1. Introduction

Two-dimensional electronic spectroscopy (2DES) is a powerful approach for studying excitonic structure and ultrafast dynamics in a wide range of systems [1,2] including natural [3–8] and artificial [9,10] light-harvesting systems, semiconductors, [11–13] and solar cell materials. [14,15] Two-color [16] and continuum probe [17] variations of 2DES are particularly useful for studying systems with large spectral congestion such as photosynthetic reaction centers, where cross-peaks can help disentangle excitonic structure and dynamics. [5,18–21] However, the cross-peak regions of 2DES spectra are often dominated by excited state absorption (ESA), the signal corresponding to the increase in absorption in the singly-excited state, which obscures the ground state bleach (GSB), the signal corresponding to the decrease in absorption in the ground state, and stimulated emission (SE) signals.

Fluorescence-detected 2DES (F-2DES) has garnered recent interest due to the sensitivity of fluorescence and its compatibility with microscopy due to the ease with which spectral filtering enables a collinear beam geometry. Multiple methods for F-2DES have been implemented [22–26] to study small molecular systems, [26–28] DNA, [29] and light-harvesting complexes. [30,31] In F-2DES, an additional pulse projects the coherent 2DES signal onto a fluorescent population. The addition of a fourth pulse results in two ESA signals with opposite signs. [27] Depending on the relative fluorescence quantum yield of the singly and doubly excited states, the ESA signals will fully or partially cancel, [27,32,33] which may offer an advantage for studying systems in which the coherent 2DES spectra are dominated by ESA. The relative advantages and disadvantages of coherent 2DES and F-2DES are still being established and appear to be system and question-dependent. [34] In coherent 2DES the signal is emitted on an ultrafast timescale determined by the dephasing of the optical coherence, while in F-2DES the excited state emits the detected fluorescence on a ∼ns time scale. The long-lived nature of the excited states in F-2DES allows for additional processes to occur that can strongly influence the F-2DES signal. These include exciton-exciton annihilation in multichromophoric systems [28,30,31,35] and Auger recombination in quantum dots, [36–38] which give rise to dominant cross-peaks in F-2DES spectra. In general, action-detected 2D spectroscopies such as F-2DES and photocurrent-detected 2D are susceptible to nonlinearities in the detection process [39] and incoherent mixing of linear signals [40] that can obscure the nonlinear signal of interest. [34,41,42]

The most commonly-used approach to F-2DES, pioneered by Marcus and coworkers, employs two Mach-Zehnder (MZ) interferometers where the phase of each arm is modulated at a unique acousto-optic frequency. [23,26,43,44] The nonlinear signals of interest are then detected at linear combinations of the applied frequencies. The phase-modulation method works well with high repetition rate lasers and offers high signal-to-noise ratios with short data collection times. We have shown that phase-modulation can be used for spatially-resolved F-2DES studies of photosynthetic bacteria. [30] Due to the high repetition rate of the laser excitation that is typically used in phase-modulated F-2DES, this method is less suitable for studying systems with long-lived excited states. Other implementations of F-2DES have employed pulse-shapers with kHz laser sources, making them more suitable for such studies. [24,25] These methods build on implementations of coherent 2DES that employed pulse-shapers to create the pump pulse pair. [16,17,45] Instead of using a separate probe pulse, a single pulse-shaper is used to create all three pulses for coherent 2DES, [46] or all four pulses for the F-2DES experiment, [24] utilizing phase-cycling to extract the nonlinear signals of interest [47]. The pulse-shaping approach has also been used in spatially-resolved F-2DES measurements [48]. These methods have limited bandwidth throughput as a result of the acousto-optic crystals used for phase-modulation/pulse-shaping. In addition, the maximum waiting time delay for the pulse-shaping method is limited to short delays determined by the characteristics of the pulse-shaper (typically ∼picoseconds).

To circumvent the bandwidth limitations of the acousto-optic crystals and expand the detection spectral range for F-2DES, we sought a method for generating phase stable pulse pairs in the visible. Cerullo and coworkers developed the Translating Wedge-based Identical pulses eNcoding System (TWINS) interferometer, which exploits birefringence to generate collinear, phase-locked ultrashort pulse pairs with a controllable time delay [49,50]. Featuring interferometric phase stability, broad spectral acceptance, high time resolution and reproducibility, the TWINS interferometer has been applied in spectroscopy and imaging from the ultraviolet to the infrared [50–53]. In particular, its high throughput over a broad bandwidth makes it a great fit for broadband applications. Here we combine our previous pulse-shaping-based approach that employed the Dazzler pulse-shaper [16,17] in the pump-probe geometry with a continuum probe pulse pair generated by TWINS to expand the bandwidth of F-2DES and enable long waiting-time measurements. We refer to this hybrid TWINS-Dazzler approach to F-2DES as TWIZZLER. We demonstrate TWIZZLER on a laser dye (IR144) and bacteriochlorophyll a.

2. Experiment

2.1 Experimental setup

An overview of the TWIZZLER setup is shown in Fig. 1. Briefly, a Ti:Sapphire regenerative amplifier (Spectra Physics Spitfire Pro) produces 4 mJ, 35 fs pulses centered around 800 nm at 1 kHz repetition rate. A portion of the output light (1.7 mJ) is used to pump a home-built degenerate optical parametric amplifier (DOPA), [54] generating near-infrared pulses between 680-920 nm. For the pump pulses, the DOPA output is partially compressed with chirped mirrors (CM, -3000fs², 700-900 nm, Femto Optics) and coupled into an acousto-optic pulse-shaper (Dazzler, Fastlite). The Dazzler compresses the pump pulse to ∼18 fs and creates a pulse pair (pulses 1 and 2) with controllable time delay (t₁) and relative phase (φ₂₁= φ₂ – φ₁). Additionally, we apply a time dependent spectral phase to scan t₁ in the partially rotating frame. [16,55] The pump pulse pair travels through a delay stage to scan the waiting time delay (T) and is picked off to be parallel to the probe beam. The pump polarization is controlled using a half-wave plate (HWP, Thorlabs AHWP05M-980) and a polarizer (Pol, Thorlabs LPVIS100-MP2). For the probe pulses, a portion of the 1300 nm pulse generated in the first two stages of the DOPA is picked off and focused into a Yttrium Aluminum Garnet (YAG, 4 mm, Newlight) crystal, producing a broadband white light continuum with a spectrum extending down to 550 nm. Short-pass filters remove residual near-infrared wavelengths. After collimation, the white light continuum is partially compressed by CMs (-280fs², 470-810 nm, Layertec) and fed into the TWINS interferometer to generate the probe pulse pair (pulses 3 and 4) with controllable time delay (t₃), implemented with a Newport LTA-HL stage. A broadband half-wave plate (HWP, Thorlabs AHWP05M-600) is employed to maximize the throughput of the TWINS by rotating the input polarization of the continuum to 45°.

 

Fig. 1. TWIZZLER experimental setup. The pulse-shaper (Dazzler) generates the pump pulse pair (pulses 1 and 2) with controllable time delay (t₁) and relative phase (φ₂₁), while the TWINS generates the broadband continuum probe pulse pair (pulses 3 and 4) with controllable time delay (t₃). Both beams are focused to the sample (S) with a spherical mirror (SM) in the pump-probe geometry. The fluorescence signal is collected in the 90-degree detection geometry. CM: chirped mirrors. HWP: half-wave plate. Pol: polarizer. APD: avalanche photodiode. Spect: spectrometer.

Download Full Size | PDF

The working principle of TWINS has been previously reported [50]. Briefly, it is composed of a birefringent plate (α-BBO, 12 × 12 × 4 mm, Shalom EO) and two sets of birefringent wedge pairs (α-BBO, 30 × 12 × 4.2(0.5) mm, Shalom EO) that are translated to vary the thickness of the material in the beam path. When a light pulse traverses a uniaxial birefringent material, the ordinary and extraordinary polarization components travel with different group velocities. Therefore, the relative time delay between two orthogonally polarized pulses can be scanned by continuously varying the thickness of the material (i.e., translating the wedge pair). The TWINS interferometer has previously been used to generate the pump pulse pair for 2D spectroscopy experiments, where pulse 1 is scanned and pulse 2 is stationary to ensure a constant T delay [49]. However, in our setup, the TWINS interferometer is used to generate the probe pulse pair. We thus require pulse 4 to arrive later than pulse 3 so that the waiting time delay (T) between pulses 2 and 3 is kept constant while scanning t₃. To ensure the correct time ordering, the birefringent plate we use in the TWINS interferometer is comparable in thickness to the wedges (4 mm thick vs 4.2 mm). Both pulses are delayed as a result, but pulse 4 is delayed further compared to pulse 3 due to birefringence, reversing the time ordering of the pulse pair. Pulses 3 and 4 are recombined after the TWINS interferometer by projecting onto the 45° polarization direction with a polarizer (Pol, Moxtek, PFU04C). One might also opt out of the last polarizer to enable other polarization schemes, as pulses 3 and 4 will be orthogonally polarized in this case.

Both the pump and probe pulses are focused onto the sample (S) with a spherical mirror (SM, f = 150 mm) in the pump-probe geometry. The pump and probe pulses are laterally overlapped but vertically displaced, with the probe above the pump as displayed in the inset (Side view) of Fig. 1. Combining the beams in this manner results in less power loss for the continuum probe compared with a fully collinear geometry. This geometry is also commonly used in coherent continuum probe 2DES making it relatively simple to add in a TWINS interferometer for F-2DES. At the sample position, the pump and probe spot sizes are ∼55 and 50 µm respectively. For the measurements we report here, the pump energy at the sample was 3.1 nJ and 8.8 nJ for IR144 and bacteriochlorophyll a respectively, whereas the probe energy was 0.5 nJ. For the IR144 experiments, the pump polarization was rotated 45° relative to the probe and the sample was in a 1 mm pathlength cuvette. For the bacteriochlorophyll a experiments, the pump polarization was set parallel to the probe and the sample was flowed through a 0.4 mm square capillary tube with a peristaltic pump to prevent photobleaching. Two distinct polarization conditions were chosen to demonstrate the ability to do polarization control in F-2DES, which is not possible in the single Dazzler phase-cycling implementation. Polarization control with the Dazzler phase-cycling would be possible with the use of two pulse shapers, which has previously been demonstrated for coherent 2DES [56]. The fluorescence signals were collected in the 90-degree detection geometry using a lens (f = 60 mm, diameter = 2”). Then, the signal was focused onto a photodiode (Femto, OE-200 or Hamamatsu, C12703-01) with a lens (f = 175 mm). Long-pass and neutral density filters were used to block scattered laser light and reduce the signal level to the linear regime of the detector, respectively. The signal was fed into a Boxcar Integrator (Stanford Research Systems, SR250) and the integrated signal was read out with a data acquisition card (National Instruments, PCIe-6321) triggered via the Dazzler. Thus, the data collection is synchronized with the cycling of the t₁ delay and φ₂₁ phase by the Dazzler. Synchronization with the TWINS stage motion is not needed since the t₃ delay is robustly determined from the linear fluorescence excitation interferogram. We need only initiate the continuous back and forth t₃ stage motion prior to starting the Dazzler streaming of the sequence of t₁ delays and phases as shown in Fig. 2.

 

Fig. 2. Scanning scheme where the Dazzler steps through the t₁ delays and ${\varphi _{21}}$ phases and t₃ delays are continuously scanned using the TWINS. The top panel shows the first cycle through the Dazzler delays and phases, while the bottom panel shows a single full scan of the t₃ delay by the TWINS. Note the delay from the TWINS is approximate and differs slightly for every wavelength.

Download Full Size | PDF

2.2 Data collection scheme

In F-2DES, the third-order polarization, ${\hat{P}^{(3 )}}({{t_1},T,{t_3}} )$ that is detected in coherent 2DES, is projected onto an excited electronic state by interaction with a 4th pulse. The measured fluorescence signal can be broken into three main contributions: the linear fluorescence from the pump pulses, the linear fluorescence from the probe pulses, and the nonlinear fluorescence-detected pump-probe and F-2DES signals. The emitted fluorescence contains the phase information encoded by the light-matter interactions, such that the phases of the rephasing and non-rephasing signals are given by ${\varphi _R} ={-} {\varphi _1} + {\varphi _2} + {\varphi _3} - {\varphi _4}$ and ${\varphi _{NR}} = {\varphi _1} - {\varphi _2} + {\varphi _3} - {\varphi _4}$ respectively. Typically, the rephasing and non-rephasing signals in F-2DES are separated from the linear fluorescence signals and the pump-probe signals through phase-cycling [22,24,25] or phase-modulation. [23,27,30,43] Here we use a combination of phase-cycling and frequency filtering. Phase-cycling of the pump pulses in the fully or partially rotating frame is readily implemented with the Dazzler. The TWINS interferometer operates in the partially rotating frame, but does not provide control over the relative carrier envelope phase for pulses 3 and 4 (φ₃ and φ₄). However, the linear and nonlinear signals appear at different locations in the frequency domain, making it possible to isolate the different signals as discussed in detail in Section 2.4. For example, the linear fluorescence excitation signal of the pump depends only on t₁ but not t₃, therefore upon 2D Fourier transformation, they will appear along the ω₃ = 0 axis. Similarly, the linear signals of the probe appear along the ω₁ = 0 axis. The F-2DES signals, on the other hand, depend on both t₁ and t₃. Nevertheless, the nonlinear signals are not well separated from the linear fluorescence of the probe because we operate close to the fully rotating frame to minimize the number of samples in t₁. To remove the contribution from the linear fluorescence of the probe, we employed 0-π phase-cycling.

To collect all the required combinations of t₁ and t₃ we continuously scan t₃ with the TWINS interferometer while rapidly and repeatedly stepping through t₁ as seen in the bottom panel of Fig. 2. The data is collected while the TWINS stage is scanned in both the forward and backward direction to increase the efficiency of data collection. Zooming on the first iteration of t₁ step scan (top panel of Fig. 2), we collect the two relative pump phases ${\varphi _{21}}$ = (0, π) for each t₁ delay while continuously scanning t₃. The pulse-shaper is synchronized with the data collection so there is no ambiguity in the t₁ delay and relative pump phase of each shot. However, since the TWINS stage runs continuously, the two phase measurements for each t₁ delay have slightly different t₃ delays. For our scanning speed of 0.48 mm/s, the spread of t₃ delays was ∼1 fs, which was corrected by interpolating the data onto a uniform set of t₃ delays.

In 2D experiments, the TWINS scanning speed and the number of shots to collect in each scan are chosen to satisfy the Nyquist sampling criteria. To minimize the effects of laser noise we collect the (t₁, t₃) time points required for the F-2DES scan as quickly as possible while staying above the Nyquist sampling rate. We first determine the range of the t₁ scan and the number of t₁ delays needed. The scanning speed for t₃ is then set such that the t₃ delay between consecutive shots with the same t₁ delay and phase meets the Nyquist sampling criteria. For IR144, the t₁ delay was scanned from 0 to 102 fs in 6 fs steps in the partially rotating frame using a reference wavelength of 850 nm and the t₃ delay was scanned around time 0 for a total of 1.1 mm of stage travel at a speed of 0.4 mm/s (corresponding to ∼-30 fs < t₃ < 30 fs). For bacteriochlorophyll a, the t₁ delay was scanned from 0 to 96 fs in 6 fs steps using a reference wavelength of 880 nm and the t₃ delay was scanned for a total of 2.8 mm of stage travel at a speed of 0.48 mm/s (corresponding to ∼-80 fs < t₃ < 80 fs).

2.3 TWINS reproducibility and calibration

Since we continuously scan the t₃ axis, the movement of the TWINS stage is not directly synchronized with the data collection and the t₃ axis is not identical for every scan. Nevertheless, the time-domain data can still be acquired reproducibly, which is demonstrated in Fig. 3 where we show a measurement of the linear autocorrelation trace of the white light continuum probe. Overall, the 100 individual scans line up well with the averaged scan. Without the use of any position tracking techniques, the standard deviation of the time jitter of the 100 scans is 1.83 shots, which corresponds to ∼0.09 fs for a scanning speed of 1 mm/s.

 

Fig. 3. (a) The averaged time-domain linear autocorrelation trace of the white light continuum probe used in the bacteriochlorophyll a experiment of 100 scans, measured by scanning the TWINS stage. (b) Zooming into the shaded area (orange) around the center of the autocorrelation in (a). Light gray: 100 repetitions of individual scans. Black: the average of the 100 scans. The scanning speed of the TWINS stage is set at 1 mm/s. Note that in linear measurements the TWINS can be scanned much faster than in 2D experiments since the t₁ scan and phase-cycling of the pump pulse pair are not needed. The standard deviation of the time jitter is 1.83 shots, which corresponds to ∼0.09 fs at the current scanning speed.

Download Full Size | PDF

The calibration of the probe frequency axis is performed by measuring the spectral interferogram of the probe pulse pair while scanning t₃ using the method originally described by Cerullo and coworkers [50]. From our experience, the calibration is robust enough to be performed separately from the actual experiment, and recalibration is only necessary when there is a major alignment change to the TWINS interferometer. To start, we block the pump beam, remove the sample, and couple the probe beam into a spectrometer. The spectral interferogram [57] as a function of t₃ is collected by continuously scanning the TWINS interferometer at a predefined speed (1 mm/s). As displayed in Fig. 4(A), the linear autocorrelation trace of each probe wavelength is plotted against the shot index (sampling time). After performing a Fourier transform along the shot index axis, we can locate a well-defined peak on the pseudo-frequency axis for each probe wavelength, which establishes a mapping between the pseudo-frequency and the real frequency. We fit the correlation of frequencies to a 3rd order polynomial function, as displayed in Fig. 4(B). The relative fitting error is consistently below 0.1% for the probe frequency range of interest, demonstrating the high accuracy of this method. As proof of validity, Fig. 8(B) demonstrates the good agreement between the linear absorption spectrum of bacteriochlorophyll a in ethanol measured with a UV-Visible absorption spectrometer (Genesys 10, Thermo Electron Corporation) and the properly calibrated linear fluorescence excitation spectrum (multiplied by the probe power spectrum) measured using the TWINS interferometer.

 

Fig. 4. (a) Spectral interferogram as t₃ is scanned with the TWINS. (b) Calibration curve and relative fitting error.

Download Full Size | PDF

The pseudo-frequency depends on the TWINS scanning speed and the data sampling rate. However, it is worth emphasizing that in an actual experiment the TWINS scanning speed can be different from the calibration speed. The scanning range also does not need to be the same as the experiment. It is only important that the physical alignment is the same. Additionally, as described in the previous section, the effective sampling rate along the t₃ axis varies according to the choice of the total number of t₁ steps and the number of phase-cycling phases. To ensure proper calibration of the probe frequency, the pseudo-frequency axis defined in the actual experiment differs by a calculated scaling factor (the ratio of the experiment speed to the calibration speed). Applying the fitting results to the modified pseudo-frequency axis gives us the properly calibrated probe frequency axis.

2.4 F-2DES data processing and phasing

To obtain phased F-2DES data we begin by averaging the round trips of t₃ and interpolating onto a common uniformly-spaced t₃ axis for each t₁ and phase combination. Following the procedure outlined in Fig. 5, we then take linear combinations of the averaged time domain signals for ${\varphi _{21}} = 0,\pi $. The sum of the two averaged time domain signals yields the linear fluorescence excitation signal from the probe: ${S_{Lin,probe}}({{t_1},T,{t_3}} )= {S_{{\varphi _{21}} = 0}}({{t_1},T,\; {t_3}} )+ {S_{{\varphi _{21}} = \pi }}({{t_1},T,\; {t_3}} )$. The difference between the measurements removes ${S_{Lin,probe}}({{t_1},T,{t_3}} )$, leaving the sum of the nonlinear signals and the linear fluorescence excitation signal from the pump: ${S_{{\varphi _{21}} = 0}}({{t_1},T,\; {t_3}} )- {S_{{\varphi _{21}} = \pi }}({{t_1},T,\; {t_3}} )\, = {S_{NL + Lin,pumps}}({{t_1},T,{t_3}} )$.

 

Fig. 5. Flow chart overviewing the data analysis procedure beginning with the measured signals, ${S_{{\varphi _{21}} = 0}}({{t_1},T,\; {t_3}} )$ and ${S_{{\varphi _{21}} = \pi }}({{t_1},T,\; {t_3}} )$, shown in purple. Signals corresponding to the linear fluorescence excitation signals from the pump and probe are shown in green and orange. Signals containing non-linear signals are shown in blue. The cartoon in the bottom center illustrates the frequency dependence of the different signals roughly scaled to reflect the different separation between the signals due to the different partially-rotating frame frequencies imparted by the Dazzler and TWINS.

Download Full Size | PDF

Time zero is precisely known for t₁ so the acquired 2D spectra do not need to be phased along the pump axis, whereas it is not precisely known for t₃ so it is necessary to phase the spectra along the probe axis to separate rephasing and non-rephasing signals and avoid phase-twisted lineshapes. Any slight differences in the scanning range between experimental runs do not matter, as t₃ = 0 is experimentally determined with the linear fluorescence excitation data collected simultaneously with 2D signals. Determining t₃ = 0 can be performed using the linear fluorescence excitation signal from the probe, either employing the approach of Helbing and Hamm, [58] as used by the Cerullo group [50], or as we have demonstrated previously. [43] We adopt the latter approach, where the time domain signals [${S_{NL + Lin,pumps}}({{t_1},T,{t_3}} )\; ,\; {S_{Lin,probe}}({{t_1},T,{t_3}} )]$ are Fourier transformed into the frequency domain [${S_{NL + Lin,pumps}}({{\omega_1},T,{\omega_3}} )\; ,\; {S_{Lin,probe}}({{\omega_1},T,{\omega_3}} )]$. Then, the linear fluorescence signals from the pumps and the probe $[{S_{Lin,pumps}}({{\omega_1},T,{\omega_3} = 0} )\; ,\; {S_{Lin,probe}}({{\omega_1} = 0,T,{\omega_3}} )]$ can be isolated by taking slices at ω₃ = 0 and ω₁= 0 respectively. The frequency domain data [${S_{NL + Lin,pumps}}({{\omega_1},T,{\omega_3}} )\; ,\; {S_{Lin,probe}}({{\omega_1},T,{\omega_3}} )$] is windowed with two Hann windows, centered around the positive and negative values of the probe frequency for every value of ω₁. This windowing removes any signals that do not depend on ω₃, such as zero frequency (ω₁= 0, ω₃= 0) contributions and ${S_{Lin,pumps}}({{\omega_1}} )$. Therefore, ${S_{NL + Lin,pumps}}({{\omega_1},T,{\omega_3}} )\; $ reduces to ${S_{NL}}({{\omega_1},T,{\omega_3}} ).\; $ The spectral phase $\Phi ({{\omega_3}} )$ is determined from ${S_{Lin,probe}}({{\omega_1} = 0,T,{\omega_3}} )$. To locate ${t_3} = 0$ and correct timing errors due to the stage motion, we compute: $S_{NL}^{\prime}({{\omega_1},T,{\omega_3}} )= {S_{NL}}({{\omega_1},T,{\omega_3}} )\ast {e^{ - i\Phi ({{\omega_3}} )}}$. Finally, $S_{NL}^{\prime}({{\omega_1},T,{\omega_3}} )$ is Fourier transformed back into the time domain, resulting in the signal with the corrected t₃ axis: $S_{NL}^{\prime}({{t_1},T,{t_3}} )$. The final phased spectra are obtained upon Fourier transform of the positive quadrant of the time domain data: $S_{NL}^{\prime}({{t_1} \ge 0,T,{t_3} \ge 0} )$.

3. Results and discussion

3.1 IR144

To demonstrate the broadband F-2DES method, we first measured IR144 (Exciton) in ethanol (Sigma Aldrich). IR144 was dissolved into ethanol to a final concentration with an optical density (OD) of 0.2 (1 mm pathlength). The linear absorption spectrum of IR144 along with the corresponding pump and probe spectra are shown in Fig. 6(A). IR144 has a single broad absorption feature peaking at 754 nm. The pump excites a narrow portion of the broad absorption, whereas the probe covers the entire absorption band.

 

Fig. 6. (a) The IR144 absorption (black), pump (orange) and probe (green) spectra. (b) Time-domain nonlinear signals of IR144. (c) Phased frequency-domain nonlinear signals of IR144, with the rephasing and non-rephasing signals clearly separated in frequency space.

Download Full Size | PDF

The resulting time domain nonlinear signals extracted from the linear combination of the cases described in Section 2.4 are shown in Fig. 6(B). The time domain data is symmetric around time zero in the t₃ axis (shot number ∼ 1431), while t₁ is only scanned in the positive direction. The data shows clear dependence on both t₁ and t₃ with the signal decaying away from the origin. The symmetric scanning of t₃ enables easy determination of t₃ = 0 from the linear interferogram. After the Fourier transformation of the positive quadrant along both the t₁ and t₃ axes, the nonlinear signals in the frequency domain are visualized in Fig. 6(C), where the rephasing and nonrephasing signals appear in different quadrants due to their differently-signed coherence frequencies during t₁ [59]. The pump-probe signals appear at (0, ${\pm} $ω₃) and/or (${\pm} $ω₁,0) depending on the time ordering of the pump and probe pulses, whereas the rephasing and non-rephasing are at $({ - {\omega_1},{\omega_3}} )$ and $({{\omega_1},{\omega_3}} )$ respectively. The pump-probe signals are suppressed relative to the 2D signals during the phasing procedure, so they do not appear in Fig. 6(C). The additional two signals are the conjugates of the rephasing and non-rephasing. By carefully selecting the reference wavelength for the partially rotating frame, the number of t₁ points needed for the Nyquist sampling criteria can be minimized while ensuring the signals are well separated in the frequency domain.

As seen in Fig. 7(A), the rephasing and non-rephasing signals exhibit broad spectral features roughly along the diagonal and anti-diagonal respectively with the expected characteristic lineshapes. At T = 2 ps, the rephasing + non-rephasing (absorptive) spectrum shows a broad response across the detection axis. Note that the response is all positive, corresponding to the GSB and SE, with no apparent ESA signal, highlighting the ability of F-2DES to suppress ESA signals. The spectral response is consistent with previous F-2DES studies of laser dyes, cresyl violet [24] and IR140 [43], with the Dazzler implementation and phase modulation implementation of F-2DES respectively. We note that the F-2DES spectral lineshapes are likely influenced by the chirp of the continuum probe, which could be post-corrected as has been done prevsiously in coherent 2DES measurements [60]. In Fig. 7(B), we compare the absorptive spectra with different data acquisition times. The signal-to-noise ratio improves dramatically in the first ∼10 minutes of data acquisition. Further averaging up to ∼22.5 minutes (250 round trips of t₃ scanning) continues to offer some improvement. We note that our data acquisition times are similar to those reported by Draeger et al. who averaged for 40 minutes to obtain F-2DES spectra of cresyl violet with a high signal-to-noise-ratio [24].

 

Fig. 7. (a) The rephasing, non-rephasing and absorptive spectra of IR144 in ethanol at T = 2 ps. Alongside the excitation and detection axes we show the product of the linear fluorescence excitation spectrum g(ω) and the power spectrum of the pump and probe respectively. Also shown are the pump (brown) and probe (green) power spectra. The modulations on the red edge of the probe spectrum arise from the chirped mirrors. (b) Comparison of the absorptive spectra with different data acquisition times.

Download Full Size | PDF

3.2 Bacteriochlorophyll a

To demonstrate the ability of broadband F-2DES to probe multiple electronic transitions we study bacteriochlorophyll a, a pigment found in the photosynthetic antennas and reaction centers of many photosynthetic bacteria [61]. Bacteriochlorophyll a has electronic absorptions in the Q_x and Q_y bands at 600 nm and 780 nm, respectively, with Q_y displaying a prominent vibronic shoulder of comparable oscillator strength to Q_x. The pump excites the Q_y band plus the edge of the vibronic shoulder while the probe spans the Q_x and Q_y regions. The sample used in this experiment was prepared by dissolving bacteriochlorophyll a (R. Sphaeroides, Fisher Scientific) in nitrogen purged ethanol to an OD of 0.18 (0.4 mm pathlength). The linear absorption spectrum of bacteriochlorophyll a is presented in Fig. 8(A), along with the corresponding pump and probe spectra used in the experiment.

 

Fig. 8. (a) Bacteriochlorophyll a in ethanol absorption spectrum (black) with pump (orange) and probe (green) spectra used in the experiment. The main absorption features are the Q_x band at 600 nm and the Q_y band at 780 nm, as well as a vibronic shoulder at 720 nm. (b) The comparison between the absorption spectrum measured with a UV-Visible spectrometer and the properly calibrated linear fluorescence excitation spectrum (multiplied by the probe power spectrum) measured using the TWINS interferometer. The spectra show good agreement, validating the TWINS calibration procedure discussed in section 2.3. Note that the slight mismatch at the Q_x peak is a result of the probe spectral shape and does not impair the accuracy of the calibration result. (c) The rephasing, non-rephasing and absorptive F-2DES spectra of bacteriochlorophyll a at T ∼ 0 ps, with the corresponding linear fluorescence excitation spectra from the pump and the probe. Due to the chirp of the probe, the waiting time delay T is in reference only to the absorption maximum of the Q_x band. The vertical dashed lines label the Q_y peak and the vibronic shoulder in the excitation axis, while the horizontal dashed lines label all three absorption features in the detection axis. The F-2DES spectra took ∼5 hours to acquire.

Download Full Size | PDF

The resulting 2D signals are shown in Fig. 8(C), where we plot the rephasing, non-rephasing and absorptive spectra for T ∼ 0 ps. Due to the chirp of the probe, the waiting time delay T is in reference to the absorption frequency of the Q_x band. Given the weak oscillator strength of the Q_x band and the vibronic shoulder, as well as the low intensity of the probe, a large number of averages is needed to obtain a decent signal-to-noise ratio. Each set of spectra for a single T delay took roughly 5 hours (1500 round trips of t₃ scanning). Apart from the dominant diagonal Q_y feature, we also observe cross-peaks between Q_y and the vibronic shoulder, and Q_y and Q_x, respectively. At T ∼ 0 ps, the cross-peak between the Q_y and the vibronic shoulder as well as between Q_y and Q_x are evident in all three spectra. The cross peak associated with the vibronic shoulder is more pronounced than the Q_x cross peak. This is likely due to the lower probe amplitude in the Q_x region and the near orthogonal orientations of the Q_y and Q_x transition dipoles. [62] Improvements to the signal-to-noise ratio could be made by increasing the probe power and fully compressing the probe. For example, the use of a continuum probe generated by a hollow-core fiber and compressed with chirped mirrors would enable higher signal levels by using higher probe power. Asymmetric scanning of t₃ would also considerably reduce the data acquisition time. Since only the t₃ > 0 region is used for the final Fourier transform, which has the correct time ordering of the probe pulse pair (pulse 3 reaching the sample earlier than pulse 4), it is possible to further reduce the t₃ scanning range to approximately half of its current value, as long as one ensures that t₃ = 0 can be robustly determined.

4. Conclusion and outlook

In summary, we have demonstrated broadband F-2DES by combining a pulse-shaper for the pump pulses with a birefringent interferometer for the probe pulses. To separate out the nonlinear signals of interest we employ a combination of phase-cycling and frequency filtering. Given the utility of coherent 2DES with a white light probe in providing insights into systems with complex and congested spectra, [5,19,63–66] broadband F-2DES has exciting potential with the advantage of reducing dominant ESA signals. In our current implementation, the white light probe has a large temporal chirp, so the waiting time (T) is wavelength dependent. Further compression or chirp correction, as has been demonstrated in coherent 2DES, [60] is necessary to extract dynamics. With an alternative method of continuum white light generation such as hollow core fiber continuum generation, [67] higher probe power can be achieved, enabling higher F-2DES signal levels and reduced acquisition time. Further reduction in acquisition time could be achieved with asymmetric scanning of t_3.

Each of the three F-2DES implementations (phase-modulation via MZ interferometers, phase-cycling via pulse-shaper, broadband via pulse-shaper and birefringent interferometer) have advantages and disadvantages. Depending on the system of interest and desired experiments, the best method will vary. The phase-modulation via MZ interferometer method offers fast signal collection and good signal-to-noise ratios given the high repetition rates of the lasers used (250 kHz – 80 MHz). It is also easily coupled with a microscope and can access a long range of waiting time delays. However, this method is only compatible with high repetition rate lasers that cannot study long-lived species and have lower pulse energies. The bandwidth of the experiment is also limited by the acousto-optic modulators that perform the phase-modulation. The phase-cycling via pulse-shaper method offers fine and precise control of the time delays, which is useful in measuring coherences in the waiting time. Pulse-shaper methods are compatible with low repetition rate lasers capable of studying long-lived species. However, the bandwidth and range of accessible waiting times are limited by the size of the acousto-optic crystal in the pulse-shaper. The maximum T delay is 6-8 ps depending on the wavelength, but it is coupled to the bandwidth throughput of the pulse-shaper so the maximum waiting time delay for the excitation spectrum used in this study would be ∼2 ps. In both previously described methods, the use of acousto-optic crystals limited the bandwidth. By generating the probe pulses with the TWINS interferometer, we were able to remove the acousto-optic crystal from two of the four pulses needed for the experiment and use a white light continuum probe. Compared to the fully pulse-shaper method, the TWIZZLER method also allows long waiting times to be accessed. Although the TWINS interferometer enables broadband throughput, the beam still travels through a lot of material, so the temporal chirp needs to be accounted for with precompensation (i.e., chirped mirrors or prism compressor) or chirp correction in the analysis. We note that Tiwari and coworkers recently reported the use of TWINS for a continuum pump pulse pair in coherent 2DES [68].