1. Introduction

Coherent two-dimensional electronic spectroscopy (2DES) is a powerful technique for resolving excited-state dynamics, such as energy transfer, within (coupled) molecular systems [1,2]. By observing the third-order nonlinear response as a function of excitation and emission frequencies as well as waiting time, 2DES provides a more detailed view than one-dimensional techniques like transient absorption spectroscopy. Many phenomena have been investigated including, among others, exciton dynamics in natural [3,4] and artificial light harvesting [5–7], electronic dynamics in semiconducting materials [8–10], or photochemical reactions [11]. Several review articles and books illustrate the broad applicability [1,2,5,12–16].

For most applications of 2DES, spectral bandwidth is a critical parameter. If one desires to resolve 2D cross peaks between substantially separated spectral features, this requires a correspondingly broad bandwidth that covers the relevant transitions simultaneously. It is also important that the phase-matching condition is fulfilled over the full bandwidth in order to keep to a minimum any 2D peak-shape distortions [17–20]. Related to that, one should seek to employ beam profiles with as little spatial chirp as possible such that the interaction of the sample with the different spectral components of the laser is uniform throughout the overlap region. In the present work, we describe 2DES that provides an improved solution to these issues.

Various 2DES implementations have been reviewed recently [21]. To date, most 2DES realizations employ non-collinear optical parametric amplification (NOPA) as a light source [15,21]. Its bandwidth determines the observable spectral range and temporal resolution of a 2DES measurement [21]. By operating at a specific phase-matching angle, NOPA is able to provide ultrabroad bandwidth and few-cycle pulse duration in cases of delicate compression [22–24]. However, as a consequence of pulse-front mismatch present in this configuration, spatiotemporal distortions (so-called spatial chirp) of the generated beam may arise [25]. In order to avoid the spatial chirp, sophisticated technical improvements on NOPA such as careful choice of focal geometry [26] and anamorphic pumping [27] or double stage amplification [28] is required. 2DES in pump–probe geometry provides the opportunity to broaden the detection frequency range by using a supercontinuum as a probe, but the excitation axis is still limited by the source (e.g., NOPA) bandwidth [21,29]. Using a white-light produced in YAG crystals for all pulses requires high oscillator strengths of the investigated transitions as the available light intensity is typically low [9].

In recent years pulse compression based on a gas-filled hollow-core fiber (HCF) [30,31] or filamentation in a gas [32,33] have provided new opportunities for nonlinear optics and ultrafast spectroscopy. In general, filamentation in gases provides higher power efficiency than HCF, but HCF provides better beam quality over a wide pressure range and the generated supercontinuum is more easily compressible by using dispersive mirrors [34]. Compared to NOPA, HCF provides higher conversion efficiency (up to 60%) upon a sub-mJ input level by properly matching the input beam to the basic mode (EH₁₁) of the fiber [31,35], and excellent output beam characteristics are reachable by HCF [31,35,36]. HCF-generated light properties can be adjusted by using different types and pressures of the gas filling. Since the supercontinuum generated in HCF is accompanied by a smooth dispersion with respect to frequency, the following pulse compression is relatively easy to achieve [37–39]. For these reasons, HCF is an attractive option complementing NOPA.

Apart from delivering the required bandwidth at sufficient intensity, it is also challenging in broadband noncollinear 2DES to achieve proper phase matching. For undistorted 2DES signals in “photon-echo geometry” both the momentum conservation law k_s = – k₁ + k₂ + k₃ and the energy conservation law ω_s = – ω₁ + ω₂ + ω₃ have to be fulfilled between all spectral components of all beams. Here the k_j denote wave vectors of the excitation beams (j = 1, 2, 3) or the signal (j = s) and ω_j their respective angular frequencies. Moreover, in order to allow heterodyne detection the signal beam has to be overlaid with the LO beam of wave vector k_LO.

The various beam geometries from the literature [21] have different advantages and disadvantages. There is likely not one particular implementation that would be best for all 2DES purposes. Instead one has to weigh the strength against the drawback for each method and may reach a different conclusion depending on the particular application. For ultrabroadband 2DES, realizing phase matching is most critical. It has been demonstrated [18,19] that if the incident beams are arranged in box geometry with all spectral components collinear for each individual beam (as achieved, e.g., by a pair of beam splitters) the energy and phase-matching conditions are not fulfilled perfectly and some extent of distortion of 2D spectra is unavoidable. Two effects are most prominent for ultrabroadband excitation [18,19]: 1) The combination of k_j (j = 1, 2, 3) of different spectral components (i.e., wave vectors of different length) leads to k_s pointing into a different direction than k_LO. The imperfect overlap leads to an apparent decrease of such an off-diagonal signal (“directional filtering”). 2) The length of |k_s| is different from ω_sc (with c the speed of light). Therefore the signals emitted from different layers of the sample destructively interfere and are attenuated (“phase mismatch”).

Broadband 2DES based on gas filamentation [40–42], HCF [43], and NOPA [44,45] light sources have been demonstrated recently. In most of these cases [40–44], conventional beam splitters were used to generate the four pulses which in general leads to directional filtering [18,19]. While using a small crossing angle in boxcar geometry reduces this peak-shape distortion, this artefact can be removed completely using a diffractive grating to generate the four pulses. This is especially relevant when dealing with broadband supercontinua, as directional filtering is proportional to the laser bandwidth [18,19]. Grating arrangements for pulse splitting and recombination have been pioneered by Nelson [46,47] and Miller [48–50] for transient-grating spectroscopy, and later this general idea has been adopted and modified to implement various 2DES geometries [45,51–55]. A main motivation at the time was to avoid “time smearing” [47,49] and to achieve phase stability between the different split-up and recombined beams [45,53]. We showed later that inherent phase stability in 2DES can also be achieved without diffractive gratings using only conventional optics [56], which has several advantages. For broadband excitation, however, phase-matching issues become increasingly relevant and diffractive optics may again become more favorable. Thus, in the present work, we employ a grating-based 2DES setup that we developed and described previously for ultraviolet 2DES [57] and adopt and modify it for broadband 2DES in the visible domain.

From the grating equation it follows that the transversal k-vector component is identical for each spectral component leading to a higher angle of diffraction for red versus blue colors. By geometrical considerations it can be shown that directional filtering and phase mismatch are absent in this arrangement (i.e., k_s(ω_s) = k_LO(ω_s) and |k_s(ω_s)| = ω_sc for all ω_s) such that, in principle, undistorted 2D spectra can be acquired for spectral widths spanning up to an octave. This is because a diffractive-optic-based 2DES setup works as a 1:1 imaging system. If all beams originate from the same grating, the wave fronts of the beams, after passing through the setup, have to recreate replica of the grating independently of their angular frequency. As the wavefronts of all individual beams must coincide in the focal plane a perfect temporal overlap is achieved, which is the second advantage of diffractive optics [47,49].

In this work, we combine a 7-fs supercontinuum generated in HCF with a diffractive-optic-based 2DES spectrometer. This combination, not reported before to the best of our knowledge, allows for ultrabroadband 2DES and reduces peak-shape distortions to a minimum. For demonstration, we obtain absorptive real 2D spectra (after phasing) of cresyl-violet perchlorate in ethanol in the 500–700 nm wavelength range.

2. Experimental details

A sketch of the experimental setup is shown in Fig. 1. The setup consists of two parts: The HCF compressor generates an intense supercontinuum in the visible region which is compressed to 7-fs pulse duration, and then these pulses are delivered into the diffractive-optic-based 2DES spectrometer. For driving the HCF, a commercial Ti:Sa regenerative amplifier (Spectra-Physics Spitfire Pro) provides 800 nm, 35 fs, 4 mJ pulses at 1 kHz repetition rate. A small part (0.3–0.5 mJ) is used to pump an HCF (UltraFast Innovations) to generate a supercontinuum for 2DES. The HCF compressor is similar to the design of Goulielmakis and associates [37–39]. Briefly, a lens (f = 1.2 m) focuses the fundamental pulses into an Ar-filled fused-silica hollow-core fiber (110 cm long, 250 µm inner diameter). A complete enclosure is used for the input beam of the HCF to reduce air turbulence and thus stabilize beam-pointing stability. To reach the optimal spectral shape, 400 mW fundamental beam is coupled into the HCF filled with 1.05 bar static pressure of Ar, which generates ~220 mW supercontinuum.

 

Fig. 1 Experimental scheme: CPA – chirped-pulse amplifier; FL – fused silica focus lens (f = 1 m) with anti-reflective coating; GV – connection to gas supply and vacuum pump; DM – dispersive mirrors; WP – fused silica wedge pair for compensation fine tuning; NDF – neutral density filter; DO – diffractive-optic cross grating; C1 and C2 – double choppers for fast data acquisition and scattering removal; DL1 – delay 1 for coherence time with piezo actuator; DL2 – delay 2 for population time with combination of piezo actuator and motorized translation stage; LO – local oscillator for heterodyne detection; SC – flow-cell sample cuvette (for 2D measurement) or 0.5 mm BK-7 window (for TG-FROG characterization); P – 45° periscope to orient the signal beam profile parallel with plane of the optical table.

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The generated supercontinuum is recollimated and then compressed by dispersive mirrors (PC70, UltraFast Innovations GmbH). The double-angle design [58,59] for oscillation compensation of the group-delay dispersion (GDD) provides PC70 mirrors with an average GDD of approximately –70 fs² per double bounce with near flat phase shape over more than an octave of bandwidth (500–1050 nm). As a result, the PC70 mirror has been demonstrated to be capable of supporting compression down to 1.4-cycle pulses (3.2 fs) [60]. The strongly amplitude-modulated spectral part of the supercontinuum in the near-infrared region close to the driving wavelength is removed by introducing two customized dispersive mirrors (BS1501, UltraFast Innovations GmbH) which were optimized to match the dispersion character of PC70 mirrors but with a spectrally narrowed high-reflective range and minimum GDD distortion at the edge of the working wavelength. We adjust the bounces on the dispersive mirrors to achieve a total amount of –420 fs² GDD, while a pair of fused-silica wedges is used for the fine tuning of GDD compensation. The GDD induced by transmission through air and an attenuator after the compressor is also compensated. The compressed pulses (~150 mW) with smooth spectral shape are further attenuated and delivered into an all-reflective diffractive-optic-based 2D spectrometer in fully noncollinear geometry. The 2DES setup corresponds mainly to the one we reported previously [57], but with some additions and modifications as described below.

Briefly, the HCF supercontinuum is focused onto a reflective crossed grating (g = 6.25 µm), and the generated four diffractive beams [(0th, 1st), (0th, −1st), (1st, 0th), and (−1st, 0th) orders of diffraction] are collimated by an off-axis parabolic mirror (f = 15 cm). Three of these beams are used for excitation and one for heterodyne detection in box geometry. They are manipulated in a pairwise fashion to ensure phase stability. Time delays are introduced for coherence time (delay between beam 1 and 2) and population time (delay of beam 3 and 4 with respect to beam 1 and 2) by using a combination of piezo actuators (PX 200CAP, Piezosystem Jena) and a motorized stage (MFA-CC, Newport). The local oscillator (LO, beam 4) passes a 1-mm-thick attenuator to reduce its intensity and to introduce ~1.7 ps time delay with respect to the other pulses. All beams are focused into the sample by a second off-axis parabolic mirror (f = 15 cm). The spectral interference between LO and nonlinear signal is recorded with a CCD spectrometer (Acton SpectraPro 2500i with PIXIS 2K). The pump beams 1 and 2 are chopped by a pair of optomechanical choppers cycling through the configurations “beam 1 open”, “beam 2 open”, “both beams open” and “both beams closed” on a five-shots-to-five-shots basis in order to eliminate unwanted scattering contributions. For the reasoning behind the choice of beams 1 and 2 to be chopped see Ref [61].

The temporal characterization of pulses is performed in the same setup. For transient-grating frequency-resolved optical gating (TG-FROG) characterization [62–64], the sample cuvette is replaced by 0.5-mm-thick BK-7 glass. Pulses 1 and 2 are temporally overlapped, and the third-order signal is recorded at varying delay of beam 3 by the CCD spectrometer, with the LO blocked. For “phasing” the measured 2D spectra [51], transient absorption measurements are performed in the same setup as 2DES, with beam 1 being used as pump and the LO beam as probe. The intensity of both beams is not changed with respect to the 2D measurements.

3. Generation and characterization of broadband pulses

By finely adjusting the in-coupling, fundamental power, gas pressure, and compression of fundamental pulses, a supercontinuum spanning from 400 to 950 nm is generated in the HCF as shown in Fig. 2(a). The EH₁₁ mode is selected by an iris, compressed by the dispersive mirrors, and used for 2DES, with the highly modulated spectral part above 720 nm removed for avoiding artifacts in 2D spectra. The resulting smoothed spectrum of the compressed pulses as observed at the sample position is shown in Fig. 2(b). It spans from 480 nm to 710 nm (blue line) and covers the entire absorption spectrum of cresyl-violet perchlorate (CV) in ethanol (orange shaded). The bandwidth at the sample position is sufficient to support pulses of ~5.2 fs duration. The stability of the compressed supercontinuum at the sample position was measured by collecting spectra every 30 seconds over a long period (> 1 h). We observed a power fluctuation of 1.8% (relative standard deviation) of HCF output, while the main peaks around 565 nm and 635 nm gave spectral fluctuations of 0.62% and 0.58%, respectively. For comparison, 4% fluctuation of signal and idler output due to the Poissonian statistics upon 0.5% fluctuation of pump energy has been reported using NOPA [65], although one has to be cautious with a direct comparison to HCF because a different driving laser has been employed in the cited work.

 

Fig. 2 (a) Supercontinuum spectrum generated in an Ar-filled HCF. (b) Supercontinuum spectrum at sample position after compression and spectral selection (blue line) and linear absorption of CV in ethanol (orange shaded).

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Regarding spatial chirp, we performed a spatially resolved spectral measurement on the focused supercontinuum by using a 50-µm pinhole at the sample position. Moving the pinhole in horizontal (x) and vertical (y) directions, the spectra at different positions in the focal plane were measured as displayed in Fig. 3. It can be seen that the spectral shapes in the periphery are quite similar to the center (x₀, y₀). This is a consequence of the homogeneous beam profile arising from the HCF. In y direction, no spatial chirp is observed; the slight alteration of spectral shape and covered region in x direction might due to non-perfect focusing using the off-axis parabolic mirror.

 

Fig. 3 Spatially resolved supercontinuum spectra at the sample position measured through a laterally translated 50-µm pinhole. The focus center is indicated by coordinates (x₀, y₀), while translations in horizontal (x) and vertical (y) directions are marked with “+” and “–”. The diameter of the focus spot is approximately 150 µm of 1/e² intensity.

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In order to characterize the compressed pulses, a TG-FROG measurement was performed in the same 2DES setup. Two stationary beams (k₁, k₂) act as optical gating and interact simultaneously in BK-7 glass, while the third (k₃) is swept temporally. The signal beam in direction k_s under the phase-matching condition k_s = – k₁ + k₂ + k₃ is recorded by the CCD spectrometer. The diffractive optic we employed for purposes of 2DES also nearly eliminates the “time smearing” which may lead to temporal broadening [47,49], while the all-reflective design ensures that extra GDD is introduced neither for the TG-FROG measurement nor for 2DES. Therefore, TG-FROG provides reliable characterization of the pulse duration of compressed pulses as well as the temporal resolution of our 2DES experiment. Figures 4(a) and 4(b) show measured and retrieved FROG traces, respectively. The retrieval was performed using commercial FROG software (Femtosoft Technologies, version 3.2.4). The retrieved temporal profile and spectrum in Figs. 4(c) and 4(d) indicates 6.9 fs pulse duration (FWHM) and 98 nm bandwidth (FWHM), leading to a time–bandwidth product of 0.58. This is close to the bandwidth limit as can be inferred from the nearly flat spectral phase in Fig. 4(d) throughout the 500–690 nm region. A spectral phase jump of 1.5π was observed in the 690–700 nm region, which might result in the satellite structures around the primary pulse as observed in the FROG trace and the retrieved temporal profile [32]. Nevertheless, the satellite remains below 5% of the maximum intensity and thus allows clean nonlinear multipulse spectroscopy experiments. The long-term phase and pulse duration stability was verified by taking 10 FROG traces within 2 hours, which gives an averaged statistical spectral phase error of 0.21 rad (~4.2%) and a temporal duration and variations of (6.9 ± 0.2) fs. The FROG retrieval error varied from 0.0054 to 0.0096.

 

Fig. 4 TG-FROG measurement in a 0.5-mm BK-7 glass at the sample position. (a) Measured and (b) retrieved FROG trace. (c) The retrieved temporal profile reveals a pulse duration of approximately 7 fs with a FROG error of 0.0082. (d) The corresponding spectral profile shows only small remaining dispersion, i.e., an almost flat phase. The phase is blanked for intensity values below 1% of the maximum.

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4. Broadband 2D electronic spectroscopy

In order to demonstrate the applicability of the HCF-based supercontinuum to our diffractive-optic-based broadband 2DES setup, we performed measurements of CV in ethanol solution using the compressed and spectrally selected supercontinuum from Fig. 2(b). A typical energy of 15 nJ per pulse was used for all four beams with s polarization, while the LO was attenuated by 1 or 2 orders of magnitude. The sample solution was prepared with ~0.4 OD absorption at 600 nm and pumped through a 0.2-mm-path-length flow cuvette with 0.2 mm fused-silica windows.

Population time (T) was scanned in 5-fs increments by the motorized stage up to 1300 fs delay. For each population time, the spectral interferometry of LO and photon-echo signal was recorded by the CCD spectrometer at a series of coherence times (τ) with 0.8 fs increment in a 160 fs range around the temporal overlap. With the double-chopped acquisition scheme, one 2D spectrum at any given population time can be measured within approximately 3.6 minutes, which includes averaging of 40 full cycles of chopper configurations for one interferogram and 10 ms exposure time of the CCD camera for each chopper configuration. This ensured a resolution of 250 cm⁻¹ along the excitation axis of acquired 2D spectra. The resolution of 100 cm⁻¹ along the detection axis was determined by the time-domain window used in the Fourier analysis. For present measurements, a 300 lines/mm grating was used for the CCD spectrometer to provide both enough detection range (495–674 nm) and spectral resolution (0.087 nm/pixel) for interferometry. Due to the high stability of the HCF light, it was not necessary to repeat the measurement at each population for further averaging. The entire scan for 264 different population times took about 16 hours. 2D amplitude spectra are obtained after Fourier evaluation and presented in Figs. 5(a)-5(c) at selected population times of T = 250 fs, 750 fs and 1300 fs, respectively. The red edge (ω₃/2πc < 14900 cm⁻¹) of the 2D amplitude spectra are slightly restricted by the pulse bandwidth along the emission axis (i.e., probe, ω₃/2πc), while the pulse bandwidth is sufficient to resolve the full peak along the excitation axis (i.e., pump, ω₁/2πc). The 2D amplitude spectra show a “regular” spectral shape and no evident amplitude suppression against off-diagonal signals that would arise from directional-filtering distortions [18]. This indicates the validity of our approach for ultrabroadband 2DES.

 

Fig. 5 2DES of CV in ethanol for population times of T = 250 fs (left column), 750 fs (middle column) and 1300 fs (right column): (a)–(c) 2D amplitude spectra, (d)–(f) 2D absorptive spectra, and (g)–(i) 2D absorptive spectra projected onto ω₃/2πc (red) in comparison with transient absorption results (blue). Contour lines in 2D spectra are provided in 5% intervals of peak values at −10%, 5%, 0, 5%, 10%, …, 100% for the amplitude (upper row) and absorptive part (middle row).

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In order to fully resolve the real (absorptive) and imaginary parts of the sample’s nonlinear response, the phase of the measured 2D spectra must be determined [2]. We perform this phasing procedure using the projection-slice theorem as described previously [51], which relates the real part of the measured 2D spectrum integrated along its excitation axis and divided by square root of the local oscillator spectrum (so-called integrated projection) with the separately measured transient absorption (TA) data in the same setup. In order to exclude any effects from intensity-dependent signal modification, the intensities of both the pump and the probe beam were kept the same for the TA and the 2D measurements. The resulting absorptive 2D spectra (real part) are displayed in Figs. 5(d)-5(f) at corresponding population times. While the 2D amplitude spectra displayed a broad and structureless positive band, in the absorptive spectra a clear negative band arises for short emission wavelengths (ω₃/2πc > 18600 cm⁻¹) that can be assigned to excited-state absorption of CV, while the positive band probed around ω₃/2πc = 14900 – 18600 cm⁻¹ originates from ground-state bleach and stimulated emission. The comparison of the 2DES integrated projection (red) and transient absorption (blue) at the optimal phasing parameter is shown in Figs. 5(g)-5(i). Their coincidence through the entire broad spectral range demonstrates successful phasing, and the resulting spectral shapes are highly consistent with previously reported transient absorption spectra of CV in solution [66]. Correct phasing results are an important indicator for the validity of ultrabroadband 2DES because insufficient phase matching (directional filtering) could lead to deviations.

Analyzing quantum beating as a function of population time is of high interest in 2DES [13,14]. The absorptive 2D spectrum of CV at T = 1 ps is presented in Fig. 6(a), in which we selected three points (marked black, green and blue) to explore the quantum beating dynamics. The population-time cross section at selected points was globally fitted by exponential decay function (not shown). The remaining intense oscillation signals can be seen in Fig. 6(b), which may originate from the coherent superposition of vibrational levels. Figure 6(c) shows the corresponding Fourier-transformed power spectra of the oscillations. All selected points show similar quantum beating dynamics. The sharp peaks at 585 cm⁻¹ and 2820 cm⁻¹ are consistent with previously reported results measured by both 2DES and transient absorption spectroscopy [41,44].

 

Fig. 6 Analysis of oscillations. (a) Measured absorptive 2D spectrum of CV in ethanol at T = 1 ps. (b) Oscillation of the 2D signal along population time T for three exemplary points marked black, green, and blue in (a). (c) Fourier-transformed power spectrum of the oscillating dynamics from (b).

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5. Conclusion

The spectral observational range in 2DES is limited by the available bandwidth of the interacting laser radiation and may be further effectively reduced by spatial chirp and directional filtering effects. Furthermore, time smearing diminishes temporal resolution. Our new implementation addresses these issues by combining state-of-the-art hollow-core fiber compression and fully-reflective diffractive-optic-based 2DES in noncollinear geometry. Thus we realize broadband (500–700 nm) 2DES measurements with 7-fs temporal resolution and minimal cross-peak distortions. This approach is especially suited to investigate multichromophore systems with broad absorption spectra. The supercontinuum with smooth spectral shape and clean spatial profile is generated in an argon-filled hollow-core fiber (HCF) pumped by a Ti:Sa laser and compressed using dispersive mirrors. We demonstrated broadband 2DES of CV in ethanol. Measuring transient absorption in the same setup allowed us to phase the 2D data and obtain absorptive 2D spectra. While the resulting spectral shape and quantum beating behaviour is consistent with previous reports, we note that with the high temporal resolution, the present setup has the potential to observe extremely fast quantum beating dynamics corresponding to wavenumbers up to 3500 cm⁻¹.

In general, the HCF-based technique could be extended to an even broader wavelength range by employing modified filtering and thus utilizing a larger range of the supercontinuum from Fig. 2(a). In the wavelength region between 780 and 930 nm the intensity fluctuations are between 1 and 2%. It should also be possible to access other ranges. For instance, driving the HCF with the frequency-doubled fundamental would provide access to the 360–450 nm region [67,68], while the application of achromatic frequency doubling on the broadband visible light could provide broadband UV in the approximate 275–350 nm region [69,70]. In the case of an HCF filled with air instead of noble gases, largely red-shifted spectra could be generated providing the opportunity of broadband 2DES in the near-IR region [71].