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We have developed a broad bandwidth two-dimensional electronic spectrometer that operates shot-to-shot at repetition rates up to 100 kHz using an acousto-optic pulse shaper. It is called a two-dimensional white-light (2D-WL) spectrometer because the input is white-light supercontinuum. Methods for 100 kHz data collection are studied to understand how laser noise is incorporated into 2D spectra during measurement. At 100 kHz, shot-to-shot scanning of the delays and phases of the pulses in the pulse sequence produces a 2D spectrum 13-times faster and with the same signal-to-noise as using mechanical stages and a chopper. Comparing 100 to 1 kHz repetition rates, data acquisition time is decreased by a factor of 200, which is beyond the improvement expected by the repetition rates alone due to reduction in 1/f noise. These improvements arise because shot-to-shot readout and modulation of the pulse train at 100 kHz enables the electronic coherences to be measured faster than the decay in correlation between laser intensities. Using white light supercontinuum for the pump and probe pulses produces high signal-to-noise spectra on samples with optical densities <0.1 within a few minutes of averaging and an instrument response time of <46 fs thereby demonstrating that that simple broadband continuum sources, although weak, are sufficient to create high quality 2D spectra with >200 nm bandwidth.
© 2017 Optical Society of America
1. Introduction
Multidimensional spectroscopies are a powerful tool for studying the dynamics of condensed phase processes [1]. In the visible region of the electromagnetic spectrum, two-dimensional electronic spectroscopy (2D ES) reveals information about electronic couplings, electronic state dynamics, and energy flow [2]. For example, 2D electronic spectroscopy has provided insight on quantum coherences in photosynthetic systems [3–7], electronic correlations in quantum dots and quantum wells [8, 9], vibronic coupling in molecular systems [10–12], and energy transfer pathways in carbon nanotube films [13, 14].
A challenge in studying condensed phase systems is the broad bandwidth over which their electronic transitions absorb. Individual electronic resonances often span tens of nanometers of bandwidth in the visible because electronic dephasing times are short (a few to hundreds of femtoseconds), can contain vibronic progressions, and may be inhomogeneous [15]. Samples that include multiple types of chromophores, like donors and acceptors in electron transfer complexes or collections of different sized nanostructures, can span hundreds of nanometers of bandwidth [5, 13]. Light absorbing materials for solar cells are purposefully made to broadly absorb across the visible and near-infrared. If the spectrometer bandwidth, dictated by the femtosecond pulses in the pulse train, is smaller than an individual electronic resonance, then the 2D lineshapes can be distorted by electronic dephasing. Additionally, it is difficult to obtain a complete picture of couplings and dynamics if the full range of absorbing species exceeds the optical bandwidth. Existing 2D electronic spectrometers typically use non-collinear optical parametric amplifiers (NOPAs) that produce pulses in the visible and near-infrared with bandwidth typically on the order of ~40 nm [2], although versions spanning up to 300 nm have been used [16]. Broadband continuum generated in bulk media has been used as a probe in 2D ES [17], and both pump and probe continua generated in gas filled fibers have also been utilized producing sub-10 fs pulses [18–23]. Continuum generation in gas filled fibers requires much higher pulse energy compared to our implementation of 2D ES [13] and in the work described here. Ideally, a 2D spectrometer would have a bandwidth that is much larger than the frequency range of the electronic resonances of interest.
The ideal 2D spectrometer would also be shot-noise limited. The so-called 1/f noise of a pump-probe (or transient absorption) spectrometer, which is a technique closely related to 2D spectroscopy, is primarily low-frequency from DC to kilohertz. For pump-probe spectrometers utilizing laser systems operating at 1 kHz, it is common to readout every laser shot in conjunction with a chopper to remove background signals. Signal-to-noise improves with shot-to-shot readout as repetition rate increases, as recently demonstrated in pump-probe experiments with readout rates at 100 kHz [24]. As we discuss in detail in this article, 1/f noise enters a 2D spectrum not only through the readout rate, like in a typical transient absorption experiment, but also in the measured coherences.
It is typical in 2D electronic spectrometers to scan the time delays mechanically in interferometers [25, 26] or with translating birefringent wedge pairs [27, 28]. While these methods are simple to implement, the faster the delays can be scanned, the better the signal-to-noise [29, 30]. Shot-to-shot iteration to arbitrary delays is possible using pulse shapers [31], whereas repetition rate, pulse delays, and scan speed are all coupled in mechanical approaches. Taken together, these two noise considerations suggest that the ideal spectrometer would scan the time delays and read-out shot-to-shot at the maximum repetition rates allowed thereby minimizing both sources of 1/f noise.
In this paper, we report a 2D electronic spectrometer that is designed for broad bandwidth pulses and is capable of incrementing the time-delays and reading the data shot-to-shot at repetition rates up to 100 kHz. This spectrometer, which we call a 2D White-Light (2D-WL) spectrometer to emphasize its large bandwidth, is made possible by combining three technologies: broad bandwidth pulses of white-light made from supercontinuum generation, high repetition rate Ytterbium lasers (high repetition rate Ti:sapphire could be used, but we do not demonstrate so here), and a broad bandwidth pulse shaper that operates shot-to-shot at high repetition rates. Data collection with this 2D-WL spectrometer is more than 100-times faster than with our previous 1 kHz 2D-WL spectrometer because the repetition rate is increased and the signal-to-noise is improved by measuring the free induction decays before the laser pulse intensities lose correlation. Thus, the signal enhancement is better than expected from the repetition rate alone due to removal of 1/f noise. Such enhancement is not achieved with spectrometers that use mechanical translation stages or other slow methods of incrementing the pulse trains. We report the performance and include a discussion of relevant issues for 2D data collection at high repetition rates. While the spectrometer can also be used with traditional NOPA sources, the broad bandwidth of white-light is especially useful for studying chemical, material, and biological light harvesting systems and photovoltaics that have wide absorption bands.
2. Experimental methods
2.1 Spectrometer layout
The layout of our instrument is shown in Fig. 1. Approximately 1 W (10 μJ) of the output of a 100 kHz Yb amplifier (Spirit, Spectra Physics) centered at 1040 nm (~400 fs) is split into pump and probe arms. In both arms, the beam profile is manipulated with an iris aperture and power is controlled with a variable neutral density filter. A 7.5 cm focal length lens focuses the pulse into an 8 mm (pump) or 4 mm (probe) YAG crystal [32, 33], and the resulting supercontinuum [Fig. 2] are collimated using 90° off-axis parabolic mirrors. Focusing conditions alter the profile and wavelength range of the continuum: in YAG, wavelengths as short as 480 nm can be generated [33]. The pump pulse undergoes partial dispersion compensation through 52 bounces (−40 fs2 per bounce) in a chirped mirror compressor (Layertec Gmbh) and enters the pulse shaper, described in detail below, to generate the pump pulse pairs. The probe pulse dispersion is compensated by 22 bounces in another chirped mirror compressor (Layertec Gmbh) designed to compensate for 1.5 mm of fused silica per bounce pair, and the waiting time, t2, is controlled with an optical delay line on a linear motorized stage (National Aperture). The pump and probe pulses are focused onto a sample using 90° off-axis parabolic mirrors (5 cm effective focal length), the pump is blocked after the sample, and the probe is dispersed in a spectrograph (SpectraPro2150, Princeton Instruments) onto a linear CCD array (e2V AviivA EM4) capable of 100 kHz line readout. 2D spectra shown in this paper were collected using a BK7 prism compressor, not the chirped mirrors, on the probe. This difference has no bearing on analysis on signal-to-noise which is done at fixed t2 waiting times. Because the spectrometer utilizes the pump-probe geometry [34, 35], the signal is emitted collinearly with the probe.
Fig. 2 Example white light continuum generated from focusing 1040 nm laser output into an 8 mm YAG crystal. Spectral profile and wavelength range can be altered with different focusing conditions.
2.2 Pulse shaper
The pulse shaper is a home-built AOM-based 4f pulse shaper that modulates the amplitude and phase of pump pulses on a shot-to-shot basis. The design of the pulse shaper is similar to the original work by the Warren group [36], although it uses a horizontal geometry with all reflective optics made possible by cylindrical parabolic mirrors [37]. The AOM is a 35.5 mm long TeO2 crystal that is 5 mm in thickness and height. In the shaper, pulses are spectrally dispersed with a diffraction grating (600 l/mm, 500 nm blaze) and focused in the plane of the laser table with a 1D 90° off-axis cylindrical, parabolic mirror onto the AOM. At the AOM, an acoustic mask is applied and the amplitude and phase of the pulse are shaped. The shaped pulse is then reconstructed with another 1D 90° off-axis cylindrical, parabolic mirror and diffraction grating. The carrier frequency of the acoustic wave is set near the center of the 100 MHz (150 – 250 MHz) bandwidth of the AOM transducer. The total aperture of the AOM corresponds to 850 individually resolvable elements (i.e. “pixels’). The maximum repetition rate, frequency resolution, and optical bandwidth of the pulse shaper in a given experiment are all coupled to one another. In the experiments, an acoustic wave duration of 4.99 μs (velocity of 4.2 mm/μs) is used, which covers 21 mm of the available AOM aperture and 499 resolvable elements in the AOM. With the chosen gratings, the 21 mm active area of the AOM transmits an optical spectrum spanning ~580-780 nm.
The theoretical background behind pulse shaping using AOMs has been covered in detail [38, 39]. Briefly, the mask corresponding to a desired waveform is programmed into an arbitrary waveform generator (AWG, Chase Scientific), and the mask is amplified in a radio frequency amplifier (MiniCircuits). After amplification, the mask is sent into the AOM in sync with the laser pulse. The mathematical form of the mask is determined by the desired output pulse shape. For example, to shape a pulse into a pair of pulses separated by time delay, τ, a complex mask of the following form is used:
In this work, additional phase factors were included in the mask for pulse dispersion correction and phase cycling. The amplitude and phase of this mask is mapped onto a sine wave with a 220 MHz carrier frequency.3. Results
3.1 Pulse compression with the shaper and instrument response
It is difficult to characterize the pump and probe pulses separately with typical approaches like via autocorrelation techniques such as polarization gate (PG), transient grating, or second-harmonic generation frequency-resolved optical gating (FROG) [40] because the white-light is weak (the pump is ~50 pJ at the sample). Instead, we use the output of a commercial NOPA (Spirit NOPA, Light Conversion) as a gate pulse for PG FROG measurements of the continuum pump with a ~100 μm thick fused silica plate as the nonlinear medium. The NOPA output (540 nm, ~40 fs, 500 nJ) is polarized at 45° relative to the continuum and light polarized at 90° is detected. Measurements of the pulse duration are shown in Fig. 3.
Fig. 3 a) Pulse duration trace for the pump without compression from pulse shaper. b) Pulse duration trace after compression from the pulse shaper. c) Pump spectrum.
While it is common to describe the spectral phase as orders of dispersion in a Taylor expansion, the phase applied with the pulse shaper can be arbitrary (within its resolution). Rather than fit to a high order polynomial expansion, the PG FROG can be used to yield a trace that intuitively represents the group delay: the first derivative of the spectral phase with respect to optical frequency. To extract the phase needed to correct for the temporal dispersion, we take the maximum value of the uncompressed trace for each wavelength as the group delay and compute the spectral phase from the extracted group delay. The opposite of the computed phase is applied to the pulse as phase modulation in the computer generated mask. The amount of dispersion applied to the pulse is equivalent to 100 fs2, −16000 fs3, plus higher order terms at 680 nm. Because the duration of the gate pulse is ~40 fs, this sets the temporal resolution limit of our measurement. However, the data shows that the continuum is compressible. According to our calculations, the time-bandwidth product of the pulse shaper is sufficient to fully compress the pulse to ~7 fs if there are no other considerations. In this example, the ~200 nm section of the white-light [Fig. 4(c)] is set by the short-wavelength cutoff (~580 nm) of the chirped mirrors and the long-wavelength cutoff (~780 nm) is set by the gratings and acoustic aperture. Lower groove density gratings and/or a longer acoustic aperture can extend the long wavelength cutoff. We note that according to our calculations, the time bandwidth product of the pulse shaper is sufficient, using the full 35.5 mm acoustic aperture, to compensate for dispersion of the optics in the spectrometer plus create two transform limited 10 fs pulses with an 800 fs delay, which is a sufficient delay to measure the coherence times of most condensed phase systems. Thus, chirped mirrors are only necessary to compress sub-10 fs pulses.
Fig. 4 Measurement of the instrument response using white light continuum pump and probe. a) Normalized pump-probe spectra as a function of pump probe delay. b) Absolute value of the normalized pump-probe signal at different probe wavelengths as a function of waiting time. c) Pump-probe signal at 650 nm (blue circles), fit of data to Gaussian convoluted with a bi-exponential decay (solid blue), and Gaussian instrument response (black dashes).
Next, we characterize the probe dispersion as well as the time resolution of the spectrometer, as the time resolution can affect measured 2D spectra [41]. To have a measure of the time resolution of the spectrometer, we characterize the instrument response function (IRF) by assuming the signal measured is a convolution of the IRF and the molecular response. To estimate the IRF, we measure continuum pump-continuum probe spectra of a carbon nanotube film as a function of waiting time, shown below in Fig. 4. This sample was chosen because their absorptions are well resolved over 200 nm of bandwidth and their lifetimes are significantly longer than the pulse duration.
The rise times of each feature, defined here as the relative time each signal reaches half of its maximum amplitude, across the probe spectrum in the transient spectra are all time-coincident to within ~25 fs [Fig. 4(b)], indicating that the chirped mirrors correct for all but <25 fs group delay across this frequency range. By fitting the magnitude of the normalized pump-probe signal at 650 nm to a convolution of a Gaussian (the IRF) and a bi-exponential decay, we obtain an upper-bound estimate of the instrument response of ~46 fs, shown in Fig. 4(c). Assuming that the pump and probe pulses have identical Gaussian shapes, the individual pulses are ~33 fs in duration which is consistent with the data shown in Fig. 4(b) and Fig. 3(b).
3.2 Noise analysis of Yb and Ti:sapphire laser systems
To characterize the noise of the spectrometer, we first measure the intensity fluctuations of the white light continuum. Figure 5(a) shows the relative intensity of 221 laser shots at a single pixel of the CCD array corresponding to 651 nm.
Fig. 5 a) Relative intensity of continuum at 651 nm over 221 laser shots. b) Fourier transform of 221 sequential shots at 651 nm on a log scale. c) Statistic autocorrelation computed for 1,638,400 sequential shots (plotted showing 150,000 shots)
The Fourier transform of the continuum intensity is the noise spectrum of the supercontinuum [Fig. 5(b)]. The noise spectrum diminishes linearly (on a log scale) until about 100-1000 Hz due to 1/f noise. The noise spectrum shows the frequencies, and thus the timescales, at which the laser intensity fluctuates. Another way to visualize this noise is by the computed statistical autocorrelation of the laser intensity, shown in Fig. 5(c). Because intensity is not recorded for an infinite amount of time, we compute the best estimate of the true autocorrelation function [42], according to Eq. (3) and Eq. (4),
which correlates the intensity of two laser shots, Ii and Ii + k, relative to the mean intensity, Ī, separated by k laser shots over the course of N = 1,638,400 shots. From the autocorrelation, it is apparent that the intensity of nearby laser shots are more closely correlated than shots that are far apart. Interestingly, this correlation drops off slowly. The correlation between the intensities of two laser pulses drops by ~50% once they are separated by >70,000 shots. The duration of the correlation has implications for the scan rate of the time delays for the coherences, as discussed more below.To put these numbers for the Yb laser in perspective, we also include data on the noise of a 1 kHz Ti:sapphire amplifier, which is the most common type of laser system used for collecting 2D electronic spectra. The intensity of 214 laser shots at 651 nm measured at 1 kHz is shown in Fig. 6(red). To facilitate the comparison between the Yb and Ti:sapphire lasers, we recalculate the noise of the Yb system but use only 1 in every 100 laser shots so that the plots cover the same data acquisition time [Fig. 6(blue)].
Fig. 6 Comparison of Yb (blue) and Ti:sapphire (red) based continua measured at 1 kHz. a) Relative intensity of continuum at 651 nm over 214 laser shots. b) Fourier transform of 16,384 sequential shots at 651 nm on a log scale. c) Statistic autocorrelation computed for 214 sequential shots (plotted showing 1,500 shots, inset zoomed in showing 200 shots).
The Ti:sapphire system measured here exhibits higher noise at all frequencies, as shown in the noise spectrum in Fig. 6(b). In addition, the correlation between laser shots is shorter for Ti:sapphire than for Yb, as shown in Fig. 6(c). Although we only measure the noise on a single Ti:Sapphire system, and that system operates at 1 kHz, the rapid drop in correlation is similar to that previously reported for a 100 kHz Ti:sapphire system that lost its correlation within ~50 shots [24]. We suspect that the Ti:sapphire has a shorter correlation time than Yb because of the difference in the fluorescence lifetime of the gain media: 3.15 μs for Ti:sapphire [43] and 600 μs for Yb gain media [44]. Regardless of the origin, the faster correlation loss of Ti:sapphire versus Yb has implications for the optimal means of collecting 2D data sets, as we explain below.
3.3 Noise contributions to 2D spectra at 100 kHz
As discussed in the Introduction, one way noise can enter a 2D spectrum is through the measured coherences, which we explore in this section. We consider three different scenarios for collecting 2D spectra, using a carbon nanotube thin film as a model system. We only consider data collection for a pump-probe spectrometer design (not a four-wave mixing setup) with either a 2-pulse phase cycling scheme (φ12 = 0 and φ12 = π where φ12 is the difference in absolute phase of the two pump pulses separated by delay t1) or a chopper to modulate the pump pulse intensity on and off (we use the pulse shaper as a chopper to modulate the pulse intensities). Regardless of the scenario, a 2D data set consists of measuring the probe spectrum (with a CCD linear array) for a given number of t1 delays (set to 50 in this example) for each of the two pump pulse phases or two chopped pump intensities (for a total of 100 individual data points per CCD pixel). A 2D spectrum is generated by calculating the difference of the probe spectra data between the two pump phases or intensities for each t1 delay and then computing the Fourier transform at each pixel of the CCD with respect to t1. Typically, the signal for each of the (100) data points needs to be averaged over multiple spectra, n, until the necessary signal-to-noise (S/N) is obtained. Thus, a 2D data set is a 3D array consisting of CCD pixels, t1 delays with 2 (or more) phase combinations, and n spectra.
We find that the noise enters the 2D spectrum differently depending on how the averaging is performed with respect to how t1 is incremented. Figure 7 graphically illustrates three scenarios for data collection, assuming shot-to-shot readout on the CCD camera for each.
Fig. 7 Different data collection schemes of 2D spectra. (left) Scheme 1: relative pump phase, φ12, and time delay, t1, are incremented with every laser shot, and the entire pulse sequence is repeated n times. (center) Scheme 2: The pump pulses are blocked every other shot and t1 is fixed for 2n laser shots before moving to the next t1. (right) Scheme 3: relative pump phase, φ12, and time delay, t1, are fixed for n laser shots before moving to the next φ12 and t1 combination. White represents φ12 = 0, grey is φ12 = π, and black indicates no pump pulse.
Scheme 1 (left) illustrates data collection with an AOM based pulse shaper that increments the phases and delays of the pulse sequence shot-to-shot. In Scheme 1, each subsequent laser shot is a modulation of the relative pump phase and time delay so that all (100) data points are collected shot-to-shot in succession, before collecting the next set of (100) data points, and repeating n times. Scheme 2 (center) mimics another common way of collecting 2D data, which uses mechanical translation stages to slowly increment t1 and a chopper instead of phase cycling for background correction. This method is the way in which our original 2D-WL spectrometer operated [13]. Because t1 is varied using mechanical stages, t1 cannot arbitrarily be incremented shot-to-shot and is therefore fixed for 2n laser shots, blocking the pump every-other laser shot, before incrementing to the next t1. Scheme 3 (right) illustrates the way in which an SLM based pulse shaper might be used to collect 2D spectra. An SLM based pulse shaper can modulate both the time delays and phases of the pump pulses, like an AOM pulse shaper, but the liquid crystals move slowly so it takes tens of milliseconds to change the pulse shape [45]. As a result, in Scheme 3, we consider t1 and φ12 fixed for n laser shots, incrementing to the next phase and averaging for another n laser shots, before repeating for the next t1. Signals are calculated for each time delay by Eq. (5) for Schemes 1 and 3, and by Eq. (6) for Scheme 2. Because the individual pump pulse phases cannot be modulated in Scheme 2, there is a transient absorption background that must be subtracted before performing the Fourier transform.
Experimental 2D-WL spectra were collected for each of the 3 schemes at a repetition rate of 100 kHz. Data is collected for t1 from 0 to 98 fs in steps of 2 fs and 2 pulse phases (or blocked pump pulses) for each t1, for a total of 100 time points per 2D spectrum. A rotating frame of 11000 cm−1 is applied to the pump pulses to ensure adequate sampling of the signals. Spectra are all at a waiting time t2 = 200 fs. Each spectrum is the average of n = 10,000, which comes to a total of 10 seconds of data collection. For Scheme 1, each individual spectrum is collected every millisecond: it takes a millisecond to measure all of the t1 delays for the free induction decay. At the end of 10 seconds, 10,000 individual 2D spectra are averaged. For Schemes 2 and 3, each t1 is averaged for 100 ms before incrementing to the next t1. As a result, it takes the entire 10 sec to measure the free induction decay, and so there is no averaging of individual spectra. The difference between Scheme 2 and 3 is that Scheme 2 uses shot-to-shot chopping while Scheme 3 removed background using slowly varying phase cycling.
By inspection, there is a difference in spectrum quality between these three schemes, shown in Fig. 8. For quantification, we calculate the signal-to-noise from the time domain signal (at a probe wavelength of 651 nm) which is normalized to the initial value (t1 = 0 fs). The signal-to-noise is the inverse of the standard deviation of the interferogram after the signal has dephased, t1 > 60 fs, following previously established procedures for calculating signal-to-noise for free induction decays [46]. Scheme 1 has the highest S/N = 20, Scheme 2 S/N = 5.5, and Scheme 3 is the worst at S/N<0.66 (the noise is so large that it is difficult to quantify). Even though the same laser is used to collect all three of these 2D spectra and all of these spectra are averaged for the same number of laser shots, the S/N is dramatically different. Thus, using mechanical stages and a chopper via Scheme 2 takes 13-times longer than shot-to-shot scanning with Scheme 1 to collect a 2D spectrum with comparable signal-to-noise. The difference has to do with the way in which the noise spectrum is incorporated into the data, which we explain in the Discussion section below.
Fig. 8 Top: 2D spectra of a CNT film using Scheme 1 (a), Scheme 2 (b), and Scheme 3 (c). Bottom: normalized time domain signals at 651 nm for Scheme 1 (a), Scheme 2 (b), and Scheme 3 (c). Regions in t1 where the noise is calculated are shown in black boxes.
3.4 Comparison between 1 and 100 kHz data collection using pulse shaping
The data above establishes that the highest signal-to-noise spectra are obtained using shot-to-shot pulse shaping. In this section, we compare the effect of repetition rate on signal-to-noise for shot-to-shot pulse shaping. 2D spectra were collected according to Scheme 1 at 100 and 1 kHz. To collect the data at 1 kHz, we use a pulse picker to reduce the repetition rate from 100 to 1 kHz. Figure 9(a) shows a 2D-WL spectrum collected at 100 kHz for 10 sec., which is an average of 10,000 individual spectra. This data is compared with two variations at 1 kHz. Figure 9(b) shows a 2D-WL spectrum also with 10 sec of data collection. At 1 kHz, 10 sec of data collection is an average of 100 individual spectra, since the repetition rate is 100-times slower. Figure 9(c) shows a 2D-WL spectrum collected for 16.67 minutes at 1 kHz, which contains the same number of laser shots as 10 sec of data averaging at 100 kHz. Thus, the data in Fig. 9(c) is averaged over 10,000 spectra just like Fig. 9(a), although it takes 100 times longer to generate.
Fig. 9 Top: 2D spectra of CNT film at different laser repetition rates. 100 kHz with 10 sec acquisition time (a), 1 kHz with 10 sec acquisition time (b), and 1 kHz with 16.67 min acquisition time (c). Bottom: normalized time domain signals at 651 nm for (a), (b), and (c). Regions in t1 where the noise is calculated are shown in black boxes
Signal-to-noise was quantified in the time-domain the same way as above. Of these three spectra, the spectrum in Fig. 9(a) has the highest S/N = 20 compared to Fig. 9(b) S/N<0.72 and Fig. 9(c) S/N = 14, for the three methods respectively. Thus, 100 kHz data collection is better than either version of 1 kHz data collection. The signal-to-noise for 10 sec of data collection at 1 kHz is the worst, which is expected since it has 100 times less averaging. Even so, the drop in signal-to-noise is larger than would be expected if it were determined solely by n1/2; it is 40% worse. Even though the spectrum in Fig. 9(c) is averaged over the same amount of laser shots as Fig. 9(a), and so would be expected to have the same signal-to-noise, the signal-to-noise is only 70% as good with 1 kHz data collection. In other words, the gain in signal-to-noise going from 1 to 100 kHz reduces the time spent acquiring data by a factor of 200, not just the factor of 100 expected by the repetition rate. As we explain below, the signal-to-noise does not solely scale as n1/2 due to the laser intensity correlation.
3.5 Sensitivity
White-light continuum is much weaker than the output of a NOPA (50 pJ versus 1 μJ), and therefore we characterized the sensitivity of our spectrometer. To this end, we measured solutions of chlorophyll a in methanol at various concentrations and optical densities shown in Fig. 10. The solutions were measured in 56 μm sample cells at three concentrations with optical densities varying from <0.1 to 0.2, which fall into the range of optical densities used by other groups using four-wave mixing and pump-probe beam geometries [47, 48]. Using Scheme 1, spectra were collected by scanning t1 from 0 to 200 fs in steps of 2 fs with a rotating frame of 12500 cm−1 at a waiting time t2 = 1 ps. Each 2D spectrum is averaged for 3 min. Contours were chosen to highlight the noise and thereby illustrate the change in signal strength. The 2D spectra match those previously published [47, 48]. Signal-to-noise is calculated in the same way as described in the previous sections, but at the pixel corresponding to 665 nm and using data points t1 >118 fs to calculate the noise.
Fig. 10 Sensitivity of the 2D-WL spectrometer. (a,c,e) Linear absorption spectra of chlorophyll a in methanol. (b,d,f) 2D-WL spectra of chlorophyll a in methanol corresponding to linear spectra to the left. Calculated signal-to-noise is shown in the inset of each 2D spectrum. Signal-to-noise was calculated from the free induction decay at the probe pixel corresponding to 665 nm using a t1 > 118 fs cutoff.
4. Discussion
From the above experiments, we learn that (1) spectrometers that update the pulse trains shot-to-shot give the highest signal-to-noise; (2) phase cycling must be done shot-to-shot to be effective; (3) 100 kHz data acquisition is 200-times faster than 1 kHz data collection when both are using shot-to-shot pulse shaping, and (4) low optical density samples are easily measured with the 100 kHz 2D-WL spectrometer described here.
To understand point (3), we discuss data collection with regard to the correlation time of the laser pulse trains. Shown in Fig. 10 are the statistical autocorrelations measured for the Yb and Ti:sapphire lasers, reproduced from Figs. 5(c) and 6(c), but plotted as a function of experimental data collection time. On each plot we include a horizontal bar that represents the time elapsed to collect a single free induction decay (one 2D-WL spectrum) generated from 50 t1 delays with either chopping or 2 phase cycles (100 total points). In Fig. 10(a), for the Yb laser system, a single free induction decay takes 1 ms to collect at a 100 kHz repetition rate whereas it takes 100 ms at 1 kHz. In 1 ms, the correlation time is much longer than the elapsed experimental data collection time, so the laser intensity is essentially constant during the measurement. In other words, at 100 kHz, the laser intensity has not had enough time to fluctuate appreciably during the collection of the free induction decay for each individual 2D-WL spectrum. In contrast, at 1 kHz, the correlation decays noticeably in the 100 ms it takes to collect the free induction decay. That means that the laser intensity fluctuates significantly during the measurement of the free induction decay. As a result, the measured free induction decay at 1 kHz is altered by noise to a greater extent than at 100 kHz, which perturbs the 2D spectrum. The 2D lineshape is particularly sensitive to alterations in the free induction decay [49]. This decay in correlation is not reflected in the n1/2 scaling one expects to see in systems with random noise. Thus, even if the same number of data points is collected at 100 and 1 kHz, the quality of the resulting 2D-WL spectra will differ. The higher pulse correlation is why the spectrum in Fig. 9(a) has 1.4-times better signal-to-noise than the spectrum in Fig. 9(c). The take home message is that 100 kHz Yb laser based spectrometers that scan the delays shot-to-shot can be collected 13-times more quickly than spectrometers that use delay stages for scanning, all other things being equal.
From Fig. 11(a) we learn that it is advantageous to scan the pulse sequence rapidly at high repetition rates: not only because data is collected faster, but also because pulses are better correlated. This conclusion is even more important in spectrometers that use 1 kHz Ti:sapphire systems because the pulse correlation falls much faster than for Yb, as shown in Fig. 11(b). A free induction decay measured at 1 kHz using shot-to-shot scanning (Scheme 1) will take 100 ms whereas slow scanning with mechanical stages (Scheme 2) will take 10,000 ms. In 100 ms, the correlation decays ~40%, but any free induction decay measured slower than that will introduce unnecessary noise into the free induction decay because the pulses have completely lost correlation. Thus, it is even more imperative for Ti:sapphire systems than for Yb to scan the delays quickly. We do not have data for a 100 kHz Ti:sapphire system, but it has been previously published for a 100 kHz Ti:sapphire system that the correlation is lost within 50 laser shots [24]. Put another way, if one swaps a 1 kHz Ti:sapphire for a 100 kHz Yb laser on a 2D spectrometer that uses mechanical stages, the acquisition rate will increase by a factor of 100 from the repetition rate, but there will be no other gain from pulse correlation because delays are scanned slowly. But by swapping in a Yb laser and shot-to-shot pulse shaper, the acquisition rate will increase by a factor of 1,300, meaning a data set that took 1 hour at 1 kHz can be done in 3 seconds at 100 kHz.
Fig. 11 Laser intensity correlation corresponding to the amount of experimental data collection time required to collect a single free induction decay consisting of 100 data points, drawn with horizontal bars. Intensity correlation data take from Figs. 5(c) and 6(c). (a) Comparison of time required for a Yb laser running at a repetition rate of 100 and 1 kHz. (b) Comparison of time required for a Yb and Ti:sapphire laser, each running at 1 kHz. Notice, only the 100 kHz Yb laser is able to measure the free induction decay before a drop in the correlation occurs.
5. Conclusions and outlook
We have designed and implemented a 2D-WL spectrometer that updates pulse sequences and reads out data on a shot-to-shot basis at repetition rates up to 100 kHz. Further, we have shown that to fully gain the benefits of high repetition rates, the free induction decay should be measured before the correlation in the laser noise has decayed. To do so, the pulse sequence must be altered with each laser shot, which is currently only possible at repetition rates >100 kHz using AOM technology. Utilizing both high repetition rate and shot-to-shot pump pulse modulation, our 2D-WL spectrometer greatly reduces data acquisition time. Thus, many new experiments are possible with this 2D-WL spectrometer.
Our 2D-WL spectrometer is designed for broad bandwidth lasers pulses. We demonstrate data collection with about ~200 nm bandwidth on chlorophyll a at optical densities <0.1 with only 3 minutes of averaging. Our current bandwidth of ~200 nm is set by the cutoff of the chirped mirrors and the choice of gratings, not the continuum itself. The white-light continuum generated with YAG cuts on at about 500 nm, but shorter wavelengths are achievable with other continuum generation methods. For example, continua generated in CaF2 can reach wavelengths as short as 250 nm [50]. This 2D-WL spectrometer is also very flexible. The gratings in the pulse shaper can be adjusted to increase the resolution or increase the bandwidth (the number of resolvable elements is fixed for a given AOM aperture). Higher repetition rate is also possible by reducing the length of the acoustic aperture, although currently the detector limits the readout rate to 100 kHz. We note that transient absorption experiments are now being performed in microscopes to create pump-probe images, such as for studying single nanostructures [51], diffusion in photovoltaic films [52, 53], and biological imaging [54, 55]. That development was made possible by using lasers with repetition rates of hundreds-of-kHz to MHz. Pump-probe and 2D spectroscopies are both 3rd order signals. Thus, adding an AOM pulse shaper to many of these new pump-probe microscopes would give them the added functionality of collecting multidimensional spectra from which hyperspectral images could be assembled from arrays of spatially mapped 2D spectra.
Funding
Air Force Office of Scientific Research (FA9550-15-1-0061); National Science Foundation (NSF) University of Wisconsin-Madison Center of Excellence for Materials Research and Innovation award (DMR-1121288).
Acknowledgments
The authors would like to gratefully acknowledge Chris Middleton for useful discussions in the experimental setup of the work shown here. Martin Zanni is co-owner of PhaseTech Spectroscopy, Inc. which sells 2D IR/Visible spectrometers and pulse shapers.
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