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In time-resolved spectroscopy, it is a widespread belief that the temporal resolution is determined by the laser pulse duration. Recently, it was observed and shown that partially coherent laser pulses as they are provided by free-electron-laser (FEL) sources offer an alternative route to reach a temporal resolution below the average pulse duration. Here, we demonstrate the generation of partially coherent light in the laboratory like we observe it at FELs. We present the successful implementation of such statistically fluctuating pulses by using the pulse-shaping technique. These pulses exhibit an average pulse duration about 10 times larger than their bandwidth limit. The shaped pulses are then applied to transient-absorption measurements in the dye IR144. Despite the noisy characteristics of the laser pulses, features in the measured absorption spectra occurring on time scales much faster than the average pulse duration are resolved, thus proving the universality of the described noisy-pulse concept.
© 2016 Optical Society of America
1. INTRODUCTION
Understanding the electronic and nuclear dynamics in atoms and molecules is an essential step toward laser control of chemical reactions. As such dynamics typically occurs on time scales in the lower femtosecond or even attosecond range, ultrashort coherent laser pulses are required to allow for a high temporal resolution. This triggered the quest for the generation of extremely broad spectra by different techniques, e.g., self-phase modulation [1] or field synthesis [2]. However, compressing these octave-spanning spectra to their bandwidth limit is currently limited by the lack of appropriate chirp-compensating optics. The development of free-electron-laser (FEL) sources led to the generation of femtosecond laser pulses, which are not fully coherent, but fluctuate statistically due to the underlying process of self-amplified spontaneous emission. These partially coherent (noisy) pulses are widely used in pump–probe spectroscopy in the x-ray range. It was observed in pump–probe experiments with deuterium molecules [3] that an enhanced temporal resolution compared to the average pulse duration was achieved [4]. The partially coherent nature of the FEL pulses leads to a temporal resolution close to the bandwidth-limited pulse duration corresponding to the average FEL spectrum despite its statistical fluctuation from shot to shot.
In recent theory work [4], the origin of enhanced temporal resolution for statistical pulse shapes in XUV-pump–XUV-probe experiments was explained by a product of a statistical two-dimensional autocorrelation (2DAC) function with a molecular response function. The key was the emergence of temporally sharp structures in the 2DAC function that allowed to sample fine-scale temporal structures of the molecular dynamics.
The influence of noise was investigated before, for instance, in two-photon absorption experiments with quantum-correlated noise [5] or in linear and nonlinear coherent Raman spectroscopy [6–9] using noisy pulse shapes. However, these works merely focused on the enhancement of the spectral resolution.
In the 80s, research groups realized that the temporal resolution is determined by the correlation time of laser pulses, which can be on much shorter time scales than the pulse width. This was shown by using incoherent light (e.g., generated by non- or incompletely mode-locked lasers) in various time-resolved measurements, i.a. [10–17].
Here, we concentrate on the intentional generation of partially coherent light fields via pulse shaping and their implications on the temporal resolution in pump–probe experiments directly studying molecular dynamics. We expand the scope of this method observed and explained for FEL light to laser pulses in the visible to near-infrared range in the laboratory. We then generalize the concept of noisy-pulse time-resolved spectroscopy to complex systems in the liquid phase.
2. EXPERIMENTAL METHODS
In a first step, statistically fluctuating pulses have to be generated in the laboratory. Our commercial laser system provides about 30 fs short, transform-limited laser pulses in the visible to near-infrared (VIS/NIR) range (central wavelength of about 780 nm, 4 kHz repetition rate). These pulses are turned into noisy pulses by applying a pulse shaper based on a spatial light modulator (SLM-S320, Jenoptik). The linear configuration of the pulse-shaper setup follows the design described in Ref. [18] and is depicted in Fig. 1(a). The laser pulses are split up into their spectral components and recombined again by plane gratings and cylindrical mirrors. The phase of the spectral components can be modified in the Fourier plane by a spatial light modulator (i.e., a liquid-crystal display with 320 pixels). The pulse shaper generates statistically fluctuating pulses by imprinting partially coherent phase patterns onto the laser spectrum. The procedure for creating these phase patterns follows the partial-coherence method described in [19]. A random phase value between 0 and is assigned to each frequency component of the laser spectrum. The Fourier transform is calculated, resulting in an infinite electric field in the time domain. A Gaussian envelope is multiplied to the electric field in order to obtain a pulse of finite duration. The width of the Gaussian envelope represents the average pulse duration and can be chosen accordingly. Then, the inverse Fourier transform of the finite electric field is determined yielding a partially coherent spectral phase pattern. These phase patterns are applied to the pulse shaper at a rate of 4 Hz, thus, creating statistically fluctuating pulses. The finite response time of the SLM between the switching of phase patterns has no adverse affect, as the phase patterns transiently existing in the transition between two random settings are also random.
Fig. 1. Sketch of the experimental setup. (a) Pulse shaper in 4f-configuration. A linear arrangement of the optical components is chosen in order to avoid aberrations. The spatial light modulator creates partially coherent phase patterns that are imprinted onto the laser spectrum, leading to statistically fluctuating pulse shapes. (b) Experimental setup for the transient-absorption and autocorrelation measurements, respectively. The laser pulses are split up into pump and probe pulses by a spatial mask and a time delay is introduced by a split mirror. In the case of the autocorrelation measurements, the pump and probe pulses are focused into a BBO crystal and the second-harmonic light generated by both pulses is detected as a function of the time delay. In the transient-absorption experiments, the BBO is replaced by the sample and the spectrum of the probe pulse is measured as a function of the pump–probe time delay.
The coherent, transform-limited as well as the noisy pulses are characterized in autocorrelation measurements. The setup for the transient-absorption experiments that was also used for the autocorrelation measurements is sketched in Fig. 1(b). The laser pulses are split up into pump and probe pulses by a spatial mask. A split mirror introduces a time delay between the two pulses. Then, the pump and probe pulse are focused into a BBO crystal (thickness of 300 μm) and the generated second-harmonic spectra are measured as a function of the time delay . The autocorrelation measurement for the case of coherent, transform-limited pulses is presented in Figs. 2(a) and 2(b). The projection onto the time-delay axis reveals a Gaussian distribution from which a pulse duration of can be derived. The autocorrelation spectra for the partially coherent pulses are shown in Figs. 2(c) and 2(d), where an average over 15 autocorrelation scans was taken. The measured autocorrelation resembles the autocorrelations of (FEL) pulses, i.e., a narrow peak sitting on top of a broad pedestal [4,20]. The broad pedestal contains the average pulse duration, whereas the narrow peak provides information about the transform limit determined by the underlying averaged laser spectrum. Gaussian fits yield an average pulse duration of and a transform-limited pulse duration of which is in excellent agreement with the measured bandwidth limit of 34 fs. These results show that statistically fluctuating pulses can be generated in the laboratory, featuring similar properties as the light pulses provided by (FEL) sources.
Fig. 2. Autocorrelation measurements. Measured second-harmonic spectra (a), and their projection (b), as a function of the time delay between pump and probe pulse for the case of transform-limited pulses. The red curve corresponds to a Gaussian fit yielding a pulse duration of about 34 fs (FWHM). (c) and (d) Second-harmonic spectra and their projection for partially coherent (noisy) pulses, generated with the pulse shaper, averaged over 15 scans. The Gaussian fits (red curves) reveal an average pulse duration of roughly 260 fs (FWHM) and a bandwidth limit of about 33 fs.
3. EXPERIMENT AND RESULTS
With the tool of creating partially coherent laser pulses in the VIS/NIR range at hand, transient-absorption measurements in the liquid phase are performed in order to study the impact of the noisy pulses on the temporal resolution. A solution of the dye IR144 in methanol with a concentration of 0.25 mmol/l serves as sample. The spectrum of the probe pulse is detected as a function of the pump–probe time delay and of the pump-pulse fluence. The time delay is scanned from negative (pump follows probe), to positive time delays (probe follows pump). The fluence of the pump pulse is varied from about 1.41 to , while the probe fluence is kept constant at about . The measured transient-absorption spectra are presented in Fig. 3 for the case of partially coherent pulses and, as comparison, for the case of coherent, transform-limited pulses. The shown optical density of the absorption spectra is given by , where is the measured probe-pulse spectrum transmitted through the sample and is the reference laser spectrum, i.e., the unperturbed probe-pulse spectrum without sample and without pump pulse. In general, the absorption is higher for negative than for positive time delays. This can be easily explained by the fact that the pump pulse has already excited the dye molecules at positive time delays, leading to a reduced ground-state population and, thus, a reduced absorption (ground-state bleaching). Close to zero time delay stronger modifications are visible. In order to further study the temporal dynamics, the absorption spectra are integrated and their projections are shown as a function of the time delay in Fig. 4. A common behavior can be observed: for negative time delays, the signal is constant. It starts to decrease exponentially close to zero time delay. In addition, a dip occurs around , i.e., the absorption decreases first and increases again afterward. The transition from a constant signal to the exponential decay is most pronounced in the case of transform-limited pulses [cf. Fig. 4(h)], as the much larger average pulse duration of the noisy pulses leads to some washing out. The previously observed wave-packet oscillations [21] could not be identified in our data, neither for the transform-limited pulses nor the noisy pulses, likely due to our lower signal-to-noise ratio.
Fig. 3. Measured transient-absorption spectra for partially coherent pump and probe pulses as a function of the pump–probe time delay for different pump-pulse fluences: (a) ; (b) ; (c) ; (d) ; (e) ; (f) ; (g) . Each two-dimensional absorption spectrum corresponds to an average over five time-delay scans. (h) Representative time-dependent absorption spectra obtained for coherent, transform-limited pump and probe pulses. Here, the pump-pulse fluence was set to .
4. DISCUSSION
In order to obtain more information about the time scales of the observed dynamics, the signals are described by a fit function, which includes the exponential decay with time constant :
The fit function is convoluted with a Gaussian of width to consider the temporal resolution determined by the pulse duration: The resulting model function reads where represents a shift in time, a constant offset, and an overall amplitude. Additionally, the dip is fitted by a Gaussian function. Since the convolution of a Gaussian with another Gaussian gives again a Gaussian function, the model function finally reads as The obtained fit functions are indicated in red in Fig. 4. The dependence of the obtained time constant of the exponential decay, , on the pump-pulse fluence is shown in Fig. 5(a). The determined widths of the dip at zero time delay are displayed in Fig. 5(b). Strikingly, for statistically fluctuating pulses the decay time increases for increasing pump-pulse fluence, i.e., the absorption signal decreases more slowly. At the same time, the decay time decreases for the case of transform-limited pulses, i.e., the fluence dependence of the decay time is reversed. For the two different pulse types, the dependence of the decay time on the pump-pulse fluence shows an opposing trend. This different behavior of the dynamics might be explained by the following: In case of the transform-limited pulses high pulse intensities are reached in a short time, enabling instantaneous multiphoton excitations of the IR144 molecules into highly excited states, leading to a faster decrease of the absorption with increasing pump-pulse fluence. For the longer partially coherent pulses the multiphoton excitations can be induced sequentially, i.e., spread over longer times. After the first photon is absorbed, the molecule can first relax to lower-lying states before the absorption of the second or even third photon in the intense pump pulse can occur. The increase of time scales with intensity [Fig. 5(a)] for the noisy-pulse case could imply that the higher fluence, with multiple absorptions of pump photons spread over longer times, could in fact lead to a stabilization of the molecular dynamics away from the ground state, which could be interesting in further applications of the technique. In the future, it will be interesting to study how the fluence dependence of the decay time changes with different average pulse durations of the noisy pulses, eventually also clearly identifying the transition from the instantaneous to the sequential multiphoton regime.Fig. 4. Integrated transient-absorption spectra as a function of the pump–probe time delay for partially coherent pump and probe pulses. The following pump-pulse fluences were chosen: (a) ; (b) ; (c) ; (d) ; (e) ; (f) ; (g) . (h) Integrated signal for the case of coherent, transform-limited pump and probe pulses. The pump-pulse fluence was set to . The red curves represent the corresponding fits given by Eqs. (3) and (4).
Fig. 5. Fit parameters. (a) Time constant of the exponential decay obtained from the fit as a function of the pump-pulse fluence. For the partially coherent pulses, increases drastically with increasing fluence. In comparison, the derived decay times for coherent, transform-limited pump and probe pulses are depicted (blue dots) for pump-pulse fluences of , , and . (b) Width (FWHM) of the dip at zero time delay.
Comparing the full width at half-maximum (FWHM) of the dip feature for different pump-pulse fluences for statistically fluctuating pulses, the following conclusions can be derived: (i) No autocorrelation is measured, but true dynamics of the dye molecule, since the width of the dip varies with the pump-pulse fluence. (ii) The width of the dip is composed of two contributions, namely the 34 fs duration of the transform-limited pulses (which determines the FWHM for lower pump-pulse fluences) and the time scale of the laser-induced, molecular-specific dynamics. The origin of the narrow dip could not be identified; however, its presence, whether due to the molecular dynamics or also in part to the (quasi-instantaneous) nonlinear response [22] of the sample, demonstrates the temporal resolution much below the average pulse duration of 260 fs.
It has to be stressed that it is not the aim to understand and explain the measured molecular dynamics extensively due to the lack of detailed theory information about the vibronic energy-level structure of the dye IR144. The important fact to be pointed out is that although the statistically fluctuating pulses exhibit an average pulse duration that is about 1 order of magnitude larger compared to the case of transform-limited pulses, the ultrafast dynamics can still be observed in the transient-absorption measurements. Most importantly, the resolved dynamics (e.g., the fast decrease and increase of the absorption signal, i.e., the dip, around zero time delay) occurs on time scales much smaller than the average pulse duration. These findings demonstrate that the beneficial impact of partially coherent pulses on the temporal resolution that was observed in pump–probe experiments at FEL sources [3,4] are general and apply also to transient-absorption experiments in the liquid phase.
5. CONCLUSIONS AND OUTLOOK
We successfully show that we can produce partially coherent light in the laboratory as we observe it at FEL sources. The statistically fluctuating pulses generated with the help of a pulse shaper allow for a time resolution better than the average pulse duration. The noisy-pulse concept thus provides an alternative approach to resolve dynamics on ultrashort time scales where extremely broad spectra cannot be compressed to their bandwidth limit due to some existing technical limitations. In addition, the application of noisy pulses might help to investigate processes in the strong-field multiphoton regime, where, also based on these results, one expects differences between instantaneous and sequential absorption of several photons in the pump-pulse driven dynamics. A promising route for future investigations both at optical as well as x-ray frequencies is the combination of statistically varying pulse sequences with advanced multidimensional data-analysis methods as employed in Fung et al. [23], not only to obtain higher temporal resolution of natural dynamics, but also to discover higher-order nonlinear dynamical motifs of molecular motion in strong-field driving situations toward understanding laser control of molecules.
Funding
Deutsche Forschungsgemeinschaft (DFG) (PF 790/1-1); European Research Council (ERC) (X-MuSiC-616783).
Acknowledgment
We acknowledge helpful discussions with Tiago Buckup.
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