyperpolarizabilities x@))and the field, E233
+
P = x(l)*E x('):EE
+ x ( ~ ) ~ E +E E... = x c d E
(1)
In this equation the frequency dependence of the susceptibilities have been omitted for simplicity. In eq 1 , xem is field dependent and is given by
xCv= x ( l )+ x(').E
+ x ( ~ ) : E+E ...
(2)
Since the refractive index relates to the optical susceptibility at the same optical frequency as n2 = 1 47rxcn, we can write a similar power expansion as (2) for n whereby
+
n = no + n,E + n2EE +
(3)
In this equation no is the linear refractive index and nl and n2 are nonlinear refractive indices. In the case where one of the input fields is static, the coefficient nl describes the linear dependence of the refractive index on the electric field. It therefore relates to the linear electrooptic effect (susceptibility ~ ( ~ ) ( o ; w , OThe )). coefficient nz describes in this case the quadratic electrooptic effect and, therefore, relates to the third-order nonlinear susceptibility x(~)(-w;o,O,O).In the case of the presence of an opticalfieldonly(forwhichEEaZ) thethird termineq 3 becomes n2I where n2 now describes the intensity dependence of the refractive index. The n2 for an optical field relates to x(3)(-w; w,-u,w) described earlier. Near an electronic resonance the refractive index n of eq 3 becomes complex, i.e., n = nRc hI,. The imaginary part of describes the linear absorption (one-photon resonance). The imaginary part of n2 and X(~)(-W;W,-O,O) has been considered to relate to two-photon absorption. There has been relatively little thought devoted to the role of the imaginary part of nl (or r coefficient). In a recent paper we presented a theoretical discussion as well as experimental results of electroabsorption
+
0 1994 American Chemical Society
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7308 The Journal of Physical Chemistry. Vol. 98, No. 30, 1994
and linear electrooptic effect to discuss the correlation between the imaginary part of nl and linear electroabs~rption.~ Here we discuss that near both one-photon resonance and twophoton resonance, n2 and, therefore, ~ ( ~ ) ( - u ; w , - u , w ) ,have imaginary components. In the case of two-photon absorption, one has intensity-dependent enhanced absorption (or loss). Therefore, nrb, or &( - w;w, - w,w), is positive. For one-photon absorption, one encounters a saturation at higher intensity. This is also intensity-dependent absorption but with an opposite sign. Therefore, the sign n 2 1or ~ x l ~ ( w ; w-, w,w) will be negative at one-photon resonance. The determination of the sign of the imaginary component of ~ ( 3 can ) thus be interpreted in terms of the dominance of one- or two-photon resonance. Using a general definition of intensity dependence of the refractive index (or susceptibility),one can also definean effective ~ ( 3 which ) contains an excited-statepopulation term. Therefore, time-resolved studies of ~ ( 3 can ) provide valuable informationon the excited-state dynamics. The details of this theoretical description are provided el~ewhere.~.~ Here we briefly review this approach. For simplicity, we consider here only the resonant behavior of a centrosymmetric(vanishing material for which the material susceptibility can be described as (4) The frequency representation is dropped again for simplicity of notation with an understanding that, in the present context, the nonlinear susceptibility is x(3)(-u;w,-u,w). In eq 4, x:) stands for the n-th order susceptibility of the medium consisting of the molecules in their ground state, and is the linear susceptibility correspondingto excited-statemolecules, their densitybeing N. NO is the total density of molecules. For example, under one-photonabsorptionnconditionsand for excited speciesdecaying with a monomolecular relaxation rate, N can be expressed as5
di)
f-Z(t')e''/'
N ( t ) = NO~e-'/'
urczyK et ai.
t
1
(a)
@)
(C)
(d)
(0)
F i e 1. Various types of resonances and excited-state dynamics contributing to the incoherent ~ ( 3 nonlinearities. )
Im(x(3)J. For example, a direct two-photon resonance (case b) will yield a nonlinear incoherent response (time-delayed component) dependent on the ffith power of intensity? The imaginary part will be positivdand the transient absorption willshow induced absorption with an instantaneousrespons~.~ In thecase of relaxed sequentialabsorption(case e), incoherentnonlinear response may show a complicated temporal profile. Depending on whether the initially populated level (2), relaxed level (3), or subsequently pumped level (4) yield the largest changeof thelinear susceptibility ($) - x!) in eq 4 above) with respect to the ground state, the time dependence of the signal will be different. Assuming that the transition 1 2 can be saturated, the Im{x(3)Jwill be negative for short time delay, yet the transient absorption may show time delayed induced absorption. In order to developa satisfactoryunderstanding of the dynamics of excited states involved in determining the resonant third-order nonlinearity, one thus needs to study the spectral profile and the time dependenceof both the magnitudes and signs (i.e., the phase of the nonlinearity) of the real and the imaginary parts of ~ ( 3 . Discussed below are the techniques which can be used to obtain this information.
-
Methods To Determine the Real and the Imaginary Part of x(3)
dt'
where K is the linear absorption cross section, 7 is the relaxation time, and I is the light intensity. Since I is proportional to F, this contribution to the susceptibility is of the same order in the light intensity as the coherent thirdsrder ~ ( 3 term. ) The temporal behavior of N depends on the kinetics of formation of excited species and their decay. Thus, one can conceptually treat a resonant third-order process as containingtwo contributions: the coherent contribution (four-photon parametric mixing) coming from the instantaneous (i.e., nonresonant) third-order susceptibility, x('), and an incoherent resonant contribution due to the (x!) - 2'') term of eq 4, coming from the population of excited states. h e latter contribution will depend on factors like the laser pulse parameters, the experimental geometry and kinetic properties of the excited species. In the case of two-photon generated species, the population, N, is proportional to P. Therefore,the incoherent contributionderived from excited-state population will have the same electric field dependenceas a ~ ( 5 ) process.5.6 The time dependence of the effective x(3), therefore, through the incoherentterm can provide valuable informationon the dynamics of excited states. Some examples of the various types of resonances and excitedstate dynamics which may contribute to the incoherent nonlinearities and also yield a significant imaginary component are illustrated in the Figure 1. These represent two-, three-, or fourlevel systems which are coupled by a one-photon resonance, a direct two-photon resonance or a sequential two-photon absorption. These different resonances and their excited-state dynamics will manifest differently in the time and intensity dependence of the real and the imaginary parts of ~ ( 3 as ) well as in the signs of
From the point of view of nonlinear spectroscopy, it is important to gain straightforward information about the signs of the probed nonlinearities. Except the interferometric methods, the z-scad and the inner referencei techniques have been widely used to access thesignofthirdsrder susceptibilities. Thenewlydeveloped method of phase-tuned optically heterodyned Kerr gate698 provides the answer about the magnitudes and the signs of both the real and the imaginary parts of nonlinearity, and, additionally, it is time effective and can be easily implemented for solid as well as liquid samples. Below we concentrateon description of the inner reference and the phase-tuned optically heterodyned Kerr gate methods, which were applied in these studies. 1. Inner Reference(Concentration Dependence) Method. The inner reference method can be most suitably used in conjunction with DFWM or optical Kerr gate techniq~es.~v6.~ It relies on measuring the values of ~ ( 3 for ) a series of solutions containing the investigated molecules. For each concentration,the intensity of the signal is compared to that obtained for a reference sample (which can be the pure solvent itself) under identical conditions. An effective value of the third-order nonlinearityfor the solution, equal to the modulus of the complex susceptibility, responsible for the effect, is then calculated from the following equation assuming homodyne detection conditions:
dz,
In this equation S stands for the recorded signal intensity and the subscripts "eff" and "ref" for the investigated solution and the reference sample, respectively. For the investigatedcase of diluted
Resonant Third-Order Nonlinear Optical Susceptibilities solutions, the refractive indices ratio ncfl/nrcf= 1. R1 denotes the correction factor for the absorption of the beams in the sample. For solution measurements, the effectivesusceptibilitydetermined for the solution contains contribution from both the solute and the solvent. Therefore, Ixi;l obtained from the preceding equation may be expressed in the form
where x:/ is the real part of the solvent's third-order susceptibility (the imaginary part vanishes for a nonabsorbing medium), Nx and yx stand for the density and the molecular second hyperpolarizability of the investigated species, respectively, and Lis the local field correction factor approximated by the Lorentz expression3L = (n2 2)/3, where n is the refractive index of the solution at the working wavelength. Thus, having a set of Ix$jl values collected for different concentrations of the solution, one can, by means of a leastsquares fit to the above equation, derive the real part,,:y and the modulus, Irk"l, of the solute molecular second hyperpolarizability. The method is relatively easy to implement; however it is time demanding. It is also important that the absorption corrections be taken into account precisely since their actual magnitude may in some cases critically affect the determination of the sign of r:, 2. Phase-Tuned Optically Heterodyned Kerr Gate. The limitations of the above method are largely overcome by our recent method of phase-tuned optically heterodyned Kerr gate.6g8 This method takes advantage of selective (Le., optically phase tuned) enhancementof either the real or the imaginary component of the nonlinear response of the medium under study, followed by a polarization sensitive (optically heterodyned) detection. The method is equally suited for the study of solid and liquid (solutions) as well as thick or thin film samples. The details of the method are described elsewhere6 but the basic idea of the method is very intuitive and will be briefly sketched here. In the optical Kerr gate process the polarization state of the probe beam is analyzed.6JO In a classical homodyne version of the Kerr gate experiment a probe beam of a given polarization, El,, interacts with a stronger pump beam. As a result an orthogonal polarization componentt, El,, in the probe beam is created through optically induced birefringence and dichroism induced by the presence of the pumping beam. This component is then detected after passing the probe beam through a cross analyzer. The measured intensity contains thus contributions from both the real and the imaginary parts of nonlinearity. Heterodyne detection involves mixing of the OKG signal with a given fraction of a local oscillator signal, which may be the transmitted portion of the original probe itself. In this case the analyzer is rotated by some angle, 4, to admit a small contribution from the x component of the field. This component, practically equal to El, (neglecting small Kerr-induced contribution), constitutes a local oscillator field. The coupled-wave equation governing this nonlinear interaction predicts that the change of the amplitude of the probing field can be presented in the following form+
+
The boundary condition is El,(z=O) = 0 with the assumption that they component of the probe beam is created in the sample due to the presence of the pump beam and the action of the proper components of the nonlinear susceptibility tensor. In general, ~ ( 3 is) complex; therefore eq 8 will contain both real and imaginary terms. The relevant component of the generated field El, due to the imaginary part of ~ ( 3 is ) in phase with the local
The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7309 oscillator, El,, whereas the component due to the real part of ~ ( 3 ) is u/2 out of phase. Hence the amplitude of the y component of the Kerr signal at the sample exit can be presented as EI,(L) = is&) - €I&), where t is a function which in the simplest case will contain field amplitudes and proper components of ~ ( 3 ) tensor, and indices Re and Im indicate the real and the imaginary parts of the function In the presented technique, the phase relation between the nonlinear response signal and the local oscillator beam is established by the presence or absence of a phase retardation element in the probe beam in front of the analyzer. For this purpose a properly oriented quarter-wave plate with one principal axis parallel to the probe beam polarization, x, is optionally inserted in the signal path. The quarter-wave plate imposes a fixed u/2 phase bias between the x component (local oscillator) and they component (Kerr signal) of the field. In order to implement phase-sensitive (lock-in) detection one often modulates the pump beam intensity. Measuring at the chopping frequency, for small angles up to first order in 4 we arrive at the detected signal
I
Qc
-2E1,(0) &,(L)4
+ const
(9)
without u/2 phase bias, and
with the u/2phase biasimposed. In the former case thedetection favors the imaginary component of the signal, € I ~ while , in the is favored. latter case the real component, Performing the dependence of the OKG signal on the analyzer ~ angle 4 we obtain linear plots of the form Z = Z I ~ ( R ~ )const, the coefficient z being proportional either to the imaginary component, (I&), or to the real component, &&). Having the z coefficients for the investigated sample, z ; ~ ( ~and ~ ) for , the reference sample, z;,,,(~~),of known effective susceptibility, x : ~ )we , can readily determine the real and the imaginary parts of the third-order susceptibility of the sample, x : ~ )according , to
+
where R: stands for the correction factor for the attenuation of the beams in the sample due to absorption. As we have shown above, phase-tuned optically-heterodyned Kerr gate technique allows one for a selective enhancement and separate determination of either the real or the imaginary part of the nonlinear response of the investigated medium. The use of femtosecond pulses additionally allows for separation of the coherent instantaneousnonlinear optical response from the delayed incoherent signal.
Sign of the Imaginary Part of x(3) in Organic Dyes As an illustration to the above discussionn and the applicability of the mentioned techniques, we present here sfme of the results of measurements of the sign of xi2 in selected organic dyes. The determination of the sign of is important for many nonlinear optical applications, as, e.g., optical parametric oscillations and upconversion lasers. If one considers the propagation of two coupled waves in a third-order nonlinear medium, then, under the slowly varying envelope approximation, one can express the variation of one of the beams by the eq 8. Here we focus on the true coherent nonlinearity which is accounted for by the first term on the right-hand side of the equation. The attenuation of the beam can be expressed as
7310 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994
Orczyk et al.
The solution to this equation is ZI= Z,(z=O) exp[-aNLz], where the intensity-dependent nonlinearcoefficient of absorption reads
We note here that, in addition to the possible nonzero imaginary part of the linear susceptibility, the nonlinear coefficient a N L originates in third-order nonlinear processes and is proportional to xiz. Two such processes are of special interest here: twophoton resonance and saturable absorption. On qualitative ground, when, at higher beam intensities, two-photon absorption becomes operative an additional oscillator strength factor responsible for the relevant transition comes into play, which creates an additional contribution to the absorption coefficient (aNL> 0). On the other hand, saturable absorption relates to a decreased oscillator strength of the dominant transition and, hence, negative contribution to the absorption coefficient ( a N L < 0). Consequently, one can expect xi: > 0 in the conditions of dominant two-photon resonance, while for the caseof saturable one-photon resonance xi? < 0 should be Observed. The measurements of the sign of x ( ~is) selected organic dyes were performed using the above-discussed phase-tuned optically heterodyned Kerr gate and the inner reference techniques. For theexperiment 100-fspulsesat615 nmobtained fromanamplified colliding pulse mode-locked (CPM) system were used. A sixmirror cavity CPM dye laser following Valdmanis-Fock configuration11 was the source of a femtosecond pulse train. It was pumped by an all-line argon ion laser (Coherent Innova 90). This oscillator generates two beams consisting of 80-fs pulse train at the repetition rate of 86 MHz centered at 615 nm with about 120 pJ of energy per pulse. One of the beams is further amplified and employed in the experiment, the other being used for pulse diagnostics. The 1-kHz transistor-transistor logic output from the electronic synchronization module (QuantaRay SM- 1) triggers the tightly folded resonator (TFR) diode-pumped NdYLF solid-state laser (Spectra Physics TFR-1). The output of TFR, which delivers 6 ns pulse with about 200 pJ per pulse at 1 kHz repetition rate, was utilized as a pump source for a doublepass two-stage dye amplifier. The amplifier is capable of delivering 4 pJ per pulse at the 1-kHz repetition rate. The experimental arrangement implemented for the employed technique is shown in Figure 2. The laser beam is split into two portions at 20:l ratio. The stronger beam is used as a pump beam, 12,and the weaker beam, after passing through a variable delay line, RR, is used as a probe beam, 11. The pump beam passes through a chopper working at a frequency of 400 Hz to implement lock-in detection. Polarizers, PI and Pz, are placed in the paths of the probe and the pump beams, respectively,before the sample. Both beams are polarized at 45' with respect to each other. Another polarizer, P3, is placed in the path of the signal beam after the sample in front of the detector, PD. A quarterwave plate, QP, can be optionally insertedin front of the analyzer, P3, in order to provide a u/2 optical phase tuning between the two orthogonal components of the signal beam. Various modifications of this setup were used to perform different experiments, which included a classical optical Kerr gate with homodyne detection, transient absorption, and other modifications of polarization-sensitive two-wave mixing. The following dyes were chosen for the purpose of the experiment: malachite green, DTDCI, LD700, sulforhodamine 640, LC4200, canthaxanthin, and BTODT (2,5-bis[2-benzothiazoyl]-3,4-bis(oxydecyl)thiophene). The first five dyes are commercially available laser dyes (Exciton Chemicals Co., Inc.),
-1-.;.--[
1
-___-----____-------M3'c--J/, - ------i
Figure 2. Experimental setup implementedfor the phase-tuned optically heterodyned Kerr gate technique. Ml-M6: mirrors; L1, L2 lenses; PI-P3: polarizers; QP quarter-wave plate; H P half-wave plate; BS: beamsplitter; PD: photodetector; R R optical delay line.
canthaxanthinwas purchased from Fluka Chemicals, and BTODT was kindly supplied by the Wright-Patterson Air Force Laboratories, Polymer Branch. Methanol was the solvent for all the dyes but canthaxanthin for which THF was used. The linear absorption spectra of malachite green, DTDCI, and LD700 show that these compounds absorb strongly at the working wavelength of 615 nm (see Figure 3). Also, sulforhodamine 64Oexhibitsmeaningful absorption at this wavelengtth. These dyes are thus good one-photon saturable absorbers. On the other hand, LC4200 and BTODT do not show any linear absorption at 615 nm (Figure 3), and only two-photon resonance can be the operative absorption mechanism here. Although the absorption spectrum of canthaxanthin reveals an absorption tail reaching the working wavelength (Figure 3), the two-photon resonance strength was recently shown6 to dominate at this wavelength. Table 1 A,B summarizes the results obtained from the measurements of third-order molecular hyperpolarizabilities of the discussed dyes using the phase-tuned optically heterodyned Kerr gate. One can see here that the dependence of the signs of the imaginary parts of the nonlinearities is consistent with the preceding discussion, where we expect saturable one-photon absorbers to exhibit a negative imaginary part of the third-order nonlinearity, whereas two-photon-dominated resonant media to show a positive one. As an example illustrating this discussion, in Figure 4 we show the angle-of-heterodyning dependencies of the Kerr gate signal for the two cases of phase tune up to the response due to the imaginary and the real part of y of sulforhodamine640 molecules dissolved in methanol. The trace corresponding to the tune up to the signal originating in the real part of the nonlinearity of methanol is also displayed for comparison. (For nonabsorbing liquids, as methanol, the imaginary part of third-order response vanishes.) An inspection of eqs 10 and 11 indicates that the sign of the slope of the dependencies is opposite to the sign of the relevant ~ ( 3 )probed in a given experimental configuration. Thus, from Figure 4, one can conclude that the signs of both the imaginary and the real parts of 7 for sulforhodamine640 are negative, as shown in Table 1B. It is worth noticing that, if the detailed knowledge about the magnitude of nonlinearity is not needed, the information about its signonlycan be reached very straightforwardly,just by rotating the analyzing polarizer and observing the direction of the heterodyne-detectedsignal changes. The sign of the real part of the nonlinearity depends in a more complex way on the position of the excitation wavelength with respect to the essential energy levels manifold of the molecule. However, in the general case of a saturable absorber excited by the laser frequency, o,close to its one-photon resonance frequency a two-level model offers the simplest description. When the
Resonant Third-Order Nonlinear Optical Susceptibilities
The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7311
0.8
e 0
0.6
VI
e 4
0.4
0.2
0.0
400
700
600
500
Wavelength [nm] Figure 3. Linear absorptionspectra of the investigated dyes; (filled circles) LC4200, (filledtriangles) BTODT, (filled squares) canthaxanthin,(hollow circles) sulforhodamine640, (hollow triangles) malachite green, (hollow squares) LD700, (hollow diamonds) DTDCI. The arrow indicates the CPM
laser wavelength of 615 nm.
TABLE 1: (A) Complex Molecular Second Hyperpolarizabilities of Selected One-Photon Dyes. (B) Complex Molecular Hyperpolarizabiities of Selected Two-Photon Dyes (A) One-Photon Dyes malachite green DTDCI LD700 sulforhodamine640 ~ ~ ( l O - ~ ~ e s+140 u) +276 +30 -12 -126 -28 -48 ~ i ~ ( l O - ~ ~ e s-470 u) (B) Two-Photon Dyes LC4200 BTODT canthaxanthin -yn (1O-34esu) -6.2 -4.4 -310 (10-34Wu) +4 +4.7 +330 ground state, [I>, is of "gerade" symmetry and the excited state, 12>, is of 'ungerade" symmetry, and r12 denotes the resonance damping factor, the governing terms of the resonant part of ~ ( 3 ) (-o;w,-w,o) can be identified as:*J2
6
1
I
I
I
-1
0
1
'
I
I
n
? (d Y
a
z7
a
k
I al
a
a
-2
2
Angle of Heterodyne [des.] Figure 4. Angle of heterodyne, 4, dependence of the optically phase
On the other hand, if a two-photon transition to a state 13> of "gerade" symmetry dominates the resonant behavior of a molecule, in a four-level scheme one obtain^:^^^
A good knowledge of the transition energies, wij, and line widths, rij, is necessary
for detailed predictions of the resonant behavior of a dye. Careful examination of eq 14 enables us,ne'thertheless, to gain information about the sign of the real part of ~ ( 3 under ) the conditions of a single-photon resonant enhancement. In the case of malachite green, DTDCI, and LD700, the laser beam wavelength (A = 615 nm) used in the phase-tuned optically heterodyned Kerr gate experiment is on the high-energy side of the resonance (o> w12, see Figure 2), where eq 14 predicts a positive sign of the real part of x ( ~ in ) , agreement with Table 1A. The opposite holds for sulforhodamine 640 where Re(x(3)J< 0 for the excitation energy below one-photon resonance. The sign
tuned Kerr gate signal. (1) and (2) the real and the imaginary parts of the response from a solution of sulforhodamine 640 in methanol, respectively; (3) the real part of the response from the pure methanol solvent. The lines are the linear least-squares fits to the data points. of the real part of third-order nonlinearity can be also accessed employing the inner reference method. Figure 5 shows the dependence of the homodyne optical Kerr gate signal on the concentration of sulforhodamine 640 in methanol. A characteristic dip at low concentrations indicates that the sign of y m for sulforhodamine 640 molecules is opposite to that of y e for the solvent (methanol) molecules, Le., negative in this case. This becomes evident upon inspection of eq 7: for 7:"< 0, the !:x L4N,-y7 term decreases initially with increasing concentration of the investigated molecules, N,, and, at a certain value, it can bring the overall x!; to zero in the case of nonresonant media with 7;" = 0. In the situation discussed, y" # 0 (compare Table lA),the signal is always nonzero with only a local minimum in the range of diluted solutions.
+
Orczyk et al.
7312 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 I
0 ' 0
I
I
2
4
I
I
I
.
6
I
a
Concentration [IO-'
I
.
I
10
M/LI
Figure 5. Concentration depcndennce of lx(3)l for a methanol solution of sulforhodamine 640. The minimum at low concentrations is indicative of the negative sign for the real part of y of the solute.
Summary In conclusion, we havediscussed someexamples of the influence of various types of dynamics of excited states on third-order nonlinear susceptibility of organic materials. It was shown that important spectroscopic information on a material can be deduced from ~ ( 3 measurements, ) provided both the real and the imaginary parts of complex nonlinearity are determined. We describe the new techniqueof phase-tuned optically heterodyned femtosecond Kerr gate which can be used to separate the contributions from the real and the imaginary parts of ~ ( 3 and ) compare it with the inner reference method which utilizes concentrationdependence of ~ ( 3 ) . Heterodyned Kerr gate method is more reliable and provides more complete information (signs of both parts of ~ ( ~ 1 ) . Furthermore, it can be used to study solid samples.
Experimentally,we investigated the effect of the influence of saturable one-photon and two-photon resonances on the sign of the imaginarypart of third-order susceptibility of selected organic dyes. It was shown that these two types of resonance introduce opposite phase shifts and thus lead to opposite signs of the imaginary part of ~ ( 3 ) . Acknowledgment. This work was supported by the National Science Foundation,Solid State Chemistry Program, Grant No. DMR-90-22017, and in part by the US.Air Force Office of ScientificResearch, Contract No. F-49620-93-CW17. We thank Dr. Bruce Reinhardt of the Polymer Branch of AFB Wright Laboratory,Dayton, for providing us with the BTODT compound.
References and Notes (1) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Eflects in Molecules and Polymers; Wiley: New York, 1991. (2) Shcn, Y. R. The Principles ofNonlinear Optics;Wiley: New York, 1984. (3) Boyd, R. W. Nonlinear Optics; Academic Press: San Diego, 1992. (4) .Bradshaw, J.; Orczyk, M. E.; Zieba, J.; Rasad, P. N., accepted for publication in Nonlinear Optics (1994). (5) Pang, Y.; Samoc, M.; Prasad, P. N. J. Chem. Phys. 1991,94,52825290. (6) Orczyk, M.E.;Samoc, M.;Swiatkiewicz, J.; Rasad, P. N. J. Chem. Phys. 1993,98, 2524-2533. (7) Sheik-Bahae, M.;Said, A.; Wei, T. H.; Hagan, D. J.; Van Stryland, E.W. IEEE Quantum Electron. 1990,26, 760-771. (8) Orcn~M.E.:Samoc,M.:Swiattiewin. J.:Manickam.N.:TomoaiaCotid, M.;h&d, P. N. Appl. Phys. Lett. 1 M , 60,2837-2839. (9) Zhao,M.;Cui,Y.;Samoc,M.;Praaad,P.N.;Unroe,M.R.;Reinhardt, B. A. J. Chem. Phys. 1991, 95, 3991-4001. (10) Etchepare, J.; Grillon, G.; Muller, R.; Orszag, A. Opr. Commun. 1980,34,269-272. (1 1 ) Valdmanis, J. A.; Fork, R. L. IEEE J. Quantum Electron. 1986,22, 112-118. (12) Yang, L.;Doninville, R.; Wang, Q.2.;Ye, P. X.; Alfano, R. R.; Zamboni, R.;Taliani, C. Opt. Letr. 1992, 17, 323-325. ~~
~
