1. Introduction

Coherent anti-Stokes Raman scattering (CARS) spectroscopy is a powerful tool to investigate vibrational modes and their dephasing parameters. The third order process is based on the interaction of three laser fields with the sample, namely the Raman pump with the frequency ${\omega }_{pu}$, the Stokes pulse at ${\omega }_{St}$ and the Raman probe field at ${\omega }_{pr}$. The frequency difference of the Raman pump and the Stokes field ${\omega }_{pu}-{\omega }_{St}$ is tuned to drive specific vibrational modes. This coherent excitation is probed with the third pulse that is usually a replica of the Raman pump pulse (degenerated CARS). Since the first reported systematic study of CARS [1] a remarkable evolution took place, often triggered by the availability of new coherent light sources. Since the development of nanosecond lasers CARS is a widely used and well established method. Especially the application to gases in combustions and flames to determine temperatures and concentrations of molecular species is very successful [2]. Using relatively long laser pulses limits the access to temporal information.

In addition, a nonresonant background interferes with the resonant molecular contributions of the CARS signal. This results in distorted line shapes and limits the accuracy in analyzing populations and temperatures [3]. In the last decades femtosecond laser sources were used to study by CARS ultrafast processes like vibrational dephasing, dynamics of wavepackets, rotational dynamics, coherence transfer or reactions in gases and liquids [4–9]. However, the gain of temporal information is accompanied by a decrease of spectral resolution. For the sake of completeness we like to mention that CARS is used with increasing interest also as non-invasive microscopic technique with high spatial resolution [10–13].

In the intermediate time regime lasers with picosecond pulse durations are used [14–18]. These laser sources are suitable for time resolved CARS spectroscopy with a spectral resolution much better than for femtosecond CARS techniques. In the 1980s Zinth et. al. showed that with narrowband picosecond probe pulses highly resolved Raman spectra can be obtained [16]. This results from two effects. On the one hand the introduced time delay between the excitation and the probe leads to a suppressed nonresonant background compared to nanosecond CARS techniques. On the other hand in liquid phase the line width of vibrational transitions observed by linear Raman is broadened due to dephasing processes caused by the interaction with the environment. CARS probes vibrational coherences and molecules which do not vibrate in phase with the ensemble average do not contribute to the signal. Homogeneous dephasing processes reduce only the signal strength but do not directly broaden CARS lines which depend then only on the width of the Raman probe [17]. Using a narrowband Raman probe results therefore in high resolution CARS spectra and signatures can be observed which might be hidden in conventional Raman spectra in the case of overlapping bands. A further development of CARS with picosecond pulses is the multiplex CARS technique. Narrowband picosecond pulses from a dye laser were combined with broadband modeless picosecond dyelasers to excite simultaneously several vibrational modes [19–21].

Nowadays a lot of CARS setups combine the advantages of a femtosecond broadband laser and a narrowband picosecond source [22–29]. The former is mainly used as Stokes pulses to excite a whole range of vibrational modes at the same time, the latter probes the coherence and defines the spectral resolution. In the reported setups the pulses are generated either with separate synchronized laser sources or by diverse pulse shaping elements. We present here a new setup based on noncollinear optical parametric amplifiers (NOPAs) for the generation of broadband Stokes and narrowband probe pulses. It provides broad tunability and simultaneously a high temporal and spectral resolution for pump-probe experiments using the CARS process for probing. After the description of the setup and the characterization of the NOPAs, the capability of the multiplex CARS setup is demonstrated in different proof of principle experiments.

2. Experimental setup

2.1 Multiplex CARS setup

The CARS setup (see Fig. 1 ) is based on picosecond pump and probe pulses generated by a narrowband NOPA and a broadband femtosecond Stokes pulse from a conventional NOPA [30]. Both NOPAs are pumped by a regenerative amplifier (Spitfire Pro, Spectra Physics) which provides near infrared (NIR) pulses at 800 nm with a typical pulse duration of 55 fs and a repetition rate of 1 kHz. A fraction of 250 µJ is used to pump the NOPA generating the Stokes pulses. They are compressed by a dense flint glass (SF10) prism sequence to reduce the pulse duration to sub-50 fs. The output of the narrowband NOPA is used for Raman pump and probe simultaneously by splitting it into two replicas. The probe pulses are delayed with respect to the Raman pump and Stokes pulses by a motorized linear delay stage. The pulse energy of each beam can be set with two wire grid polarizers independently without changing the polarization. Typical pulse energies used in all experiments are in the range of several 100 nJ.

 

Fig. 1 Sketch of the multiplex CARS setup. Raman pump and probe beam consist of narrowband pulses. They are overlapped in the sample with a broadband femtosecond Stokes pulse using a folded BOXCARS geometry.

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Pump, Stokes and probe beam are focused into the sample cuvette with a 200 mm lens, applying a folded BOXCARS configuration [31]. The incoming beams are arranged parallel with distances of about 10 mm to the optical axis given by the center of the lens. The exact values are calculated using phase matching conditions. The investigated liquids are filled into a 2 mm thick fused silica cuvette positioned at the focal plane. In a phase matched BOXCARS geometry the blue shifted CARS signal is spatially separated from the input fields and therefore easy to filter with apertures. To further reduce stray light a short pass filter is used (colorfilter DT-blue, Linos). The signal is then focused into a glass fiber with a core diameter of 200 µm. The fiber is coupled to a spectrometer with a focal length of 500 mm and a holographic diffraction grating with a groove density of 1800 mm⁻¹. There the dispersed signal components are detected with a CCD array consisting of 2048 x 64 quadratic pixels with a size of 14 µm (S11071-1106, Hamamatsu).

2.2 Narrowband NOPA

The spectral resolution of the shown CARS setup should be given by the spectral width of the probe beam (see above). To enhance the resolution we build a narrowband NOPA similar to those presented in [32–34]. It is described here in more detail. The setup which is shown in Fig. 2 consists of a modified broadband NOPA followed by a spectral filter and a final parametric amplification stage. A fraction of 650 µJ of the Ti:sapphire output is used as pump. 250 µJ are split off from the NIR beam to pump the first NOPA stage which generates femtosecond pulses with a center frequency chosen that the difference frequency of pump and Stokes pulse ${\omega }_{pu}-{\omega }_{St}$ is suitable to drive the vibrational coherences of interest.

 

Fig. 2 Setup of the narrowband NOPA. The output of a modified femtosecond NOPA is spectrally filtered by a monochromator and subsequently amplified in a second parametric stage. For details see text.

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In the NOPA a small fraction of the NIR light is focused into a 3 mm thick sapphire crystal to produce white light pulses by self-focusing and self-phase modulation [35]. The pump beam for the parametric amplification is generated by frequency doubling the remaining NIR radiation in a 0.7 mm thick BBO crystal cut for type I phase matching (θ = 29°). The continuum is overlapped with the blue pump beam in a 2 mm long BBO crystal (Type I, θ = 32.5°) in a noncollinear geometry to achieve a simultaneous match of the phase and group velocities [36]. To reduce the bandwidth we modified the standard setup by introducing linear chirp in the white light as well as in the pump pulses by placing appropriate fused silica (FS) substrates in the respective beam paths. Chirping the white light seed reduces the bandwidth that is temporally overlapping with the pump pulse. This leads to a spectrally narrower output. This consideration only holds if the blue pump pulses are temporally long enough. Parametric amplification takes place only in the time window during which the pump pulse overlaps with the seed pulse. If the pump pulses are too short this may lead to an increase of the signal bandwidth compared to the seed according to the Fourier limit [32]. We found that a combination of a 5 cm long FS block in the white light beam and a 1 cm thick FS plate in the blue pump beam reduces the signal bandwidth to approximately 300 to 500 cm⁻¹ without a significant loss of output power.

These generated fs-pulses are further spectrally narrowed to a width of less than 15 cm⁻¹ by a monochromator with a focal length of 300 mm equipped with a grating blazed for 500 nm with a groove density of 300 mm⁻¹ (SP2355, Princeton Instruments). This filtering is accompanied by a strong decrease of intensity. To compensate for it a second parametric amplification stage is used. The stage is pumped by blue pulses at 400 nm generated by converting the remaining 400 µJ fraction of the Ti:sapphire output to its second harmonic in a 0.2 mm thick BBO crystal (Type I, θ = 29°). The crystal length was selected as small as possible to achieve broadband phase matching in order to avoid spectral narrowing. The length of the blue pump pulses is increased by chirping them with a 20 cm long FS block. From the spectrum of the pump pulses and the dispersion of the FS block we calculated a duration of 1.2 ps. In the case of Fourier limited pulses this length is equivalent to a spectral width of 12 cm⁻¹ which corresponds in principle to the expected minimum bandwidth of the amplified signal.

The narrowband seed and the chirped pump pulses are overlapped in a 4 mm thick BBO crystal cut for type I phase matching at an angle of 32.5°. To provide broadband phase matching a noncollinear geometry is used which is necessary due to the spectral width of the blue pump pulses. The pump pulse is focused with a combination of 500 mm lens and a spherical mirror with a radius of 300 mm. Best results are obtained if the seed pulse undergoes an intermediate focus before it is focused with a combination of two lenses with focal lengths of 300 mm and 250 mm into the BBO crystal. The use of respectively two focusing elements allows for optimizing the size of the foci and their positions with respect to the BBO crystal. Both foci are placed about 4 cm in front of the crystal.

Typical pulse spectra and energies of the narrowband NOPA are shown in Fig. 3 . The NOPA can be tuned through a wide spectral range from 490 nm to 740 nm. The energies are found to be in the range of 0.1 to 4 µJ with a maximum around 540 nm. The shape of the curve is quite similar to the energetic profiles measured for a similar setup [32]. From the beam profile of the narrowband NOPA output and its focus we calculate an average beam quality factor of M² = 1.4.

 

Fig. 3 (a) Normalized spectra of the narrowband NOPA pulses for the accessible tuning range. (b) Typical pulse energies. The broken line is a guide to the eye.

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At all wavelengths we observe an increased spectral width of the signal compared to the seed. Very narrow spectral widths of approximately 19 cm⁻¹ – 22 cm⁻¹ are observed between 510 to 520 nm (see Fig. 3(a)). By measuring the cross-correlation of the narrowband NOPA output at 510 nm with 30 fs long pulses from a second NOPA we determine the pulse duration to 1.14 ps. From the spectral width of 19 cm⁻¹ (FWHM) a time-bandwidth product of 0.65 is calculated which is 1.5 times larger than the Fourier limit. This broadening compared to the expected 15 cm⁻¹ (see above) is possibly caused by the parametric amplification process itself. Spectral broadening in the parametric amplification in a similar setup has been already reported [33]. In the case of a narrowband seed interacting with a broadband pump an idler with a broad spectral width comparable to the width of the pump is generated. During the amplification process the idler in turn produces signal photons. If the frequency difference of the interacting idler and pump photons is not equal to the original seed frequency new components appear in the seed spectrum. Since the pump is strongly chirped and the group velocities of pump and idler are not equal a systematic frequency variation of the additionally generated signal contributions occurs during the propagation through the crystal. However, no attempt was made to model this effect quantitatively and it is an open question if it can fully account for the observed signal broadening.

3. Results and discussion

CARS measurements on several solvents are presented in the following to demonstrate the capabilities of the setup. Chloroform (Sigma Aldrich) was used as a test substance because the Raman spectrum of the CH stretch vibrations consists just of a single well known mode at 3020 cm⁻¹ [37]. The pump pulse was set to approximately 510 nm and the Stokes to 610 nm respectively. Although the difference $\left({\omega }_{pu}-{\omega }_{St}\right)$ is not exactly 3000 cm⁻¹, we measured an intense CARS Signal. This is due to the broad spectrum of the Stokes pulse that allows exciting Raman modes in a range of more than 1500 cm⁻¹. The dispersed CARS signal measured as a function of the delay time between the driving pulses and the probe pulse is shown in Fig. 4(a) . Two main features are observed in the spectra, a spectrally broad signature centered at time delay zero and a peak like structure at 3019.5 cm⁻¹. This peak exists apparently longer as the background and is assigned to the Raman active CH-stretching mode. An underlying theoretical description of the signal will be given briefly in the following.

 

Fig. 4 (a) Time resolved CARS spectra of CHCl₃. (b) Time trace at 3019.5 cm⁻¹ in comparison with a modeled curve (red). The model consists of a nonresonant (black solid line), a resonant (blue dash dotted line) and an additional contribution due to the exchange of the role of pump and probe pulses (dashed line).

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The time resolved and spectrally dispersed CARS signal resembles the Fourier transformation of the anti-Stokes field ${\tilde{E}}_{AS}\left(t_D,\omega \right)$ in dependence on the delay time $t_D$ [14]. This field can be obtained from solving the nonlinear wave equations, which represent the propagation of light pulses including the light matter interaction. The latter is described by the nonlinear polarization ${\tilde{P}}_{AS}\left(t_D,\omega \right)$ [38]. Using the slowly varying amplitude approximation and assuming that the phase matching condition is fulfilled the solution of the wave equation directly correlates the third order polarization with the anti-Stokes field ${\tilde{E}}_{AS}\left(t_D,\omega \right)=i\left(2\pi \omega L/nc\right){\tilde{P}}_{AS}\left(t_D,\omega \right)$ for a given medium with the index of refraction $n$ and the interaction length $L$ [39].

${\tilde{P}}_{AS}\left(t_D,\omega \right)$ may have several resonant contributions ${\tilde{P}}_{R,j}$ due to independently excited vibrations $j$ with the Raman polarizabilities $\partial \alpha /\partial q_j$ and a nonresonant background ${\tilde{P}}_{NR}$ caused by the electronic subsystem. Following [38] the polarization ${\tilde{P}}_{AS}$ can be written as:

The real valued nonresonant contribution ${\chi }_{NR}^{\left(3\right)}$ varies only weakly with frequency [40] and will be treated as a frequency independent constant. Assuming much shorter Stokes than pump and probe pulses, the nonresonant polarization will mirror the cross-correlation function of the probe pulse with the pump and Stokes pulse in the time domain [38].

In the following we will consider just one excited vibration. The ensemble averaged coherent vibrational excitation of the molecules is described in a two level scheme by the expectation value for the displacement $〈q〉$. In the limit of negligible population of the excited state the coherent vibration at the frequency ${\omega }_q$ is treated as an exponentially damped oscillator with amplitude $Q$ and decoherence time $T_2$ accounting for vibrational dephasing and the lifetime of the excited level [41,42]:

The vibrational mode is excited by the pump $E_{pu}\left(t\right)$ and Stokes $E_{St}\left(t\right)$ field at $t=0$ in the limit of an ultrashort Stokes pulse and the corresponding driving force is proportional to the product $E_{pu}\left(t\right)E_{St}^{*}\left(t\right)$ with the carrier frequency ${\omega }_{pu}-{\omega }_{St}$. The vibrational coherence $〈q〉$ is monitored by the probe field $E_{pr}(t_D,t)$. According to Eq. (1) the Fourier transformed resonant polarization ${\tilde{P}}_R(t_D,\omega )$ can be obtained from

The experimentally observed signal is proportional to the intensity of the anti-Stokes field $S(t_D,\omega )\propto {\left|{\tilde{E}}_{AS}(t_D,\omega )\right|}^2$. For a single vibrational mode the signal is centered at $\omega ={\omega }_q+{\omega }_{pr}$ and decays exponentially with $\exp \left(-2t/T_2\right)$. In the discussed case we presume that the phase matching condition is fulfilled. In the case of spectrally broad Stokes pulses this assumption cannot be satisfied for all frequencies. The simulated intensity spectra have to be modified by the factor ${\text{sinc}}^{\text{2}}\left(\Delta kL/2\right)$ [43].

These basic equations allow us to discuss qualitatively the observed signal of chloroform (see Fig. 4(a)). The broad feature is assigned to the nonresonant background. The signal decrease at the low frequency side as well as at the high frequency side is caused by the phase mismatch. The coherent nature of the signal leads to interference effects between the resonant and nonresonant polarization and an asymmetric line shape of the resonance. At its low frequency side constructive interference is observed whereas at the high energy side the nonresonant part cancels partly the resonant contribution. At later delay times the nonresonant part vanishes and only a Gaussian shaped signal remains, which shape reflects the spectrum of the probe pulses.

Figure 4(b) shows a time trace of the CARS signal at 3019.5 cm⁻¹. The signal decomposition is done with a simulation of the nonresonant background and a single vibrational contribution as described above. However, to reproduce the CARS signal satisfactorily an additional contribution has to be taken into account which originates from the degeneracy of the pump and probe pulses. In the region of temporal overlap the probe pulse can act also as pumping field and the pump pulse in turn as probing pulse. Close to the vibrational resonance this contribution increases the signal whereas it has no effect far off resonance. The decay time of the signal, which corresponds to the dephasing time $T_2/2$, is found to be 0.55 ps which is in very good agreement with reported values [37].

Cyclohexane has a more complex Raman spectrum which exhibits around 2900 cm⁻¹ three strong Raman bands resulting from CH-stretch modes [44]. In this case we used pump and probe pulses at a center wavelength of 519 nm and Stokes pulses at 617 nm. A time series of CARS spectra of cyclohexane is presented in Fig. 5(a) . The Raman band at 2857 cm⁻¹ is well separated from the other Raman modes. With increasing probe delay the nonresonant background disappears and the shape of the band stays then constant. The signal decays mono exponentially with time (see Fig. 5(b), upper panel). The situation is much different for the other two Raman modes around 2930 cm⁻¹. If features in the spectra are that close to each other, that they are within the spectral width of the probe pulse, the corresponding signal contributions interfere with each other. This is nicely seen in the temporal evolution of the two Raman bands. At a delay time of e.g. 2.5 ps both contributions add constructively whereas a picosecond later the individual Raman polarizations cancel each other partially due to destructive interference. In Fig. 5(b) a time trace of the overlap region is presented. The beating time is directly correlated to the frequency spacing of the contributing Raman modes. The calculated frequency difference of 14.7 cm⁻¹ is in good agreement with the linear Raman spectrum. While the frequency spacing can be measured very accurately, it is due to the interference effects not straight forward to extract from CARS spectra absolute vibrational frequencies with high accuracy. Especially if many modes are close to each other the resulting signal will be rather complex in the frequency as well as in the time domain. In ongoing work the simulation of complex spectra and their time evolution is performed in order to assign absolute frequency values and dephasing times.

 

Fig. 5 (a) Selected CARS spectra of cyclohexane at different delay times. The spectra are normalized with respect to the mono exponentially decaying signal at 2857 cm⁻¹. (b) Time traces of the signal at 2857 cm⁻¹ and at 2930 cm⁻¹ where a beating due to the overlap of two modes appears. The beating period $T$ = 2.27 ps is highlighted.

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[C2mim][NTf2] is an ionic liquid [45] which we are investigating with Raman techniques. The Raman spectrum between 2800 cm⁻¹ and 3050 cm⁻¹ can be assigned to CH-stretch vibrations of the alkyl chain. Due to a large number of overlapping vibrations originating from different normal modes of the CH₂ and CH₃ groups as well as due to the existence of many structural conformations a broad spectrum results [46,47]. It is a challenging task to decompose these contributions. In the following we demonstrate that CARS with narrowband probe pulses can result in spectra which exhibit clearer and more pronounced structures compared to linear Raman measurements which may help to interpret them. In Fig. 6(a) a comparison between a linear Raman and a CARS spectrum is shown. The CARS spectrum is obtained with a time delay of 1.35 ps of the probe pulse with respect to the excitation pulses. This time delay ensures that the nonresonant contribution is suppressed and only the resonant contributions originating from the excited vibrational coherences are present. All contributing vibrational modes to the linear Raman spectrum are also seen in the CARS spectrum. Although the exposure time for the data acquisition in the CARS experiment is three orders of magnitude shorter compared to the linear Raman measurements the signal to noise ratio is much better. Additionally the CARS spectrum is more structured and the signatures are more pronounced. The peak positions are slightly shifted with respect to the Raman spectrum. The shifts arise from beating phenomena discussed in the previous section. A clear indication for this is the observation that the peak maxima originating from beating partners are shifted to opposite sides due to destructive interference in the overlap region. Nevertheless, the example shows a significant improvement of the spectral resolution using CARS with narrowband probe pulses.

 

Fig. 6 Raman and CARS spectrum of the CH stretch vibrations of the alkyl chain of the cation in the ionic liquid [C2mim][NTf2].

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4. Summary and conclusions

We presented a NOPA based CARS setup with broadband excitation using a femtosecond Stokes pulse in combination with narrowband Raman pump and probe pulses. The pump and probe pulses are generated by a two stage narrowband NOPA applying spectral filtering after the first parametric stage and chirped broadband pump pulses for the second parametric amplifier. The design allows choosing the center frequencies of Stokes and of pump and probe pulses independently. This gives the freedom to tune the frequency difference of the pulses to the frequency range of the vibrational modes of interest as well as to match with electronic resonances. With an appropriate time delay between excitation and probe pulses the nonresonant background is efficiently suppressed and Raman modes can be investigated with high sensitivity. The picosecond resolution allows the characterization of vibrational dephasing processes in liquids. Closely lying Raman modes cause beating in the time traces and the beating period is directly determined by their frequency spacing. In the case of spectra with coalescing bands more pronounced spectral structures are observed as in linear Raman measurements.

The pulse duration of the Stokes pulses defines the time window in which the vibrational coherences are excited. This predestines the presented CARS setup for pump - CARS probe experiments e.g. in combination with an infrared pump laser. In this way it should be possible to measure vibrational redistribution processes with sub-50 fs resolution. In principle similar information can be revealed from pump – Raman probe experiments [48,49]. But the low Raman cross section calls for long accumulation times and a narrowband Raman laser is needed for high spectral resolution which simultaneously limits the time resolution.