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Fundamentals of Nonlinear Spectroscopy

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  • III.A Introduction

    Non-linear polarizations are more readily generated when applying high electric field intensities to the sample.  The use of ultra short pulses serves two purposes: 1) the generation of non-linear polarizations and 2) higher time resolution in the measured signals.  The shorter the laser pulses, the higher the instantaneous electric field intensity at the pulse maximum.  Recent advances in ultrafast laser technology have spurred the development of lasers systems capable of generating short laser pulses (~20 fs FWHM) at a wide range of wavelengths from the UV through the visible to the IR.  

    In investigating non-dipolar solvation, a complex experimental setup is required to generate ultrashort pulses with the desired pulse duration and laser color necessary to produce and measure the non-linear signals.  However, more than complicated experimental equipment is needed for the successful collection of meaningful data.  Detailed information is required in selecting the appropriate system for study, with careful tuning of its properties to best probe the desired dynamics.  The trick though, is to still satisfy the experimental conditions required for use with time-domain, non-linear spectroscopic techniques.

    In this chapter, the experimental concerns that posed difficulties in measuring the solvation dynamics of non-polar systems are outlined.  Particular emphasis is placed on the requirements for collecting non-linear signals, whether in polar or non-polar liquids.  The experimental setups used to measure the data presented in this manuscript are then discussed, with importance placed on the laser beam geometry used to generate the non-linear signals.


    III.B System Considerations

                In the ideal world, the nonlinear response of any system can be observed and characterized.  Unfortunately, certain considerations must be accounted for before such responses can be observed in the laboratory.  For example, many systems do not generate a non-linear signal with significant intensity to be separated from the weak scattering of the excitation laser pulses.  Other technical concerns arise when considering experimental systems of study. 

    The selection of appropriate experimental conditions, involves the system (both probe and solvent), and the apparatus. In the course of studying non-dipolar solvation dynamics, several difficulties arose that required due consideration.  Figure III.1 displays just a subset of the potential probes investigated for use with the non-linear spectroscopic study of non-polar solvation.  The PERY molecule proved the most successful in satisfying the requirements outlined below.  The following list describes


    Figure III.1 Schematic of several of the potential probes considered for the non-linear spectroscopic investigation of non-polar solvation (Chapter 4) or for the investigation of vibrational effects on the non-linear signals (Chapter 5).  Solutes include: A) Coumarin 153, B) 9,10 dichloroanthracene, C) dimethyl-s-tetrazine, D) perylene, E) N,N, bis-dimethylphenyl 2,4,6,8, perylenetetracarbonyl diamide (PERY) F) Nile Blue G) Rhodamine 6G, H) BBOT,  I) Nile Red, and J) Rubrene.


    Figure 1


    many of the experimental aspects that hampered the collection of the non-linear signals for non-polar systems.

    1. Large Solubility
    2. Large Extinction
    3. Absorption Wavelengths
    4. No Reaction Dynamics
    5. Simple Probe Structure
    6. High Photo-Stability


    1) In some systems (e.g. biological systems) the chromophores are anchored in place by external constraints such as covalent bonds, but for solvation dynamics studies, the probe molecule must be dissolved in the liquid.  Laser dyes, which are often used as probe molecules for solvation studies,1-5 exhibit high solubilities in polar solvents.  Unfortunately, their solubility in non-polar solvents is limited due to the fact that these molecules are often ionic species.6 Therefore, the main requirement for the selection of a suitable probe for study required the identification of a chromophore that will dissolve in the non-polar solvents.  Organic chemists have well-established tricks for increasing solublilites.  The addition of solvent-attractive side groups increases solubilites without significantly affecting the absorption spectra of the probe molecules.  For example, the removal of the side dimethylphyenl groups  on the PERY probe molecule (Figure III.1) reduces the corresponding molecule to a near-zero solubility in non-polar solvents.  An alternate technique is to dissolve the chromophore at elevated temperatures for long durations (days) and then slowly cool to the desired temperature.  This trick can increase the solubilties for weakly soluble chromophores, especially large non-polar molecules often used for single molecule studies (e.g. terrylene or bisanthrene).

    2) Detected of the homodyne nonlinear signals measured in the experiments discussed in this manuscript requires the generation of signals with enough intensity to be observe observed over pulse scatter.  The intensity of induced non-linear polarizations is proportional to the fourth power of the transition dipole magnitude (Equation II.13).  Since the photon echo is a homodyne signal, where the square of the polarization is measured, the intensity of the signal is extremely sensitive to the extinction coefficient of the electronic transition.  Hence, potential probe molecules with large extinction coefficients are desired since they produce stronger, more easily measured signals than those with weaker absorbances.  Laser dye molecules6 and photosynthetic systems7 in bacteria and plants have been optimized either by nature or by man to exhibit large transition dipole magnitudes and are ideal systems for non-linear studies. 

    The use of other types of probe molecules requires careful consideration of the absorption cross-sections.  For comparison, photon echo signals were collected from both IR 144 and Nile Red laser dyes.  The maximum absorbance for the IR 144 laser dye in ethanol is 14.1 x 104 L mol-1 cm-1, while the maximum absorbance for Nile Red in ethanol is 2.8 x 104 L mol-1 cm-1.6 While the signals from IR 144 were easily measured,3 the Nile Red signals were barely observed.  Collecting homodyned photon echo signals for probe molecules with smaller absorbances requires great care.

    The polarization is also proportional to the concentration and hence the generated signal is proportional to the square of the concentration.  Although the signals are not nearly as sensitive to the concentration as to the extinction, increasing the solute concentrations can partially compensate for weak absorbances.  Care must be exercised, however, because increased concentrations can lead to aggregation.  Determining the optimized chromophore concentration must be considered with concentration dependent absorption spectra studies.

    3) The excitation frequencies for the non-polar systems are generally higher than those used for polar studies.  Though many potential probe molecules were identified with significant extinction and strong solubilities, they only absorbed in the UV, which was not attainable with the experimental setup described in Section III.C.  Additional complications could exist in UV studies since two-photon solvent signals may overwhelm the desired resonant signals.8 

    4) If the goal of the experiment is to study the dynamics of the bath, then both intramolecular and intermolecular dynamics associated with the probe molecule will adversely affect the collected signals.9 In the selection of potential probe molecules for solvation studies, chromophores that undergo such process are not desirable.  Potential interfering reactions include: i) excited state or ground isomerization,5 ii) excited state absorption,10,11 and iii) energy or electron transfer reactions.9

    5) Conformational disorder associated with floppy molecules may show up in the measured signals.12 Therefore, small, rigid probe molecules are desired.  Large floppy molecules may also exhibit large amplitude, low-frequency vibrational motions that may not be distinguishable from solvent contributions in the signals.13

    6) The photo-stability of the probe molecules is a potential problem.  For example, the vibrational bonds of the dimethyl-s-tetrazine molecule were not strong enough to withstand the repeated excitation produced by the laser pulses, and the molecules literally destroyed generation of any signals.  In experimental setups that may not introduce new sample fast enough between laser pulse interactions, this effect is particularly noticeable.  An translation cell was design specifically to reduce this effect in temperature dependent studies (Appendix C).

    III.C Experimental Setup and Data Analysis

    The signals were collected using either a commercial or a home-built laser system.  The details of the laser systems have been given elsewhere,14,15 but are briefly reviewed here for completeness.  The signals measured for the PERY and R6G data shown in Chapters 4 and 5 were collected on the commercial system, while the Nile Blue data, also in Chapter 5, were measured on the home built system. 

    The home built system (Figure III.2) consists of a mode-locked Ti:Sapphire laser pumped with ~4W of 532nm laser power from a solid state Nd:YVO4 laser (Coherent Verdi: V-5).  The resulting 87.8 MHz train of ~22fs pulses then seed an intra-cavity stretched regenerative amplifier16 creating a 1.46 kHz train of ~45-65 fs pulses centered near 800nm.  These amplified pulses were then compressed and converted to ~40 fs pulses in the visible region in an optical parametric amplifier (Coherent OPA 9450).17,18 The OPA presented in Figure III.2 is also home made, but was not used to collect any of the data presented in this manuscript.  Preliminary echo signals of PERY were measured with this OPA prior to replacing it with the coherent version.


    Figure III.2 Table layout of the homebuilt ultrafast system capable of generating 40 nJ/pulse of tunable laser pulses in the visible.  Setup was used with a Coherent commercial OPA, instead of the shown homemade OPA, to collect several data sets discussed in Chapter 5.  Abbreviations:  (CP) cube polarizer,  (NLC) non-linear crystal, (CD) cavity dumper, (SD) sapphire disk, and (TFP) thin film polarizer.


    Figure 2


    The commercial system (Figure III.3) consists of a Ti:Sapphire laser (Coherent Mira Seed) pumped with a large frame Ar+ ion laser (Coherent INNOVA 400).  The resulting 76 MHz train of ~40 fs pulses, centered at 790 nm are then stretched by a grating expander before seeding a regenerative amplifier (Coherent RegA 9050).  The amplified pulses are then compressed with an optical parametric amplifier (Coherent OPA 9450),17,18 used to create the final pulses at the desired center wavelength. 

    The pulse durations of both systems range from 38 to 46 fs intensity FWHM following pre-compensation of the pulses with a prism pair compressor (SF-10 glass).  Auto-correlation functions were measured with a 0.3 mm thick BBO crystal located at the sample position and the laser spectra were measured either with a home-built spectral analyzer or a commercial spectral analyzer (Ocean Optics S2000).

    The experimental setup for the 3PEPS and TG studies is shown in Figure III.4 and has been described previously in detail.3 In short, the three laser beams, with wave vectors: k1, k2 and k3, are arranged in an equilateral triangle geometry and are focused into the sample with a 20cm singlet lens.  The integrated echo profiles are then simultaneously measured in two different phase-matched directions, k=k3±(k1-k2), as a function of the coherence time, t, for fixed values of the population time, T (Figure III.5).  The two integrated echo signals are mirror images of each other, since they differ only in the sign of the pulse timing.  Consequently, the peak shift values are determined by measuring half of the span between the peak maxima of the signals in the two phase matched directions.  Determining the peak shift values in this manner improves the accuracy of the peak shift value by removing the uncertainty of determining the absolute


    Figure III.3 Optical layout of Coherent laser system used to collect much of the data presented in Chapters 4 and 5. 


     Figure III.3


    Figure III.4 Spatial configuration for collecting homodyne detected photon echo signals.  I) Spatial configuration for the experiments.  Three consecutive laser pulses with wave vectors: k1, k2 and k3 are focused in an inverted triangular geometry into the sample.  The resulting nonlinear signals are measured along the two phase matched directions k3+k2-k1 (B) and k3-k2-k1 (B’).  II) Photograph of non-linear signals generated for Rhodamine 6G in methanol.  The three bright spots in the center are the strong excitation pulses, and the outer nine spots correspond to the (two and three pulse) photon echo signals.  The signals collected in the 3PEPS study are the middle left and middle right spots.


    Figure 4


    value of t.  In the TG measurements, the signals were recorded as a function of T while t is set to zero.  

    As the integrated photon echo profiles generally peak at positive t values, only signals collected at positive coherence times are needed to determine the peak shift value from a specific phase-matched signal.  We use a seemingly complex method of measuring the signals to concentrate on collecting useful data effectively and quickly in order to minimize experimental variations (e.g. laser fluctuations and timing drift), that contribute to the total intensity of the signals.  We scan t at fixed values of T until t is 0, then both t and T are stepped such that the difference is constant.  In this collection scheme, negative t values correspond to the positive coherence time for the left signal (Figure III.4a) and positive t values correspond to the positive coherence time for the other signals (hence the symmetry of the two signals). 

    The uncertainties in the peak shift values are estimated at around ±300-500 attoseconds at a 95% confidence.  The peak shift values were determined by fitting the integrated echo signals to Gaussian functions at long population times (T>50fs) and fitting only the positive edges of the echo signals to Gaussian functions at earlier times as shown in Figure III.5.  As observed previously,15 the integrated echo signals exhibit a pronounced asymmetry at short population times that obscures the determination of the peak shifts values from full Gaussian fitting.  This asymmetry originates from the different time ordering in the experiment between negative and positive coherence times.3,19 Other fitting schemes, such as cubic and higher order polynomials and asymmetric Gaussian functions were used previously,15,20 but we found that partial Gaussian fitting at short times best describes the echo profiles.


    Figure III.5.  Integrated photon echo profiles for Nile Blue in acetonitrile, at 640 nm, in the two phase matching directions –k1+k2+k3 (filled circles) and k1-k2+k3 (open circles) are displayed with fits (solid lines) used to calculate the peak shift for fixed population times. (a) T=0 fs, (b) T=250 fs, (c) T=10 ps.  The peak shift values are 15.1 fs, 2.1 fs and 0.2 fs respectively.  Echo profiles are fit only to the positive edges with Gaussians at short times and to the entire profile with Gaussian functions at longer times (T>50 fs).


    Figure 5


    The solutes and the solvents were used without further purification.  The samples were flowed through either a 100 or 200 mm quartz cell with a peristaltic pump at 30 ml/minute to decrease local heating of the solvent.  All measurements were made at room temperature (20.5° C ± 0.5° C) and the sample concentrations were kept low (0.1-0.15 OD in a 200 mm cell) to reduce the possibility of aggregation and solute-solute interactions.  In the temperature dependent 3PEPS experiment in Chapter 5, the temperatures were controlled via a Neslab RTE-111 recirculator and measured with a home built thermocouple detector.  A large sample reservoir (6 liters) and increased pumping rate (50 ml/minute) were used to ensure that the sample temperatures remained within ±0.5 °C of the desired value. 


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