|Wachsmann-Hogiu, Sebastian: Vibronic coupling and ultrafast electron transfer studied by picosecond time-resolved resonance Raman and CARS spectroscopy |
The response of a medium to incident electromagnetic radiation is formulated in terms of induced macroscopic polarization. In the electric dipole approximation, the induced polarization may be written as a Taylor expansion on the strength of the applied electric field :
is here the linear susceptibility, and the quantities and are the second- and third-order nonlinear susceptibilities, respectively. is a second-rank tensor describing optical linear processes like (linear) absorption or refraction, is a third-rank tensor describing three-wave interactions (like Second Harmonic Generation SHG, sum-and difference-frequency generation), and is a fourth-rank tensor describing the four-wave interactions (four-wave mixing) like for example third-harmonic generation or Coherent Anti-Stokes Raman Scattering (CARS).
At this point it should be mentioned that the susceptibilities from Eq. 3.1 are bulk quantities. They are related to the microscopic quantities , and named polarizability, the first and second hyperpolarizability, respectively.
Although higher order terms in the expansion (3.1) could play a role if working with very high incident intensities, for the purpose of this thesis their contribution can be neglected.
When an electric field with strength f is applied to a molecule, an induced dipole moment µ is created:
Here, is the molecular polarizability. In the general case, the vectors µ and f do not coincide, and equation (3.2) can be rewritten in the following form:
where ij are the elements of the second rank polarizability tensor , defined in a space-fixed coordinate system (i,j=x,y,z). is a symmetrical tensor (ij=ji), and therefore has only six independent components. In this representation, the components of depend on
24the space orientation of the molecule but not on the direction of the applied electric field.
For each symmetrical tensor, a special set of Cartesian coordinates x‘, y‘, and z‘ exists with respect to which the tensor can be diagonalized. acquires then the following form:
In this case, the induced dipole is parallel to the external field vector.
The tensor is characterized with two invariants with respect to any reorientation of the molecule in space. These are the mean polarizability and the anisotropy :
It can be easily seen that vanishes for molecules possessing spherical polarizability.
If linearly polarized light is used to illuminate the sample, the scattered light may be depolarized to some extend, and contain radiation polarized either parallel (with intensity I() or perpendicular (with intensity I^) with respect to the polarization of the incident beam.
In every scattering experiment, for rectangular geometries and by using polarized light, the depolarization ratio = I(/ I^ is defined, which can be correlated with the two invariants like in the following:
It should be emphasized that alternative sets of coefficients for and should be used for experiments with unpolarized (natural) light and different experimental geometries.
Because vanishes for distortions belonging to non-fully symmetric species, the depolarization ratio becomes 3/4. On the other hand, reaches its minimum for totally symmetric vibrations. Thus, the depolarization ratio offer the possibility for examining the symmetry of vibrational transitions.
The intensity of Raman lines is given by the changes in molecular polarizability during vibrational transitions. The polarizability matrix element for a transition from a vibronic initial state i to a vibronic final state f is given in quantum mechanics by:
where are the vibronic wave functions of the initial and final states.
For small molecular vibrations, the polarizability of the molecule can be expanded in a Taylor series along the normal coordinates :
is here the polarizability tensor in an equilibrium non-perturbed state. All the derivatives are taken at the equilibrium geometry of the molecule.
25By combining Eq. (3.7) and (3.8) and neglecting the contribution from higher order terms, the following integral is obtained:
The first term in Eq. (3.9) is responsible for Rayleigh scattering, and the second term gives rise to Raman scattering, if two conditions are fulfilled (under non-resonant conditions):
(i) the polarizability derivative , i.e., the polarizability of the molecule must change during a particular vibrational transition, and
(ii) the integral . The latter condition requires that the vibrational quantum number of the transition differs only by 1 for Stokes Raman scattering and -1 for anti-Stokes Raman scattering.
The intensity of the i-th Stokes Raman line is given by :
where and are the intensity and frequency of the incident laser, respectively, is the number of molecules in the vibrational state i with the frequency , c is the speed of light, and the Planck constant. The term is the vibrational partition function and it is due to the contribution of hot bands, i.e. to transitions of the type , etc. to the Stokes Raman intensity and of the type , etc. for the anti-Stokes Raman intensity. Eq. 3.10 can be written in a simplified manner as:
where is the Raman cross-section defined as:
Fig. 3.1: Schema for Stokes (a) and anti-Stokes (b) Raman scattering. The vibrational levels are labeled with 0, 1, 2, ....
Anti-Stokes Raman scattering occurs only from excited vibrational levels, as shown in Fig. 3.1., and gives a direct indication of the population of the respective excited vibrational levels. Therefore, it is a very useful method in probing hot molecules.
If the excitation light frequency approaches to (pre-resonance condition) or equals (resonance condition) the frequency of an electronic transition of the molecule, the dependence of the molecular polarizability on the incident light frequency has to be considered. The molecular polarizability is than given by :
with being the energy of the -th vibrational state in the excited state, the energy of the -th vibrational state in the ground state, the energy of the incident light, a phenomenological damping factor, and the respective transition dipole moment operators. From Eq. (3.13) it can be seen that if , some components of the molecular polarizability are strongly enhanced, and thus, some Raman lines increase in intensity hundreds or even thousands of times.
Investigation of vibrational spectra of molecules in condensed matter by using spontaneous Raman scattering is often very difficult due to the high fluorescence background coming from the solute or solvent. Measuring transient species is even more complicated because of (i) the overlap of the ground state Raman spectra with spectra originating from the transients, and (ii) radiative emission which is, in most cases, very high compared with the Raman intensity. Subtraction of the contributions from the ground state and background, respectively, should be made in this case.
Another possibility is to use nonlinear coherent techniques like CARS and Coherent Stokes Raman Scattering (CSRS), which are, in special cases, very useful. Specifically, the advantage comes from (i) the nonlinear dependence of the generated signal on the laser power which implies that short pulses with high power are more efficient, and (ii) the possibility of fluorescence suppression owing from the coherent nature of the emitted signal.
In the classical picture, the spontaneous Raman scattering is seen as a modulation of the oscillating dipole moment ( is the molecular polarizability and E is the monochromatic radiation field) by a molecular vibration , exhibiting Stokes ( ) and anti-Stokes ( ) frequencies. Because the modulation is brought by the random-phased vibration of molecules, this emission is not coherent .
On the other hand, coherent Raman scattering comes from the forced molecular vibration generated by two different laser radiations E1 and E2 with the frequencies 1 and 2, respectively. The vibrational motion is generated in every molecule with a phase defined by the phase matching condition (Fig. 3.2). Consequently, Raman scattering due
27to this vibration forms a coherent radiation which propagates along the oscillating molecules. In this way, besides the incident frequencies 1 and 2, other frequencies 3=21-2 (for CARS) and 4=22-1 (for CSRS) are generated (see Fig. 3.2 and 3.3).
Fig. 3.2: Experimental schema of CARS and CSRS alignment (top) and the phase matching condition (bottom) for the wave vectors ki
If one of the incident electric fields has a fixed frequency , and the second field is spectrally very broad and centered around , the generated CARS signal contains more information than the spontaneous Raman spectrum. In addition to Raman frequencies and intensities, the third-order electronic hyperpolarizabilities can be derived.
Fig. 3.3: Schema of the CARS (left) and CSRS (right) generation
28Because the CARS spectrum occurs on a background coming from the electronic contribution of the solute and solvent (which reproduces the spectral distribution of the broad band dye laser), it is necessary to divide the spectral distribution of the CARS spectrum through the spectral distribution of the glass plate. Thus, the normalized CARS spectrum is obtained. In a neat medium, it results from the modulus squared of the overall (molecular) third order hyperpolarizability  during the Four-Wave-Mixing (FWM) process:
CARS is measured at the signal-frequency around . R and NR means here Raman resonance and non-resonance, respectively, is the Raman amplitude of the mode with the vibrational frequency and line width . The susceptibilities NR and are constants or - in the case of electronic resonance - they vary very slowly within the range of a Raman spectrum (depending on the detuning of the excitation frequencies from the comparatively broad electronic transitions ). In non-absorbing materials, such as most solvents used, laser frequencies are far from electronic resonance. In this case NR and are real valued quantities. Near electronic resonance they become complex values [5, 6].
The total coherent Raman four-wave mixing spectrum at for a solute (which may be also a short living transient) in a solution is given by:
Here is the relative concentration of the solute, (N is the number of molecules per cm3). It is obvious from the expression (3.14) and (3.15) that the CARS spectrum contains interference terms between different contributions. As a consequence an isolated vibrational resonance is characterized by a constant (electronic) background (amplitude A), by a positive or negative dispersion-like shaped (B) and by a Lorentzian shaped (C) contribution:
C is always positive in the nonresonant case, and can be positive or negative under electronic resonance. Depending on the sign of the parameter C , dips or peaks in the CARS spectrum can be observed. Dips (i. e. C < 0) are generated with complex parameters only, indicating electronic resonance.
Due to interference with the electronic background the vibrational frequencies coincide neither with the spectral position of the peaks nor with that of the dips in the CARS spectra (see Eq. 3.16). Thus, a fitting procedure as outlined in Chapter 4 is applied to get Raman frequencies, intensities and phases as well as the electronic contribution to the hyperpolarizability [5, 6].
The nonlinear polarization responsible for CARS is:
29where is the third order nonlinear susceptibility, which is a fourth rank tensor, most generally consisting of 81 components defined by:
where i, j, k, l=1, 2, 3 represent Cartesian coordinates.
In the case of isotropic media (like for example in liquids and gases) there are only 21 nonzero components. Among them, for symmetry reasons, only two can be independent. They are designated as and , corresponding to the polarization schemes:
\|[boxv ]\|\|[boxv ]\| \|[boxv ]\|\|[boxv ]\| and
\|[bottom]\| \|[boxv ]\|\|[boxv ]\| , respectively. represents here the linear polarization vector of radiation.
The polarization character of the CARS resonances, i.e., the CARS depolarization ratio can be expressed as :
Fig. 3.4: Scheme of polarization CARS. E1(1) and E2(2) are the planes of polarization of the laser radiations at 1 and 2. PR(3) and PNR(3) are the planes of Raman resonant and Raman non-resonant contributions. R and NR are the projections of the polarizations of PR(3) and PNR(3) on the transmission plane \|[PSgr ]\| of the polarizer.
with the mean polarizability as defined in Eq. 3.5a, and the antisymmetric and symmetric anisotropy (R in the superscript indicates Raman resonance). is the analogue of the depolarization ratio known from spontaneous Raman scattering and allows to distinguish qualitatively the symmetry of vibrational modes. This is possible because, in general, the vibrational polarization vectors and the polarization vector (NR indicate non resonance) of the electronic contribution of the third order susceptibility are all different.
can be obtained by measuring with parallel and perpendicular polarization of the two laser beams at and , respectively. However, a more convenient method often
used to determine its value is by using a polarization CARS scheme, as shown in Fig.3.4.
The polarization vectors of the laser radiation with the frequencies 1 and 2 were chosen to form an angle of =71.50 with each other. In this case, for (from Kleinmann symmetry) becomes 450 ( is the angle of polarization PNR of the non resonant electronic background - see Fig. 3.4). By tuning the angle \|[PSgr ]\| of the analyzer A to a position perpendicular to the plane of polarization of the Raman resonances, where the Raman resonances disappear in the CARS spectrum (i.e., for \|[PSgr ]\|=90\|[ogr ]\|- , where R=0), the depolarization ratios R of the vibrations R can be obtained using the expression [7, 8].
Another advantage of the polarization CARS scheme is that background-free spectra can be obtained, i.e., spectra free of the electronic background. Tuning the angle of the analyzer A perpendicular to the polarization plane of the nonresonant background PNR (i.e., for \|[PSgr ]\|=90\|[ogr ]\|-NR, where NR=0), the pure vibrational contributions can be seen, however, on a much lower signal level .
SHG has become, after the invention of pulsed laser systems, an important method used
Fig. 3.5: Scheme of SHG generation in a nonlinear crystal
for the extension of the wavelength range in a lot of applications. Schematically, this nonlinear process is illustrated in Fig. 3.5.
The nonlinear polarization responsible for SHG generation is:
where i, j, k=1, 2, 3 represent Cartesian coordinates. Symmetry considerations of the susceptibility tensor show that systems with macroscopic inversion symmetry posses only vanishing second-order coefficients . Consequently, SHG, like other three order processes, is restricted to :
(i) single crystals of certain crystal classes,
31(ii) surfaces, and
(iii) systems where the inversion symmetry is broken by an electrostatic field or a density gradient.
The intensity of the new generated radiation can be evaluated for incident collimated plane monochromatic waves with the following equation :
Here C is a constant, l is the crystal or interaction length, IL the intensity of the incident monochromatic wave, the mismatch between the SHG and fundamental wave vectors. For optimum SHG, perfect phase matching is required, allowing large interaction lengths. A more realistic condition is . Phase velocity dispersion effects ( with n-the refractive index, the frequency of the electromagnetic wave and c-the speed of light) makes efficient phase matching difficult. Using birefringent crystals, with polarization and orientation dependent refractive index, a long interaction length can be achieved, and high conversion efficiencies can be obtained. Assuming perfect phase matching, the following equation for the SHG conversion efficiency is obtained:
The dependence of on tanh2 function results in a slower increase of the conversion efficiency for conversion factors larger than 0.1.
For short pulses, the interaction length in nonlinear crystals is also limited by group velocity dispersion. The group delay (difference of the transit times) is :
with c the speed of light. In the case of picosecond pulses, (tp is the pulse duration) and these effects do not play any role in the conversion efficiency. In this limit, the new radiation obtained in the nonlinear process will have a slightly shortened duration by a factor of compared with the duration of the incident pulse of Gaussian shape.
Another method used to extend the wavelength range for spectroscopy is stimulated Raman scattering. This effect, governed by the susceptibility, occurs at high
Fig.3.6: Schematic representation of the spontaneous (top) and stimulated (bottom) Raman scattering as a quantum process from the initial state i to the final state f.
incident intensities. It is a partially degenerate four-wave mixing process, where the two non-degenerate components are the laser frequency and a Stokes (or anti-Stokes) Raman line. A theoretical treatement of the SRS has been given by Bloembergen in 1967 . A schematic diagram of the process is presented in Fig. 3.6.
According to , a light wave at frequency (the Stokes Raman wave) is incident on the material system simultaneously with a light wave at (the incident laser wave). A quantum is added to the wave , which thus becomes amplified, while the incident light beam looses a quantum and the material system is excited by a quantum . The two level system involved in the stimulated Raman emission is described by an amplitude and a relative population change, equivalent to the off-diagonal and diagonal elements of the density matrix . Under stationary conditions, an exponential amplification of an initial Stokes intensity IS(0) can be derived:
where is the amplified Stokes intensity after passing the length z, and is the gain coefficient which includes the Raman polarizability, the dephasing time of the Raman line and the incident laser intensity.
For laser intensities of 109 W/cm2, which are normally achieved for focused picosecond pulses, a gain coefficient cm-1 is obtained.
By using ultrashort laser pulses having a duration comparable with the Raman dephasing time, the interaction is less effective and deviations from Eq. (3.21) occur. In this case, higher pump intensities are required to obtain a good gain coefficient.
33It should be pointed out that by using ultrashort laser pulses for generating SRS, the Raman amplification is often accompanied by other competing nonlinear effects like self-focusing and self-phase modulation.
Intense stimulated Raman emission has been observed in various liquids, liquid mixtures and crystals [13-16], with conversion efficiencies up to 50%. Even higher conversion efficiencies and a better pulse quality were obtained for several high pressure gases for both vibrational and rotational transitions [17, 18].
A frequently used method in the time-resolved spectroscopy for investigating transient species is the pump-probe method. A pump pulse with high energy density interacts with the molecule under investigation and excites it to a higher state. The new state is a non-equilibrium one and will tend to achieve the potential energy minimum by relaxation. A second probe pulse of low energy density tuned to a wavelength so that it will be able to monitor the molecule in the new state, is spatially overlapped with the pump pulse with an adjustable delay time. By changing the delay between the pump and probe, one can monitor the changes taking place in the molecule. The characteristic spectra obtained from these transient species give specific information about the dynamics and changes in the molecular structure during the transition. The delay between the two pulses can be easily changed by varying the optical path for one of the two pulses with the help of delay lines which can achieve 1 µm resolution. For example, in air the light waves need ca. 3.3 ps to propagate through 1 mm and ca. 3.3 fs through 1 µm.
The excitation of the sample molecules with ultrashort (femtosecond) pump pulses creates coherent vibrational excitation of the Franck-Condon-active modes which have a period of vibration comparable or longer than the duration of the laser pulse. The delayed probing pulse monitor the subsequent dynamics of these vibrational modes. If the pump laser is resonant to an optically-allowed electronic transition in the molecule, coherence is generated in both ground and excited state vibrational manifolds. The theoretical treatment of the coherent effects visible in femtosecond pump-probe experiments has been done by Pollard et. al. in a series of papers at the beginning of the 90‘s [19-22]. In these papers, the pump-probe experiments are described in terms of time-dependent overlap of bra and ket wave-packets generated by the pump and probe pulses, respectively [19-21]. Experimentally, the coherent effects are seen as oscillations in time of the measured spectroscopic property (for example transient absorption). These oscillations decay, in solutions, on a fs to ps time scale, due to anharmonic coupling to other vibrational modes.
In experiments with pulses of picosecond duration, coherent effects do not play a major role, and for the interpretation of the pump-probe time-dependent results an incoherent treatment under the form of rate equations can be used, as presented in the following.
Taking the cross-correlation between the pump and the probe lasers as , and the time-evolution of the system , it is possible to write the measured response function of the system in the form of a convolution function:
If the time scale of the process under investigation is much larger than the pulse duration, the laser pulses can be approximated with -functions. In this case, the time response of the system can be simplified to a sum of exponential functions:
In particular, the measurement procedure for time-resolved resonance Raman and CARS spectra of transient species or excited states follows the scheme:
(i) excitation of the molecule in the absorption band for preparation of the transients,
(ii) probing of the transients by resonance Raman or CARS, i.e., the probe laser wavelength is chosen to match an absorption band of the respective transient.
The time resolution in the experiment is, for picosecond pulses, limited only by the duration of the laser pulses, i.e., by their cross-correlation time. Group velocity dispersion of the laser pulses does not play a role in this case.
If a laser active medium is excited and the laser medium is placed between two parallel mirrors, a set of frequencies will oscillate depending on the gain bandwidth and the loss in the cavity. Transversal and longitudinal modes can be observed as field distribution normal to the resonator axis and an infinite set of eigenfrequencies separated in frequency by c/2L, respectively, where L is the optical length of the cavity and c the speed of light. If the longitudinal modes are somehow forced to maintain a fixed phase and amplitude relationship, the laser output will consist of trains of regularly spaced pulses, which are called mode-locked pulses. These pulses have a temporal width which is approximately equal to the reciprocal of the spectral bandwidth, and a temporal periodicity equal to 2L/c. To give an example, for a resonator length of 2 m, pulses of about 100 ps duration will be generated with a periodicity of 76 MHz. These values are very similar with the parameter values of the Nd:YAG mode-locked laser used for the experiments carried out in our laboratory.
Two methods are used for mode-locking: (i) active mode-locking, which means sinusoidal modulation of phase or loss by active elements (for example acousto-optical crystals) introduced into the optical cavity that are driven at the frequency corresponding to the mode spacing, and (ii) passive mode-locking, where saturable absorbing elements (dyes or even gases and solids) are inserted in the cavity.
A very successful method used for a long time for generation of tunable picosecond pulses is the synchronously mode-locking of dye lasers. Synchronous mode-locking is a method of actively mode-locking, where mode-locking is achieved by pumping with a mode-locked laser . Because the modulation of the gain medium by the short pumping pulse provides the coupling mechanism, it is very important to carefully match the cavity lengths of the pump and dye lasers. In this way, the gain of the dye laser is modulated at a cavity round trip. The rise time of the gain modulation is approximately equal with the time integral of the pump pulse, and is thus more effective in mode-locking than the sinusoidal loss modulation.
The laser close to threshold saturation switches the gain off, and consequently, the pulse duration of the dye pulse will be much shorter than that of the pump laser.
In fact, the first observation of synchronous mode-locking in Rhodamine-6G was made by Soffer et al. in 1968  by using a mode-locked Nd:glass laser as an optical pump. The same procedure was later used by numerous groups (see for example ) to produce tunable picosecond pulses from dye lasers, and has also been used for the experiments presented in this thesis.
A continuous-wave Nd:YAG laser (Quantronix 4216) was mode-locked by an acousto-optical loss modulator, giving rise to pulses of 1064 nm with a duration of about 100 ps - measured with a fast photodiode - at a repetition rate of 76 MHz. These pulses were further frequency doubled in a KTP crystall to 532 nm and used for synchronously pumping a dye laser. Tunable dye laser pulses with energies up to 1 nJ/pulse were generated with the same repetition rate as the pumping laser. The duration of these pulses was measured with a procedure described in the next paragraph.
In every time-resolved experiment it is important to know the duration of the laser pulses. For the experiments carried out here, the auto-correlation technique is applied.
The laser radiation is split into two beams of equal intensity, with the help of a beam-splitter. The two beams take different optical paths relative to each other, before they are focused onto a nonlinear crystal under phase-matching conditions. By nonlinear mixing of the two radiations, the second harmonic is generated. The time evolution of the new frequency is the correlation function of the two incident radiations:
The SHG signal can be monitored on an oscilloscope. By calibrating the divisions on the oscilloscope, it is possible to determine the correlation width defined as the Full Width at Half Maximum (FWHM). The real pulse duration can be further obtained from Eq. (3.24), with the pulse shape characteristic in each particular experiment. For example, in the case of Gaussian pulses, the pulse duration is given by the correlation width divided by the factor 1.44 .
The duration of the pulses obtained in our experiment is 1.5-8 ps, depending on the mismatch between the cavities of the Nd:YAG and dye laser lengths.
The picosecond pulses obtained from a synchronously pumped dye laser do not exceed 1 nJ/pulse in energy. Instead, pulses up to 200 µJ are required in our experiment, and this demands for amplification of these pulses.
The dye amplifier build in our laboratory has been realized according to the design made by Perry et al.  and Dolce et al. . It consists of three dye cells of 1, 4 and 10 mm length in the first, second and third stage, respectively, pumped by the second harmonic of a 50 Hz Nd:YAG regenerative amplifier (Continuum RGA-50).
The dye concentrations were approximately 1x10-3, 2.5x10-4 and 1x10-4 M/l, and the pumping beam diameters approximately 0.5, 3 and 8 mm in the first, second and third stage, respectively. Variable delay lines composed of prisms mounted on translation stages are used to maintain precise timing of the pump pulse and the dye pulse in each stage. By carefully choosing the dye in each cell, the amplifier is tunable from 575 to 610 nm, when using rhodamine 6G for the seed laser, and from 680 to 740 nm, when using pyridine2 in the seed laser. To reduce the contribution of Amplified Spontaneous Emission (ASE) to the amplified signal, in the third stage a dye has been used which has the maximum of absorption band shorter than that of the dyes in the first and second stages. For example, to obtain a maximum of amplification at 600 nm with an ASE contribution lower that 5%, sulphorhodamine 101 was used in the first and second stages, and sulphorhodamine B in the third stage. The total amplification is about 2x105, which is distributed over the individual stages as follows: 1x103 in the first, 33 in the second and 6 in the last stage.
Picosecond pulses up to 200 µJ energy per pulse are obtained after amplification.
Fig. 3.7: Picosecond time-resolved CARS spectrometer. DA is a three-stage dye amplifier, FR is a Fresnel romb, P is polarizer, F symbolized filter and CCD is a Charge Coupled Device.
37The experimental apparatus used for CARS measurements is presented in Fig. 3.7. The
frequency doubled radiation of about 100 ps time duration at 532 nm originating from the mode locked Nd:YAG laser is used for synchronously pumping a dye laser, which delivers pulses of 1.5-8 ps with 76 MHz repetition rate at 710 nm (with pyridine2 as laser dye). These pulses were amplified up to 200 µJ by the three stage dye amplifier described in the preceding paragraph.
For photoexcitation of the DPH sample, either pulses of the frequency doubled dye laser radiation or the third harmonic of the regenerative amplifier were used. For CARS generation, a small portion (5 %) of the dye laser pulse was mixed with the radiation of a broad band dye laser which was directly pumped by the second harmonic of the regenerative amplifier. Broad band CARS signals obtained in this way were recorded, after spatial filtering and dispersion by a polychromator (SpectraPro 275, focal length 275 mm, with a 2400 l/mm or with a 1200 l/mm grating), with a liquid nitrogen cooled CCD-camera (Spectroscopy and Imaging, LN/CCD 1100PB/UVAR CCD, backilluminated).
Spectra were recorded without and with additional UV radiation, with different delays between UV excitation and CARS probing. In addition, CARS spectra of a thin (0.5 mm) glass plate were recorded. In the frequency range 1000 cm-1 - 2000 cm-1 this CARS spectrum is dominated by the constant electronic contribution of glass . Consequently, it reproduces the spectral distribution of the broad band dye laser. All the spectra are normalized to this reference.
The investigations were carried out with parallel polarization between all beams. For determination of frequencies of very broad vibrational bands and of the depolarization ratios of the CARS resonances, the polarization-sensitive CARS scheme was applied, as described in 22.214.171.124 [7, 8, 28], to suppress interference with the electronic background in the spectra. For an improved suppression of the Raman-nonresonant background, we used an additional phase compensator (/4 plate) in front of the analyser to minimize residual ellipticity of PNR.
Both stationary resonance Raman scattering, as well as time-resolved anti-Stokes resonance Raman measurements, were carried out with a spectrometer based on the picosecond dye laser system used for the CARS measurements (see Fig. 3.8). The difference is that the dye used in the synchronously pumped dye laser was rhodamine 6G, which provides pulses at 606 nm with spectral width of 15-20 cm-1 (FWHM) and 3.2 ps duration. The pulses were amplified by the three stage dye amplifier described in paragraph 126.96.36.199, resulting in an energy per pulse of approximately 150 µJ. Pulses of 10 µJ were generated at 303 nm by frequency doubling in a BBO crystal of 2 mm length. The signal detection was the same as for the CARS set-up, with the difference that for Raman spectra with 606 nm excitation a notch filter was placed in front of the polychromator to reduce stray light originating from the laser beam. Raman spectra with 303 nm excitation were recorded without additional spectral filtering. The spectral resolution is mainly limited by the spectral width of the probe pulse (15-20 cm-1 for 606 nm and 20-30 cm-1 for 303 nm excitation, respectively).
Stationary Stokes Raman spectra were recorded in quartz cells (10x10 mm2) without stirring. Time-resolved Raman spectra were recorded in free flowing jets of 0.1 mm thickness (for ethanol and propylene carbonate solutions) or of 0.3 mm thickness for the
38glycerol triacetine solution. The energy of the probe pulses used for recording the Raman spectra of B-30 solutions was below 10 µJ. In order to avoid multiple interaction
Fig. 3.8: Picosecond time-resolved Raman spectrometer. DA is a three-stage dye amplifier, FR a Fresnel romb, P polarizer, F filter and CCD is a Charge Coupled Device. SRS is the cell for new frequency generation by Stimulated Raman Scattering .
with individual molecules, the pump beam was focused onto the sample by a cylindrical lens resulting in a relatively large irradiated area of about 0.15x1 mm2. At tenfold lower energies of the probing pulses (<1 µJ) we checked possible changes in the Raman pattern compared to the higher energy level. No such changes were observed, confirming that contributions from populated excited electronic states were negligible. Spectra were accumulated up to 200 seconds.
Measurements of the Raman spectra in the excited singlet state of B-30 need the extension of the pump and probe wavelenghts. This was realized by using the SRS effect. Using methane under high-pressure (60 bar), stable laser emission shifted with 2917 cm-1 by the first Stokes component of the methane gas was obtained. A conversion of about 50% from the 600 nm incident laser to the 740 nm SRS output has been achieved. This radiation was further frequency doubled in a BBO crystal of 2 mm length. In this way, pulses of about 5 µJ were generated at 370 nm.
39The time resolution in the experiment was measured with the cross-correlation method. This method is similar with the auto-correlation method which was described in paragraph 188.8.131.52. The difference is that by the cross-correlation method two pulses of different colors are mixed resulting in a signal which depends on the time-delay between the respective pulses.
Cross-correlation traces of pulses of different wavelengths were measured by recording the time-resolved stimulated emission from a solution of sulforhodamine 101 in methanol excited by the 303 nm pulses. The small signal amplification -A = log(T/T0) of the probe pulse at 606 nm was measured as a function of delay time relative to the pump (T, T0: sample transmission with and without excitation, respectively). By differentiating (-A), a cross-correlation width (FWHM) of about 4.9 ps has been measured. The pulse duration and the zero delay between the pump and probe pulses have been optimized by sum-frequency mixing and by optical Kerr effect in CS2 (relaxation time ca. 1 ps).
The cross-correlation recorded by amplification in sulphorhodamine solution and by sum-frequency mixing in a KDP crystal are shown in Fig. 3.9.
Fig. 3.9: Cross-correlation between the pump and probe laser. Left: amplification in sulphorhodamine solution (top) and diff(-A) (bottom). Right: sum frequency mixing signal. Solid lines represent the fit with Gaussian expressions. Cross-correlation values are given in the inserts.
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