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We developed pulse-shaper-assisted coherent two-dimensional (2D) electronic spectroscopy in liquids using fluorescence detection. A customized pulse shaper facilitates shot-to-shot modulation at 1 kHz and is employed for rapid scanning over all time delays. A full 2D spectrum with 15 × 15 pixels is obtained in approximately 6 s of measurement time (plus further averaging if needed). Coherent information is extracted from the incoherent fluorescence signal via 27-step phase cycling. We exemplify the technique on cresyl violet in ethanol and recover literature-known oscillations as a function of population time. Signal-to-noise behavior is analyzed as a function of the amount of averaging. Rapid scanning provides a 2D spectrum with a root-mean-square error of < 0.05 after 1 min of measurement time.
© 2017 Optical Society of America
1. Introduction
Coherent two-dimensional (2D) optical spectroscopy has emerged as a powerful tool to reveal dynamic processes in various quantum systems [1,2], for example delivering information about energy transport and molecular structure [3], photochemical reactions [4], semiconducting materials [5,6] or solvent effects on catalyst dynamics [7].
Originally developed for nuclear magnetic resonance techniques [8], optical coherent 2D experiments have been suggested [9,10] and experimentally reported for nonlinear optics [11] as well as measurements of quantum dynamics with spectral ranges from the ultraviolet [12,13] over the visible [14–16], the near-infrared [17] and the infrared [18], up to the THz regime [19]. Various implementations have been reviewed recently [20], and the 2D method in general is covered in several books [21–23] and further review articles [1,24–26].
Many 2D experiments employ three excitation pulses, and the coherently emitted nonlinear four-wave-mixing signal is measured in amplitude and phase. Fourier transformation over coherence times yields the desired 2D spectra as a function of population time. Extracting the desired signal component of a certain nonlinear order (such as the photon-echo contribution) is generally achieved in the noncollinear box geometry under a suitable phase-matching condition, i.e., choosing an appropriate excitation and detection geometry [1].
Instead of measuring an emitted coherent signal one can also utilize action-based spectroscopy [27–32]. For that purpose a fourth pulse is added to the excitation sequence, leaving the quantum system in a final population state, rather than a coherence. This final-state population can be probed, for example, via fluorescence [27–29] or electron current [31,32]. The coherent information is encoded in the train of excitation pulses and their phase relations [30]. Fluorescence 2D spectroscopy in the visible regime has been demonstrated in the gas phase [27] as well as in liquids [33] and matrices [34].
Performing coherent 2D experiments is challenging with respect to phase and intensity stability of the laser as well as spatial and temporal alignment of the excitation pulses because any drifts or fluctuations might lead to experimental artifacts, especially considering the phase-sensitive nature of the spectroscopy method and its Fourier evaluation process. Additionally, the high-intensity light fields that need to be applied for obtaining nonlinear signals may lead to decomposition of the investigated quantum systems such as permanent bleaching via photochemical reactions. Further, when one wants to make comparative studies of a series of quantum systems via 2D spectroscopy, one needs to ensure that the experimental conditions remain constant. All of these challenges make it desirable to keep the acquisition time down to a minimum.
In the present work, we report a new variant of rapid-scan, single-beam, fluorescence-detected 2D spectroscopy. The apparatus has no movable parts (i.e., no delay lines), and all required excitation pulses are created collinearly by a pulse shaper. Since the shaper is operated on a shot-to-shot basis at the repetition rate of the laser system (1 kHz), we realize rapid scanning, i.e., each shot out of the laser corresponds to a different setting of interpulse time delays and/or phases. This has advantages with respect to signal stability. Further, all possible signal contributions are acquired simultaneously (such as photon echo, double-quantum coherence and others) and can be reconstructed in the analysis. The setup is evaluated using cresyl violet in ethanol [39–43].
2. Theory
For coherence-detected 2D spectroscopy, signal ambiguities are excluded in noncollinear geometry by spatially separating the desired nonlinear signal from the excitation pulses as well as from other nonlinear signal components. For example, the rephasing photon echo is emitted in direction kS = −k1 + k2 + k3, where ki, i = 1, 2, 3, are the wavevectors of the three excitation pulses and kS is the wavevector of the coherent signal.
In collinear geometry the different contributions of the system response cannot be distinguished spatially and anyway with incoherent fluorescence detection no phase-matching condition exists. Accordingly, a different approach for separation has to be applied. We use phase cycling to obtain all nonlinear contributions, such as rephasing, nonrephasing and double-quantum coherence [30]. For this purpose, a pulse shaper is used to apply prescribed phases to each of the excitation pulses as described below, and the desired signal is then obtained as a suitable linear combination of fluorescence intensities.
In order to measure a fluorescence signal, the system has to be in an excited state after the fourth interaction. The Feynman diagrams corresponding to the rephasing and nonrephasing “photon-echo” signal in a two-level system are depicted in Fig. 1.
Fig. 1 Feynman diagrams for (a) rephasing and (b) nonrephasing contribution in a two-level system. Solid arrows signify excitation pulses, dashed arrows the fluorescence signal.
In the case of three-level systems, other pathways also contribute to the signal, e.g., further excitation to the second excited state. For most molecules there will then occur a radiationless decay to the first excited state, followed by fluorescence to the ground state (Kasha’s rule [44]). The fluorescence signals induced by those alternative pathways cannot be distinguished from the signals depicted in Fig. 1, but can be neglected if the resonance condition is not fulfilled for a 1 → 2 transition. If necessary, they can be accounted for by a suitable correction factor [45].
The time-dependent electric field of the four-pulse excitation sequence can be formulated as a linear combination of four identical, time-delayed pulses that may vary in their phase. The nonlinear fluorescence signal depends on the time delays (first coherence time τ = t2 − t1, population time T = t3 − t2, second coherence time t = t4 − t3) and the phases (ϕi, i = 1, 2, 3, 4) of the pulses. For example, the induced fourth-order population of the rephasing contribution (ϕ1 = −1, ϕ2 = 1, ϕ3 = 1 and ϕ4 = −1) is given by
as a function of time t′, where QRP is the system response convoluted with the incident electric field that contains the rephasing contribution. The parameter γ0 is a frequency scaling factor that is implemented in pulse-shaper-based 2D spectroscopy to realize measurements in the rotating frame (γ0 = 0) or the laboratory frame (γ0 = 1) or an intermediate regime (0 < γ0 < 1). The wave vectors ki cancel each other out since they are approximately identical in the same-frequency limit in collinear geometry. Analogously, the nonrephasing fourth-order population can be accessed by choosing the respective phases (ϕ1 = 1, ϕ2 = −1, ϕ3 = 1 and ϕ4 = −1).Experimentally we do not cycle the interpulse phases continuously but in 1 × L × M × N discrete steps for the four excitation pulses, with L, M and N the number of sampling points for Δϕ21, Δϕ31 and Δϕ41, respectively, and where Δϕij = ϕi − ϕj is the phase difference between pulses i and j. We extract a specific nonlinear contribution p̃(4)(β, γ, δ) from the measured signal p(τ, T, t, lΔϕ21, mΔϕ31, nΔϕ41) via discrete Fourier transformation [30],
It has been shown that cycling the phases with a sampling resolution of L = M = N = 3 steps is sufficient to acquire all nonlinear contributions in fourth-order population, i.e., corresponding to the conventional third-order coherently detected 2D spectroscopy. This results in 27 time-domain maps [30].
3. Experimental
The employed setup is depicted in Fig. 2(a). We use a commercial Ti:Sa amplifier system (Spitfire, Spectra Physics) to generate 120 fs pulses at a center wavelength of 800 nm and a repetition rate of 1 kHz. We take 1 mJ of the 800 nm beam to generate pulses with a center wavelength of 590 nm via noncollinear optical parametrical amplification (TOPAS, Light Conversion). The obtained 590 nm beam is guided to a commercial acousto-optical programmable dispersive filter (AOPDF) (Dazzler, Fastlite) after being pre-compressed by a single-prism compressor [46] to partly correct for the positive group-delay dispersion of 20000 fs2 that is introduced by the Dazzler crystal. The pulse is compressed close to the bandwidth limit and characterized via pulse-shaper-assisted collinear frequency-resolved optical gating (cFROG) [47], yielding pulses with a duration of 25 fs with an error of < 0.01. A train of four identical pulses with variable phases is generated by the Dazzler and focused with an f = −150 mm focusing mirror into a capillary-type flow cell with square cross section (250 × 250 μm2, 131.310-QS, Hellma) and four polished sides. The sample is pumped through this cell using a micro annular gear pump (mzr-2942-cy, HNP Mikrosysteme GmbH). The focus has a diameter of 60 μm with an excitation energy of 55 nJ when all pulses overlap. The induced incoherent fluorescence signal is collected with a 0.25 NA microscope objective (04OAS010, CVI Melles Griot) in a 90° angle with respect to the excitation beam. This geometry, in combination with setting the excitation polarization to point in the direction of fluorescence detection, efficiently prevents any scattered light from reaching the detector. A second microscope objective of the same type images the fluorescence light of the excitation volume on a 0.22 NA multimode glass fiber with a core diameter of 400 μm (QP400-2-SR, Ocean Optics). The fluorescence signal can then be guided to an avalanche photodiode (APD, A-Cube S500-3, Laser Components) or a spectrometer (HR 4000, Ocean Optics). The spectrometer is used to confirm that only fluorescence signal is detected. For the actual 2D measurements we utilize the sensitive APD while attenuating the signal to suitable levels with absorptive neutral density filters (FS-3R, Newport). Hence, detection sensitivity can be increased easily for molecules that do not exhibit a high fluorescence quantum yield or for measurements at low optical density.
Fig. 2 Experiment. (a) Setup for rapid-scan 2D fluorescence spectroscopy, consisting of a Ti:Sa laser, a noncollinear optical parametrical amplifier (NOPA) (TOPAS, Light Conversion), a single-prism compressor, a pulse shaper and an avalanche photodiode. The core item is the pulse shaper based on an acousto-optical programmable dispersive filter (AOPDF), facilitating compression of the incoming pulses as well as the generation of multiple-pulse sequences with arbitrary phases and delays on a shot-to-shot basis. Neither spatial beam splitting nor mechanically moving components are necessary and therefore no adjustment of spatial overlaps in the excitation path is required. (b) Absorption (blue) and emission (green) spectra of cresyl violet in ethanol, and spectrum of excitation pulses (red).
Phase cycling is carried out as described in Section 2 in order to extract specific nonlinear contributions to the total fluorescence signal. We employ a 1×3×3×3 phase-cycling scheme [30], cycling all of the phase differences Δϕi1 through 0, 2/3π and 4/3π. Using a pulse shaper grants full control over amplitudes and phases of the pulses within the excitation sequence. The envelope and the carrier phase of each pulse can be either shifted in time together (γ0 = 1, laboratory frame) or only the envelope is shifted while the carrier phase is kept constant (γ0 = 0, rotating frame). The former leads to an oscillating signal as a function of coherence-time scans, while in the latter case any recorded oscillation reflects purely the system response. In order to keep the number of required sampling points low while still fulfilling the Shannon-Nyquist limit, we conduct the measurement in the rotating frame centered at the central wavelength of the excitation spectrum [46]. The exponential term in Eq. (1) containing γ0 then vanishes due to γ0 = 0, leading to 2D spectra centered around the origin in frequency space.
We acquire both coherence times, i.e., the time intervals between the first and the second as well as between the third and the fourth pulses, in steps of 6 fs from 0 to 84 fs each, thus requiring a total of 15 × 15 × 27 = 6075 pulse shapes for each population time. To account for the time evolution of 2D spectra, we scan the population time from 0 to 300 fs in 31 steps of 10 fs. Hence, the measurement of the entire data set consists of 188325 different pulse combinations. From the raw data the desired nonlinear signal contributions are reconstructed via Eq. (2). The temporal pulse shifting and phase cycling is carried out on a shot-to-shot basis with the 1 kHz repetition rate of the laser, thus taking 6 s of acquisition time for a full 2D spectrum at each population time and about 3 min for the entire data set. Additional intervals can be used for other population times or averaging. Note that it is possible to abort the measurement after each averaging interval, e.g., when a satisfying signal-to-noise ratio is reached or when investigating molecules that might not be stable enough for long measurements.
The maximum possible delay is limited by the Dazzler crystal size to 8000 fs, which can in principle be reached by fully compensating the group-delay dispersion using, e.g., the single-prism compressor. For many experiments on ultrafast dynamics this is sufficient. If one wants to investigate longer population times, one could combine two AOPDFs and sample the population time via a mechanical delay stage [35]. This approach offers the possibility of additional polarization pulse shaping at the cost of giving up the single-beam-path geometry and inherent phase stability between all four pulses. Phase drifts could still be compensated automatically in such an arrangement using the pulse shapers [36].
Currently, the repetition rate of our rapid-sampling implementation is limited to 1 kHz as determined by the Dazzler crystal size and the driver software. In other implementations using phase modulation, 250 kHz [33] or MHz repetition rate lasers were used [32], or a 2D spatial light modulator facilitated switching between phase matching and phase cycling conditions [37]. It is difficult, however, to compare directly the various implementations in terms of total acquisition time required for reaching a certain signal-to-noise level. This difficulty arises because the noise sources depend on details of the sample, the laser, the setup, and the environmental conditions that differ between laboratories. Nevertheless, quoting measurement times from the papers, Warren et al. reported 3 s for recording 65536-pulse phase-cycled data in an atomic gas sample [28], while other implementations take up to 1200 ms waiting time for each time delay step [29].
We have established the usefulness of shot-to-shot sampling previously for transient absorption spectroscopy in a direct comparison between various modes of averaging [38]. This demonstrated that measurement times can be reduced dramatically under appropriate conditions, and thus shot-to-shot rapid sampling is also beneficial in 2D spectroscopy. A detailed analysis of the noise level reached as a function of averaging is provided in Section 4 below. The present single-beam geometry offers the additional advantage of compactness, inherent phase stability and ease of alignment.
We validate our technique using commercially available cresyl violet (Radiant Dyes GmbH) dissolved in ethanol with a concentration of 0.1 mM at ambient conditions.
4. Results and discussion
The employed 1 × 3 × 3 × 3 phase-cycling scheme results in a set of 27 time-domain 2D maps for each population time. This raw data set (not shown here) contains all different nonlinear contributions. The raw data is weighted according to Eq. (2) with the factors β, γ and δ chosen for a specific nonlinear contribution. Fast Fourier transformation of the weighted time-domain data with five-fold zero padding yields the 2D frequency maps. Figure 3 shows the real-valued time-domain (a, c) and frequency-domain (b, d) maps of the rephasing (β = 1, γ = 1 and δ = −1; a, b) and the nonrephasing contribution (β = −1, γ = 1 and δ = −1; c, d) at a population time of T = 50 fs.
Fig. 3 Real part of the time-domain (a, c) and frequency-domain maps (b, d) of the (a, b) rephasing and (c, d) nonrephasing contributions to the total signal with axes labeled for the rotating-frame measurement. The color bar indicates the signal amplitude at each pixel and has been normalized to the highest absolute value for each graph separately.
Adding up the rephasing and nonrephasing frequency-domain maps for each population time yields absorptive 2D spectra, three of which are shown in Fig. 4(a) for T = 0, 100, and 200 fs. While the spectra in Fig. 3 are displayed in the rotating frame, we have shifted the absorptive spectra to the center frequency of the rotating frame by relabeling the axes correspondingly, making the results directly comparable with laboratory-frame measurements. Note that the sign of the absorptive signals is negative in the investigated frequency range. This results from an odd amount of interactions from the right side of the Feynman diagram [10].
Fig. 4 (a) Absorptive spectra at selected population times (0 fs, 100 fs, 200 fs); the color bar indicates the amplitude of the signal at each pixel and has been normalized to the highest absolute value for T = 0 fs. (b) Time evolution of the signal integrated over the region of interest marked with a green square in (a).
The absorptive spectra are exemplarily analyzed by integrating a selected region of interest [green square in Fig. 4(a)] for each population time step. Figure 4(b) shows the integrated signal plotted against population time and revealing an oscillatory behavior with a wavenumber of 625 cm−1. This result is in fair agreement with literature (585 to 595 cm−1) [39–43].
The spectra shown in Figs. 3 and 4 have been averaged 400 times, but it is possible to use far less averaging and thus decrease the measurement time dramatically down to about 6 s for one population time. Figure 5(a) provides a comparison of absorptive spectra for different amounts of averaging. An increasing number of averaging steps naturally improves the signal-to-noise ratio, but it is apparent that the relevant part of the 2D information is available already with very little or even without averaging. We evaluate quantitatively the error of a 2D spectrum containing X × X pixels with amplitude xij in column i and row j after A-fold averaging,
where the map with the maximum amount of averaging A = 400 is taken as the reference.Fig. 5 (a) Absorptive 2D spectra at a population time of T = 50 fs for varying amounts of averaging, from left to right: 1×, 10×, 400×; the color bar indicates the amplitude of the signal at each pixel, normalized individually for each plot to the maximum value. The normalization factor is further adjusted in the evaluation of the error for each A such that e(A) is minimized. (b) Blue: Error e(A) of the absorptive 2D maps for various amounts of averaging A with respect to the absorptive 2D map using A = 400 as a reference; red: expected errors for Gaussian statistics with .
The error is plotted as a function of averaging steps in Fig. 5(b) (blue) and follows qualitatively the behavior expected for Gaussian statistics (red). In order to obtain an error of < 0.05, it is sufficient to perform 10-fold averaging. For the presented parameter settings this corresponds to a total measurement time of 10 × 6 s = 1 min for all 15 × 15 coherence times and 27 phase-cycling steps. This results in an interesting perspective for experiments for which fast data acquisition is required, enabling one to measure, e.g., molecules that are not stable over extended periods of time.
5. Conclusion
We implemented a novel setup for pulse-shaper-assisted rapid-scan 2D fluorescence spectroscopy and demonstrated it on cresyl violet in ethanol. A 2D spectrum can be acquired in about 6 s for one population time and 15 pixels resolution for each coherence frequency axis. The acquisition of 31 population time steps was performed in 3 min without averaging. We observed a signal oscillation over population time, in agreement with literature [39–42] and own measurements [43]. The presented method grants rapid data acquisition due to the shot-to-shot modulation of the pulse train, combined with the sensitivity of fluorescence measurements that can in principle be carried out down to the single-molecule limit [48,49]. Additionally, rapid scanning offers the opportunity to investigate photochemically unstable substances or systems undergoing kinetic photochemical transformation processes. Error analysis revealed that a 2D spectrum for one population time can be measured within 1 min in order to obtain a root-mean-square error of < 0.05. Given that neither beam splitting nor recollimation nor mechanically moving components are required, the method is inherently phase stable, compact, and easy to align.
Funding
European Research Council (ERC) Consolidator Grant “MULTISCOPE” and European Cooperation in Science and Technology (COST) Action MP1403 “Nanoscale Quantum Optics”.
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