J. Phys. Chem. 1993, 97, 2811-2883
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Recent Advances in Nonlinear Spectroscopy and Nonlinear Optical Materials Larry R. Dalton' and Linda S. Sapochak Department of Chemistry, University of Southern California, Los Angeles, California 90089- 1062
L u h g Yu Department of Chemistry, University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637 Received: September 23. 1992; I n Final Form: January 22, 1993
High-symmetry, r-electron, ladder oligomers and polymers, theoretically capable of supporting polarons and bipolarons, have been synthesized and examined by degenerate four wave mixing experiments employing picosecond and femtosecond pulses. The results of these experiments have been analyzed employing density matrix theory with explicit consideration of radiation field-matter interactions and of molecular relaxation processes consisting of (1) electron-hole recombination/exciton decay, (2) structural relaxation to gap states, and (3) decay of the populations of gap states. On the basis of correlation of observed effects with optical changes induced by chemical/electrochemicaldoping, we tentatively assign these gap states to bipolaron states and rationalize the ultrafast generation of these structurally-relaxed, bond-alternation defect states along the lines suggested by Su and Schrieffer (Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 5626). An alternate model, which also describes the temporal response, is structural relaxation of free excitons into self-trapped excitons followed by relaxation of the self-trapped excitons to the ground state asmggested by Kobayashi (Synth. Met. 1992, 49-50, 565). The femtosecond and picosecond structural relaxation times observed for these and many other r-electron materials are important both in a fundamental sense of understanding how ultrafast charge separation occurs and in terms of developing materials for nonlinear optical applications, e.g., development of materials for sensor protection and exploiting excited-state optical nonlinearities (Nature 1992, 359, 269).
Introduction High-symmetry, *-electron, oligomers and polymers have attracted considerable attention in the past two decades because of interesting electrical, magnetic, and optical properties.' The suggestion by Su and Schrieffer2that structurally-relaxed,charged solitons can be photogenerated within 100fs sparked considerable interest in the femtosecond spectroscopy of these materials.3d4 Fast structural relaxation, associated with strong electron-phonon coupling, is intriguing both in terms of providing insight into ultrafast charge-separation processes such as those observed in the photosynthetic relaxation centersof bacteria and green plants and in tems of potential nonlinear optical (photonic) applications. It is impossible in this paper to do justice to both a discussion of the femtosecond spectroscopy of *-electron systems and the relevance of these systems to the rapidly developing field of nonlinear optics. We will, however, attempt to provide an abbreviated review of these topics with emphasis on those aspects most relevant to our study of ladder materials and nonlinear optical applications. Hopefully, the references listed will provide the reader with an adequate discussion of aspects not covered here. The first point to be made is that the observation of temporal responses is not sufficient to understand the detailed nature of excited-state species. Temporal analysis can prove useful in identifying bimolecular recombination processes (detecting the deviation from first-order kinetics) and one-dimensionaldiffusion processes (from a square root time dependence) and in identifying thesymmetry of theexcited-state relaxation processes (two levels, three levels, etc.). However, to understand the nature of the species photogenerated in r-electron systems, it is useful to consider photoconductivity data, photoluminescence data and photoinduced EPR data and to correlate the data obtained from photoexcitation experiments with optical changes observed upon chemical and electrochemical doping. It will also prove useful in our discussion of photoexcitations in r-electron materials to divide materials into three classes: namely, (1) polyenes (such
as trans-polyacetylene) of symmetry -(A=A),,-, considered to be capable of supporting solitons,',* (2) poly(diacetylenes), where bulky substituents inhibit interchain interactions, and (3) heteroaromatic materials, which can be considered to be of symmetry -(A=B)"or -(A=B-B=A)"and to be capable of supporting polarons and/or bipolaron~.~~.6~ Although fast structural relaxation processes appear to be observed for all of these materials, they differ in terms of precise photoinduced absorption/bleaching phenomena and in terms of auxiliary properties such as photoconductivity,photoluminescence,etc. In considering the correlation of doping and photoexcitation experiments discussed in the following paragraphs, it is useful to keep in mind some basic differences: namely, in doping experiments only like charges are generated while in photoexcitation overall neutral configurations apply. Moreover, counterions present in doping experiments may, through the action of their pinning potentials, lead to effects beyond those considered in simple isolatedchain (independent electron/Huckel type) theories. Doping studies carried out in solution may more closely match the results of photoexcitation than doping studies carried out on solid-state materials. Although trans- and cis-polyacetylenes have been studied by a variety of nonlinear spectroscopic techniques, including third harmonic generation (THG)and degenerate four wave mixing (DFWM), most of the mechanistic investigations have focused upon employing pumpprobe experiments. An advantage of pumpprobe experiments is that analysisof the temporal behavior of photoinduced absorptions can be carried out without some of the theoretical complexity of methods such as DFWM which we shall discuss shortly. Since the original work of Orenstein and Baker,3 many workers have studied different aspects of the problem.'-64 After some initial disagreement, several features of photoinduced absorptionappear to be reasonablywell established. In trans-polyacetylene, an induced absorption at 0.45 eV is interpreted as arising from photogenerated solitons. This absorption appears at considerably lower energy than the dopantinduced peak observed at 0.1 eV, a discrepancy attributed to the
0022-3654/93/2091-2811%04.00/0 0 1993 American Chemical Society
2812 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993
effect of dopant counterions. A simultaneous photobleaching has been observed at 1.40eV and has been interpreted as partial suppression of the absorption from neutral solitons in pristine polyaceytene.16 Such suppression is not unreasonable for moderately large Coulomb interactions established for polyacetylenes by electron nuclear double res0nance.6~ The assignment of gap photoexcitations to charged soliton pairs is supported by the observation of IR-active modes characteristic of charged specie~.68+6~ However, the low-energy absorption survives into the longtime regime in contrast to what might be expected if the excitations remained on a single chain and thus experienced more opportunities for recombination.6 It is now generally accepted that a single-chain mechanism is not sufficient to explain photoinduced absorption phenomena in polyacetylene and that interchain charge separation occurs. As expected from the above results and from independent-electron theories, photoconductivity has been observed at the bandedge.27-30This photoconduction has both fast and slow componentsagain suggestingan interchain contribution.30 Unfortunately, photoinduced EPR studies,which could provide crucial informationconcerning concentrationsof excitons, neutral solitons, and polarons, have proven inconclusive.-’I--’-’ The analysis of the temporal response of pumpprobe experiments performed on polyacetylenes has largely focused upon charged soliton relaxation (recombination). Since the time scale of these processes is significantly greater than femtosecond pulse periods, only the molecular relaxation matrix needs be considered in solving the kinetic equations describing the system evolution under pulsed excitation. In particular, the effects of symmetry, i.e., one-dimensionaldiffusion has been considered in the analysis of temporal data in the picosecond regime. The second class of materials, poly(diacetylenes), typically contains large side groups separating very long conjugated chains. It is quite reasonable that these systems would exhibit different behavior than that of the polyaceytlenes. This is indeed the case; the optical absorption edge is dominated by a singlet exciton at approximately 2.0eV while photoconductivity sets in only at 2.5 eV and is observed to be considerably more anisotropic than in polya~etylene.-’~.35Charge recombination is on the order of picoseconds, and there is no evidence of a low-energy peak in many polydiacetylenes although photobleaching of the excitonic transition is observed.5333*43 Pratt et al.4i have studied poly(diacetylene) with small side groups and have suggested a lowenergy peak at approximately 0.25 eV. Although photoinduced absorption in poly(diacety1enes)has been interpreted in terms of bipolarons, there is no signature of polaron absorptions even at very short times. Moreover,K ~ h a y a s hhas i ~ madea ~ compelling case, based upon the analysis of pumpprobe and photoluminescence data, for structural relaxation of free excitons to selftrappcdexcitons followed by thedecay of the self-trappedexcitons. Kobayashi has also noted contributions from triplet excitons and instantaneous (less than 100-fs) processes giving rise to hole burning, coherent coupling between pump polarization and the probe pulse, Raman gain, inverse Raman scattering, and inducedphase modulation. The third class of materials, aromatic r-conjugated polymers, include materials such as polythiophene, polypyrrole, poly@phenylenevinylene), polyaniline, etc. which within the independent-electron (Su, Schrieffer, Heeger) theoretical framework’ can be treated as pseudopolyenes.65,66The symmetry of these materials can, at least theoretically, support polarons and bipolarons. Perhaps the most extensively studied materials have been polythiophene and poly(pphenyleneviny1ene) and their associated derivatives. Similar features are observed: namely, two broad subgap absorptions and bleaching in the interband region. For example, polythiophene shows absorptions at 0.45 and 1.25 eV; photoinduced IR activity at lower frequencies indicates that the associated defect is charged.4244 Although
Dalton et al. SCHEME I
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EPR measurements indicate the possible formation of polarons (species with spin = ‘/z), the induced subgap absorptions are qualitatively consistent with the formation of bipolarons. However, the energies and transition moments of the gap state transitions are not in quantitative agreement with predictions of independent-electron theories, i.e., the measured values sum to less than the gap energy and the measured peak intensities are comparable. This discrepancy between theory and experiment has been attributed to the limitations of independent-electron theories: namely, the neglect of electron Coulomb correlations and other interactions. Both photoconductivity and photoluminescence have been studied in several aromatic polymers.6 Photoconductivityappears to be somewhat similar to that of trampolyacetylene occurring at energies somewhat higher than the onset of interband absorption. Photoluminescence appears to result from a polar exciton, Le., a neutral species bound presumably by a combination of electron-phonon and electron-clectron Coulomb forces. The radiative decay is quite rapid; however, the very small quantum yield suggests that various additional nonradiative decay channels are likely important.4549 The absence of clear polaron signaturesin photogenerationexperiments remains a puzzle for quasi-one-dimensionaltheories. A possible explanation is transverse coupling reflecting a true three-dimensional nature of these materials; this argument would seemingly explain some of the differences observed between doping and photogeneration experiments. The effects of transversecoherence and disorder may also explain the result of Vardeny and coworkers,20 observed for polythiophene, that the number of photoinduced spins drops below the detection limit after improvement of structural order. Recently, Kobayashi-3 has carried out extensive femtosecond pumpprobe experiments and has interpreted the femtosecond and picosecond responses of polythiophenes and poly(2,5-thienylenevinylene) as arising from the structural relaxation of free excitons to self-trapped excitons. In our study of ladder oligomers and polymers (see Scheme I for a generic structure), we have carried out photoinduced EPR measurements including magnetic resonance imaging experim e n t ~ . ~Clearly, ~ . ~ ~ on longer time scales polarons are prod ~ c e d . However, ~ ~ , ~ ~ it is not clear that these measurements are relevant to our observation of photoexcitationsin the femtosecond and picosecond regimes. What is relevant is the apparent excellent correlation between solution doping studies and the results of photogeneration experiments as will be discussed shortly. Also, we have observed IR bands characteristic of charged species.68 Before we proceed to a detailed discussion of our nonlinear spectroscopicstudies of ladder materials, it is useful to comment on the relation of the above photoexcitation results to the field of nonlinear optics and photonics.
Spectroscopy and Nonlinear Optical Materials -
e
I
t
6”
Figure 1. Energy level diagram appropriate for the experimentsconsidered in this work. Thisdiagramillustrates thesimplest scheme for photoinduced absorption; namely, population of an absorbing excited state(s) b by intersystem crossing. Two induced transitions, characterized by applied field-molecule matrix elements VsBand V&, are shown. The molecular relaxation transitions are electron-hole (or exciton) recombination (denoted by subscripts eh), intersystem crossing or structural relaxation (denoted by sr), and relaxation from the gap state back to the ground state (denoted by bp).
Although assigning the precise nature of the structurallyrelaxed photoexcitation is no easy task, it is clear that all the *-electron systems mentioned thus far have the common feature of exhibiting ultrafast structural relaxation (Le., occurring on femtosecond to picosecond time scales). This structural relaxation is inherently a mechanism of optical nonlinearity as pointed out by Heeger and co-worker~.~OIn the simplest sense, the process can be represented schematically by Figure 1. To be concrete we have used notation consistent with bipolaron production; however, this diagram can also be used to describe the photogeneration of structurally-relaxed, self-trapped excitons. In the initial step of Figure 1, resonant interaction with an applied light field (a laser pulse) leads to generation of an electron-hole pair. In materials with extensive orbital interaction, the excited state is appropriately described as an exciton. Intersystem crossing can lead to population of states within the original bandgap which, in turn, can lead to absorption of energy of longer wavelength, Le., the materials become absorbing in a region of initial transparency. Both nonlinear absorption (imaginary component of the nonlinear susceptibility) and nonlinear index of refraction (real component of the nonlinear susceptibility) phenomena can be exploited for nonlinear optical applications. The application of sensor protection can exploit either of these components but is trivially visualized considering the phenomena of nonlinear absorption, Le., photoinduced absorption. The characteristics of a pulsed laser threat define material requirements. Obviously, the photoinduced absorption must turn on rapidly to avoid damage to the sensor which it is protecting. The photoinducedabsorption should have an oscillator strength greater than the original absorption and should turn off rapidly after the threat has passed (to minimize detector dead time). Returning to Figure 1, we note that a fast turn-on time requires a fast intersystem crossing rate and a fast cycle time requires that the populations of the states involved in photoinduced absorptionrelax relatively quickly. The efficiencyof photoinduced absorption depends critically upon the ratio of the intersystem crossing rate to the electron-hole recombination (exciton ground-state decay) rate. Since intersystemcrossing rates are frequently spin-forbiddenand since structural relaxation (rearrangement of the nuclear lattice) often accompaniessuch transitions, these processes have typically been predicted and observed to be slow. In fact, the observation of photoinduced absorption from such states typically has required pulses long compared to electron-hole recombination times so that the initial transition can be pumped many times permitting a small fraction of excitation to make its way to the gap states and be trapped by the long lifetimes of such states. Sensor protection utilizing photoinduced absorption provides an example of exploiting a resonant optical nonlinearity. One can also exploit nonresonant optical nonlinearity associated with
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The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2873 excited states as proposed and demonstrated by Garito and c o - w o r k e r ~ . ~ IHere, - ~ ~ one is making use of the real component of the excited-state optical nonlinearity, i.e., the nonlinear index of refraction. The essential experiment is that a pulse of a given wavelength is used to prepare an excited-state population and a light pulse of wavelength which is nonresonant is used to access the nonlinear index of refraction. The material requirements are similar to those of sensor protection. Fast turn-on and cycle times are necessary for high-speed optical switching and modulation achieved by exploiting the nonlinear index of refraction, n2. Our discussion also emphasizes that workers in the fields of nonlinear spectroscopy (mechanistic studies) and nonlinear optics have different objectives which have traditionally led to the utilization of different measurement techniques. Mechanistic studies have found pumpprobe experiments,which measure only the imaginary component of the optical nonlinearity at wavelengths removed from the pump frequency, to be most useful in characterizing excited-state dynamics. An obvious reason is that such experimentsexhibit minimal dependenceon pulse conditions and the photoinduced transition frequencies are signatures of the species generated. Unfortunately, such experiments do not provide information concerning the real component of the optical nonlinearity and it is this component which is often of greatest interest for development of nonlinear optical device~.~3*~8 Thus, techniques such as degenerate four wave mixing (DFWM), dynamic Kerr effect (DKE), and third harmonic generation (THG) have been the more frequent tools of the spectroscopist interested in nonlinear optical applications. It is obvious that the ideal situation is to simultaneously measure both the real and the imaginary components of the nonlinear susceptibility (employ phase-sensitive detection as in magnetic r e ~ o n a n c e ~ ~ and J ~ to ) carry out both four and two wave mixing experiments. Also, it is appropriate to consider modification of four wave mixing techniques to realize some of the intrinsic advantages of p u m p probe experiments. For example, for study of the evolution of excited-state populations it is useful to employ nondegenerate multiple wave mixing experiments; a simple example of this is shown in the top panel of Figure 2. This experiment is analogous to multidimensional experiments of magnetic resonance in that a prepulse proceeds the traditional pulse sequence and prepares the system in a specific state. Variation of the first pulse delay provides a convenient mapping of the dynamics of the prepared state. In addition to increased instrumental complexity, four wave mixing experiments can necessitate increased theoretical complexity in the analysis of experimental results. Traditionally, third-order susceptibilities of a sample of interest, [ x ( ~ ) ] have ,, been calculated by comparison with the phase conjugate signal from a reference sample such as CS2. Namely,
where ns and n, are the refractive indices of the sample and reference, h and Lrare the path lengths of the sample and reference, a,is the absorption coefficient of the sample, and C, and Crare the third-order susceptibilitycoefficientsof the sample and reference obtained by fitting the DFWM signal to a function of laser intensity, I, of the form A BI Clj with the last term the dominant term. Such analysis assumes that the optical nonlinearity of the sample is dominated by a single mechanism (e.g., purely electronic optical nonlinearity ideally from virtual excitation processes), thus the sample and reference exhibit the same temporal response (ideally, a single exponential). With this assumption the signal heights can be compared at zero delay time. However,a characteristicof DFWM signalsalready alluded to is that the signals are sensitive to all mechanisms which affect electronic and nuclear configurations, i.e., purely electronic effects,
+ +
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Dalton et al.
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 Pre-Preparation Pulse (w.) . U.
Preparation Pulse (on')
Preparation Pulse
Detection Pulse (on") . U .
Detection Pulse
photoinduced absorption (more than one transition matrix must be considered) involving (hyperbolic) secant pulses. Treatment of processes involving nuclear motion as well as purely electronic (and coupled electron-nuclear) motion are discussed within the framework of a phenomenological treatment. We would emphasize that application of the density matrix method to the analysis of optical experiments is not new; however, as in the case of modern magnetic resonance theoretical developments, our objective is to develop general and efficient numerical methods to analyze a significant range of experiments and materials, particularly we would like to systematicallyanalyze ?r-electron oligomers and polymers existing in condensed phases.
Instrumentation and Measurement Protocols
In the present work, we will focus upon degenerate four wave mixing (DFWM) and itsvariants. However, we would emphasize that these experiments can be viewed from a general schematic and theoretical framework. In particular, both two and four wave mixing experiments can be thought of as a preparation period where one or more pulses prepare the system in a specific manner, the system is then allowed to evolve under the influence of internal or molecular relaxation fields, and finally the state of Figure 2. Schematic representation of the crucial time periods in a onedimensional ( 7 ) pulse (two- or four-wave mixing) experiment (bottom the system is interrogated with a probe pulse during a detection figure) and in a two-dimensional (T, 7 ) pulse experiment (top figure). period (Figure2). In thecaseof four wave mixing, the preparation The experiments performed in this paper can be described by the bottom period consists of two pulses arriving at the system and producing figure where pulses of frequencies 01 = w2 arrive at the sample during an intensity grating which in turn produces an excited-state (or the preparation period and a pulse of frequency w3 (= W I = w2) arrives coherence) grating. Consistent with wave vector conservation, at the sample during the detection period. In a two-dimensional DFWM the probe pulse generatesa phase-conjugate signal which reflects experiment, a pulse of frequency u,I arrives at the sample during a preparation period; after a delay T, two pulses of frequency o, arrive at the nonlinear index of refraction (and in turn the excited-state the sample and create a grating; finally, after a decay 7 , a probe pulse electronic) grating. This signal contains both the real and of frequency w, arrives at the sample. imaginary components of the third-order susceptibility tensor. Separationof these components requires phase-sensitivedetection. structural relaxation phenomena, spatial diffusion, librational Two wave mixing experiments can normally be thought of as motion, thermal and acousticdiffusion effects, etc.74-78If different pumpprobe (PP) or dynamic Kerr effect (DKE) experiments effectsoccur with competitive rate constantsa more sophisticated which measure respectively the imaginary and real components analysis must be carried out. In the case at hand, not only do of the third-order susceptibility. DKE measurements are acexciton and structural relaxation events occur with comparable complished by placing crossed polarizers before and after the rate constants, these processescan occur on time scales comparable sample so that only the component of the probe beam rotated by to pulse periods, which necessitates the explicit treatment of the 90° is detected. In PP and DKE experiments, a single pulse applied radiation field-molecular electronic dipolar interaction. arrives at the sample during the preparation period. Initially, we74carried out this analysis within the framework of Since our femtosecond DFWM spectrometershave not been Feynman, Vernon, Hellwarth (Bloch-Feynman) theory;79howdescribed elsewhere,we provideschematic representations of these ever, the present case where a more complicated molecular energy instruments in Figures 3-6. These figures also illustrate the level scheme applies necessitates utilization of density matrix backward (Figure3) and forward (Figure6) mixing configurations theory. Like the development of advanced instrumentation, it is that we have employed in this work. Figure 3 illustrates our no simple matter to develop numerical theoretical methods which femtosecond system operating in the wavelength range 590-690 can be employed to analyze a large number of complex molecular nm (with most common operation at 630 nm). In this system a and experimental (complexpulse sequences)situations. However, Coherent Antares Nd:YAG laser is used to pump a Coherent such numerical methods have proven highly successfulin magnetic Satori dye laser and the pulses are subsequently amplified by resonance and are being increasingly utilized in analysis of optical Continuum RGA and PTA amplifiers. Figures 4-6 illustrate experiments. Again, we would emphasize that the application our femtosecond system operating in the wavelength region 700of fundamental density matrix concepts to the interpretation of 950 nm (with most common operation at 790 nm). Figure 4 magnetic resonance and optical experiments is not new and very readable introductions to basic concepts are readily a~ailable.~~-lO~ illustrates the low-power laser source which is a Coherent Mira Ti:Sapphire laser pumped by a Coherent Inova Argon Ion laser. In thesections that follow, we introducevarious instrumentation Figure 5 illustrates our homemade amplifier for this system which and measurement protocols developed and utilized in our utilizes a Continuum Nd:YAG laser as a laser amplifier. Both laboratory. Specifically, we discuss equipment used to effect of the above femtosecond systems are typically operated at a 20 70-200 fs pulse experiments in wavelength regions 590-690nm Hz repetition rate. The rationale for development of these two and 700-950 nm and picosecond pulse experiments in the systems is to obtainwavelength coverageover the importantvisible wavelength region 532-1064 nm. Techniquesfor effecting phaseand near-infrared spectral regions. sensitive detection are discussed as are techniques for determination of third-order susceptibility tensors (by variation of beam DFWM has also been accomplished with 1-25-ps pulses as polarizations) for amorphous materials. Femtosecond experihas been described el~ewhere.~&~8 In Figure 7,we illustrate one ments on both ladder oligomers and the commonly utilized CS2 of the schemes which we have used for achieving phase-sensitivereference standardarediscussedto illustratedifficultiesassociated detection in DFWM experimentsemploying picosecond pulses." with absolute measurements of third-order susceptibilities. This is an interferometric scheme permitting the measurement Next, we introducethe fundamentals of density matrix theory of phase shift of the DFWM signal from a sample of interest with relevant to analyzing two and four wave mixing experiments. respect to that of a reference sampleof known optical nonlinearity Particular attention is focused upon conditions relevant to (e.g., CS2). Representativeresults for a ladder chromophore are
The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2075
Spectroscopy and Nonlinear Optical Materials Signal Photodiode
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Coherent's Antares Nd:Yag Laser I
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Figure 3. Schematic representation of a DFWM system, employing femtosecond pulses of wavelengths in the range 590-690 nm. A backward mixing configuration is shown. Output typically 120-1 50 fs,
Coherent lnova 400 Ar Ion-Laser
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Figure 4. Schematic representation of the laser source used to achieve 70-200 fs width pulses in the wavelength region 700-950 nm. The output of this system is fed to the laser amplifier shown in Figure 5.
shown in Figure 8. In the lower part of this figure, the imaginary component of the optical nonlinearity (normalized to constant one-photonabsorption) is compared to optical absorptionchanges observed upon oxidativechemicaldoping. As discussed elsewhere, such comparisonsare useful in assigning various contributions to optical n~nlinearity.~~,~* In particular, correlated optical, conductivity, and EPR studies of doped materialsestablish reasonably well that the observed optical changes arise from bipolarons (or at least from charged, spinless species) and the good correlation of photoinduced and doping-induced optical changes supports the contention that the imaginary component of the third-order susceptibility derives from the bipolarons. Of course, photoconductivity studies and photoinduced EPR studies would be useful as discussed in the Introduction; unfortunately, no such data are available at this time. Other schemes for phasesensitivedetectionhave been discussed by Nunzi and CharraI" and by Prasad and co-~orkers.~05 We have also adopted the DKE configuration used by Prasadlos and note that such phase-sensitive detection minimizes artifacts associated with precise orthogonal alignment of the polarizers. It is important to understand the dependenceof observed phaseconjugate signals obtained in DFWM experiments upon experimental conditions such as the nature of the grating (e.g., 2k or Ak), pulse intensity, and beam polarizations. We and others have demonstrated in previous publications that the spatial tensorial natureof thirdsrder susceptibility tensors can bedefined by analysis of the dependence of the signal upon beam polarization~.~"~* We illustrate this feature in Figure 9. Note that the two gratings used to obtain the data shown in this figure sense different tensor componentsof the third-order susceptibility.The long time (greater than 1 ps) response of CS2 is dominated by rotationaldiffusion, and theobservationof different rate constants reflects the fact that the signal componentsare sensitive to different
Figure 5. Schematic representation of the laser amplifier used to amplify pulses from the laser source of Figure 4.
elements of the rotational diffusion tensor. A detailed analysis of the temporal response of the phase-conjugate signal for CS2 indicates that four processes contribute to the time evolution of the signal. Analysis of these processes (diffusive reorientation, translationalanisotropy and intermolecular distortion of molecular polarizability, coherently driven molecular librational motion, and purely electronic hyperpolarizability) has been discussed at length elsewhere,'@jand we simply note that our present analysis reproduces numbers already reported. We note that individuals using CS2 as an absolute reference standard for the calculation of magnitude of optical nonlinearity should be aware of these contributionsand how the relative importanceof each contribution depends upon pulse conditions. The dependence of the DFWM signal upon the nature of the grating is an established means of identifying contributions to optical nonlinearity from thermal and acoustic diffusion mechani~ms.~"~6Analysis of data influenced by both electronic and nuclear mechanisms can yield the relative signs of the optical nonlinearities associated with these
2876 The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 From
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h (nm) Figure 8. Representative data obtained employing the phase-sensitive detection system of Figure 7. These data are for a POL ladder oligomer (see synthetic Scheme I). The top figure shows the real component of the third-order Susceptibility (indicated by triangles) plotted as a function of measurement wavelength. Data has been normalized to a constant one-photon absorption by dividing by the linear absorption a. Also shown (indicated by a solid line) are optical changes observed by chemical oxidation of the oligomer by antimony pentachloride. As expected no correlation between these results is observed. The bottom figure shows the imaginary component of the third-order susceptibility (denoted by circles) plotted as a function of wavelength. The solid line reflects optical changes associated with thegenerationofbipolaronsby chemicaloxidation with antimony pentachloride. Note that correlation of the imaginary component (nonlinear absorption phenomena) with the chemicallyi n d u d optical changes suggesting that the photoinduced and chemical effects reflect the same specica (bipolarons). Finally, we note that within experimental error the real and imaginary componentsof the susceptibility are apparently related by the Kramers-Krocnig relationship (although enough data d m not exist for a meaningful transform).
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Figure 7. Schematic representation of phase-sensitive detection, accomplished employing Twyman-Green interferometers and a backward mixing geometry. A typical output is shown in the inset; specifically the responses for a carbon disulfide reference sample and a five-ring ladder (POL)type polymer is shown. A piezoelectric transducer (PZT) is used to vary the path length difference of the two arms. This scheme permits the phase shift batween reference and unknown samples to be measured accurately. This data, together with phase conjugate signal amplitude data, permits the real and imaginary components of the third-order susceptibility to be calculated.
different contributions. Analysis of the dependence of the phase conjugate signal upon pulse power (e.g., see Figure 10) is useful in identifyingmechanisms,in particular multiphotonmechanisms. =ry
For third-order materials,nonlinear susceptibilities,measured far from single- and multiplephoton resonanusand photoindud (nonlinear) absorptions, have proven too small for device application^.^^ When large optical nonlinearities have been reported,their origins are usually traced to a mechanisminvolving resonance enhancement. Thus, increasing attention is given to measurement protocols which permit definition of mechanisms of optical nonlinearity and to schemes for exploiting large optical
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Figure 9. Effect of beam polarizations upon experimental data using carbon disulfide and the experimental laser system described in Figures 4-6. These. gratings sense different components of the third-order susceptibility tensor. This is reflected by the different decay constants observed in the long time tails of these phase conjugate signals; this temporal region is dominated by rotationaldiffusion. Systematicvariation of beam polarizations permits extraction of both static and dynamic tensorial data.
nonlinearities deriving from photoexcitation (Le., population of excitedstates). Examplesof promisingresearchdirectionsinclude
Spectroscopy and Nonlinear Optical Materials
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The Journal of Physical Chemistry, Vol. 97, No. 12, 1993 2311 where the system Hamiltonian, H,is given by
H=Ho+Y; V=-pE The term HOis the time-independent Hamiltonian,and Vdescribes time-dependent interactions, e.g., with the applied radiation field. The experimentalobservable, the polarization, is the sum over the diagonal elements of the product of the dipole operator, M, and the density matrix
p(rjJ) = T r b j ~ ( t )+l The polarization so calculated can be substituted into the wave equation for electric fields given by PULSE INTENSITY (a.u.)
a2E/at2- C2a2E/aX2= -NpoqC2a2P/at2
Flpre 10. Experimental variation of phase conjugate signal amplitude with pulse intensity (squares). The solid line is a fit to the analytical theoretical expression presented in this paper. No significant deviation from third-order behavior is observed a t available power levels.
exploitationof coherent parametric mixing optical nonlinearities associated with excited states as suggested by Garito and ~0-~0rkers,71-~3 exploitation of saturable ab~orption,~8 and exploitation of photoinduced absorption/bleaching phenomena associated with structural relaxation p h e n ~ m e n a . ~ ~ In order to discuss the definition of mechanisms of optical nonlinearity by time-resolved nonlinear spectroscopictechniques, it is useful to draw an analogyE7v88to magnetic resonance techniques.80-86 For both magnetic resonance and optical techniques, we can describe the three most simple mechanisms. (1) Processes which do not involve generation of significant excited-state populations (the dominant diagonal elementsof the density matrix are those of the ground state) but rather the induction of phase coherence between states. Such coherent processes can lead to an exponential temporal decay following turnoff of the electromagnetic radiation pulse. The relaxation time is referred to as a phase or T2 relaxation time (spin-spin relaxation time in magnetic resonance). For optical experiments performed at ambient temperatures, such relaxation times often lie in the femtosecond regime and will be observed only for experimentsemploying very short pulses (
