1. Introduction

Coherent two-dimensional (2D) electronic spectroscopy recently emerged as a powerful tool for studying molecules and multichromophore systems [1,2]. It is a femtosecond four wave mixing technique where three laser beams are used to excite the sample and third order polarization is created. The emitted electric field signal is mixed with the fourth, so called local oscillator (LO) beam and measured in the spectral interferometry detection scheme. 2D spectroscopy technique provides simultaneous spectral and time resolution that is not limited to the resolution dictated by uncertainty relationship of the laser pulses and also the possibility to manipulate each laser pulse separately. This flexibility enables investigation of molecular systems in previously unavailable detail, for example molecular couplings and exact energy transfer pathways on the energy map can be explored directly.

In many potential applications of 2D electronic spectroscopy, especially when organic or biological samples are studied, requirements for the maximum irradiation fluence applied as well as the maximum energy per pulse are strictly limited. This is due to sample photodegradation, generation of higher than third order optical response signals, accumulation of undesirable long-lived species, such as isomers, triplets, or thermal gradients, or when creation of multiple excitations in a single system are unfavorable, e. g. in large dendrimers, aggregates, conjugated polymers or light-harvesting complexes. 2D spectroscopy measures transient grating type signals and therefore it is especially prone to accumulation of long lives species – a long lived grating is “burned” in a sample by pulses 1 and 2, then pulse 3 is diffracted in the phase-matching direction of the signal and reaches the detector.

Several experimental implementations of 2D spectroscopy with their own advantages and disadvantages have been suggested. For example, fully collinear [3] or partly collinear geometries [4] are intrinsically phase stable, free of phasing issues (separation of real and imaginary parts of 2D spectrum, most commonly done by matching its projection to pump-probe data [5]), but suffer from a strong background, lower sensitivity and homodyne signal contributions. Solutions based on non-collinear geometry offer background-free signals [6–9], leading to superior sensitivity due to more efficient use of detector’s dynamic range. Moreover, additional flexibility is achieved, since all the excitation beams (and LO) are accessible individually for optical manipulations such as filtering, shuttering, shaping, and polarizing.

In some cases, unfavorable effects of relatively high excitation densities can be alleviated by using various kinds of sample circulation methods, such as, flow cells, cells with a stirring mechanism, sample jets, etc. Each of the methods has its own shortcomings, for example, flow in a flow cell has an irregular spatial profile – the central layer of the solution is flowing fast, while the boundary layers, close to the cell walls, remain almost still and accumulate photodamage. In some cases, for example, when measuring frozen samples in a cryostat or when the sample volume is tiny, none of these methods can be applied.

Another major source of artifacts in 2D spectroscopy is scattering as most samples, especially biological pigment-protein complexes, scatter light to a large extent. It is easy to see that the ratio of third order signal and scattering contributions in the obtained 2D spectrum (in electric field units) is proportional to the energy of the laser pulse from which all three interacting pulses are derived. Reduction of excitation energy per pulse eventually leads to a situation when the intensity of scattered excitation light reaching the detector exceeds the signal intensity.

In general 2D spectroscopy is quite resistant to scattering effects due to the use of spectral heterodyne technique – windowing of the signal in time domain effectively eliminates the scattering artifacts caused by pulses 1 and 2, when population time t₂ exceeds the pulse length by a factor of 2 – 5, depending on scatter amplitude. However, an important region of interest for population time t₂ in many of 2D spectroscopy experiments is from zero to a couple of hundreds of femtoseconds, the range where signal windowing does not suppress scattering artifacts completely.

Brixner et al. have suggested a method for scatter suppression [7], where shutters are used for blocking certain beams, measuring scattering contributions, and subtracting the acquired spectra afterwards. This method greatly suppresses scatter-induced artifacts in 2D spectra, especially at early population times t₂, when windowing of the signal in time domain does not help. Another effective scatter suppression method is the phase-cycling used by Vaughan et al. [8].

Scattering caused by pulse 3 cannot be separated by windowing, but since t _LO doesn’t change during the measurement, scatter remains static and artifacts end up as zero frequency components after Fourier-transforming the results along the coherence time axis (t ₁).

While sample circulation, when applicable, greatly reduces photodamage and undesired accumulation effects, it introduces an additional problem – dynamic scattering. If the scattering properties at the measurement spot are rapidly changing, then two separate data acquisitions contain different scatter patterns and the methods described in [7,8] are not efficient. In fact, when scattering is dominated by the dynamic component (i. e. scatter is uncorrelated between two measurements), scatter subtraction can even increase the amplitude of artifacts and noise level overall.

Moreover, dynamic scattering from beam 3 differs for each coherence time step, so scatter artifacts do not end up as zero frequency components after Fourier-transforming the results along the coherence time axis. Since scatter of beam 3 cannot be separated from the signal by windowing, it causes additional distortions in obtained 2D spectra.

The most critical problem caused by scatter is the fact, that it does not result in random noise, but often creates artifacts of certain shape and temporal behavior, which hamper “phasing” procedure or can even be mistaken for spectroscopic signals from the sample, such as cross-peaks or quantum beating.

In this paper we demonstrate a method that can dramatically suppress static and dynamic scatter induced artifacts in 2D spectroscopy which cannot be addressed by the methods mentioned above. As a result, it allows using relatively low (in comparison to commonly used several nJ/pulse) excitation densities on highly dynamically scattering samples, such as solutions of pigment-protein complexes. In addition, the method suppresses the signals caused by accumulation of long lived (>1 ms decay time) species.

2. Experimental setup

The experimental setup is shown in Fig. 1 and is based on the design by Brixner et al. [9]. The setup is highly phase stable due to use of diffractive optics and inherent passive stability of the geometrical arrangement of optical elements [7]. 1030 nm 170 fs light pulses are generated by Yb:KGW amplified laser system (“Pharos”, Light Conversion Ltd.) operating at 1 to 600 kHz repetition rate. Conversion into the visible and near-infrared spectral range (470 to 900 nm) is achieved by a home-made non-collinear optical parametric amplifier (NOPA), resulting in ~1500cm⁻¹ (FWHM) spectral width pulses. The pulses are compressed to 10-20 fs, by means of a combination of chirped mirrors (Layertec GmbH) and a fused silica prism compressor. The energy per each excitation pulse is attenuated down to 10 pJ-10 nJ by a variable neutral density filter. A broadband dielectric beam splitter splits the output of NOPA into two beams of equal intensity, one of which (3&4 in Fig. 1) is delayed with respect to another (1&2) by a translational delay stage (time t ₂). The two beams are split into pairs by a transmission diffractive grating and the resulting four beams are focused by a spherical mirror onto the sample in a box car geometry configuration. The fine time delays in beams 1, 2, and 3 are introduced by wedge pairs (W1 and W2 are motorized and W3 is stationary), while beam 4 is attenuated by a neutral density filter, see Fig. 1 for details. Beams 1 and 2 are separately modulated by two phase-locked mechanical choppers C1 and C2 (Thorlabs) The signal emitted in phase-matching direction from the sample, together with collinear LO pulse, which in our case arrives before pulse 3 (t _LO ≈1 ps), is focused onto a spectrometer and accumulated by a 16 bit thermoelectrically cooled 1340 × 100 (horizontal × vertical) pixels charge coupled device (CCD) camera (PIXIS 100BR, Princeton Instruments). For any given coherence time t ₁ an interferogram is recorded. The accumulated sequence of spectra is processed by the Fourier transform method and a 2D spectrum is obtained [10]. The procedure is repeated for a set of population delays t ₂.

 

Fig. 1 Schematics of the experimental setup (distances are not to scale). Two parallel beams of femtosecond laser pulses (1&2 and 3&4) are focused by a spherical mirror SM1 onto a transmission diffractive grating G. Only the first positive and negative diffractive orders are generated with high efficiency, the rest is blocked by a mask (not shown). The resulting four beams are directed to a spherical mirror SM2 and focused into the sample S. Beam 4 (LO) is attenuated by the neutral density filter F (OD = 3). The time delays of beams 1, 2, and 3 are finely adjusted by movable fused silica wedge pairs W1, W2, and W3, respectively. W1 and W2 are scanned during the measurement, while W3 is kept constant. Beams 1 and 2 are modulated by choppers C1 and C2, respectively. The emitted third order signal field and LO propagate in the same direction through the iris I, while beams 1, 2, and 3 are blocked. M1 and M2 are planar folding mirrors. Inset shows the timing diagram of the pulse sequence used.

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The step-by-step data acquisition and processing sequence is shown in Fig. 2 . The CCD of the spectrometer can be used in an integrating or time-resolved mode. Time resolution is achieved by simultaneously exposing and reading the CCD. The signal is imaged onto a narrow strip of pixels (approx. 1340 × (3-5)) on the CCD (Fig. 2(a)). When the CCD is exposed and read simultaneously, the image is smeared vertically, resulting in a two-dimensional image, which is actually a one dimensional interferogram (horizontal axis) time-resolved along the vertical axis. Additional vertical hardware binning is applied during the readout: n CCD rows (usually 3-5) are shifted into the register and read as a single line (Fig. 2(b)), thus the illuminated strip of n rows results in a single line in the acquired data set (Fig. 2(c)). Usually the number of rows read in a single acquisition (typically 1000-2000) exceeds the physical number of rows of the CCD sensor (100). The readout rate f _read (number of the data set lines acquired per second) can range from tens of Hz up to more than 2 kHz, depending on timing and hardware binning and cropping parameters; we typically use 1-1.2 kHz for optimal performance.

 

Fig. 2 Data acquisition and processing sequence (schematics). For clarity, all the data except of chart (f) is displayed for a single modulation case. (a) A strip of pixels of the CCD sensor (3-5 rows) is illuminated by interfering signal and LO beams. (b) Hardware binning is applied: groups of n CCD rows are shifted into the register and read-out resulting in single lines in the acquired data set (c). A spike rejection and a high-pass filters are applied to the columns of the acquired data set: (d) – a single column before filtering, (e) – the same column after filtering. (f) The view of the filtered data in the frequency domain (a double modulation case, see text for details). (g) An interferogram extracted by calculating the Fourier coefficients at the signal modulation frequency: f _mod for the single modulation case, |f _mod1-f _mod2| and/or f _mod1 + f _mod2 for the double modulation case.

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Let’s first assume that the signal is modulated with a frequency f _mod. An example of modulated signal (single column of the acquired data set) is shown in Fig. 2(d). Since the measurement is done in the non-collinear four wave mixing configuration in a flowing sample, the main part of the noise comes from the scattering of intense, in comparison to the signal and LO, excitation pulses. The frequency profile of this noise is approximately proportional to 1/f. In addition to this relatively uniform noise, rather rare spikes of scattering can be caused by very large particles or bubbles. The signal-to-noise ratio of the acquired data is greatly improved when a spike-rejection filter is first applied. Due to the finite number of the sampled rows (1000-2000) spectral leakage occurs and the signal at f _mod is contaminated by the scatter (which is modulated by approx. 1/f noise) to a certain degree. As the readout frequency is rather high (>1 kHz), further signal-to-noise improvement can be achieved by applying a non-linear high-pass filter to suppress the most intense part of the noise at low frequencies (typically 0 –100 Hz). The filtered data column is shown in Fig. 2(e).

If the signal reaching the CCD is harmonically modulated by a frequency f _mod and the readout is performed at a frequency f _read, then the signal intensity I (only the modulated component in CCD counts) can be extracted by calculating the Fourier coefficients at the modulation frequency f _mod:

In addition to noise suppression, the modulation technique virtually eliminates the contributions of slowly accumulating long lived species such as thermal grating, long lived triplet states or isomers, or permanent sample damage. This is achieved due to two effects – first, since only the relatively rapidly oscillating part of the signal (at the frequency f _mod) is acquired, the amplitude of the oscillating signal component of slowly accumulating and slowly decaying species is significantly suppressed. Another factor to be taken into account is the fact that the signal is growing when the excitation is on and decaying when the excitation is off, resulting in a phase shift between the excitation and the signal. As a result – the long lived species produce mainly imaginary Fourier coefficients (Eq. (1)), though only the real part is extracted as a signal. Due to both, amplitude reduction and phase shift, the undesirable contributions of long lived species are reduced by a factor of ~1 + (2πf _mod τ)² in comparison with scatter subtraction technique. Here τ is the lifetime of the long lived species. For example, if f _mod = 500 Hz then the undesirable contributions are reduced by about an order of magnitude for τ = 1 ms and by about three orders of magnitude for τ = 10 ms. Of course, other factors should also be taken into account, for example, if the sample is rapidly stirred and a fresh spot is provided for nearly every new shot of laser pulses, then the undesirable contributions are virtually eliminated and the lock-in technique loses advantage over simple scatter subtraction in this respect.

In the non-collinear 2D configuration, modulation of the signal with a frequency up to several kilohertz can be achieved by modulating any of the 4 beams with a mechanical chopper. A frequency selective detection can suppress the undesirable contributions in the detected signal. For example, modulation of beam 1 at half of the laser repetition rate (500 Hz) was employed by Prokhorenko et al. [11] to suppress the homodyne part of LO. However, modulation of any of the excitation beams together with frequency selective detection cannot suppress all the undesirable contributions – the scatter from the modulated beam itself remains unattenuated. To tackle this problem we modulate beams 1 and 2 with two different frequencies f _mod1 and f _mod2, respectively, by means of phase-locked mechanical choppers (C1 and C2 in Fig. 1). The signal is then detected at the sum or differential frequency: f _sum = f _mod1 + f _mod2 and f _diff = |f _mod1 - f _mod2|. In the frequency domain plot (Fig. 2(f)) it is clearly seen that the signal modulated at f _mod1 + f _mod2 and |f _mod1 - f _mod2| is separated form scatter contributions from beams 1 and 2 at frequencies f _mod1 and f _mod2, respectively. If possible, both signals (modulated at f _sum and f _diff) are measured and extracted simultaneously and their average is taken for further processing reducing the noise level by a factor of up to 2^1/2, depending on the correlation of noise components in the signals.

The reason we choose beams 1 and 2 for modulation is as follows. When the modulated beams are both scattered and interfere on the detector, the resulting interference pattern is modulated by f _sum and f _diff and contaminates the 2D spectrum. Since the range of delays between pulses 1 and 2 for a typical room temperature 2D experiment is usually within ± 200 fs and rarely exceeds ± 500 fs at cryogenic temperatures and the delay between pulse 3 and LO is ~1 ps, windowing of the signal in time domain always eliminates this contribution when beams 1 and 2 are modulated. If e. g. beam 3 was modulated, this would not always be the case.

3. Experimental results

To demonstrate the advantages of the technique, we performed 2D electronic spectroscopy experiments on a solution of tetraphenyl porphyrin sulfonate (TPPS₄) aggregates in a flow cell. TPPS₄ aggregates form long (up to several microns) tubules of ~20 nm in diameter. The tubules tend to stack into much larger multi-tubular bundles and networks [12]. As a result, the solution of TPPS₄ aggregates is rather scattering. The solution was flown in a 0.2 mm light path cell at approximately 0.3 m/s speed. 15 fs (FWHM) laser pulses at 200 kHz repetition rate with ~1500 cm⁻¹ bandwidth, centered at 685 nm were used for the excitation. The excitation density used was 100 pJ per pulse per 100 μm diameter spot, which results in ~4·10¹² photons/cm² per pulse and total fluence of ~0.75 W/cm².

The results of the experiment are shown in Fig. 3 . The 2D spectrum in Fig. 3(a) is obtained by direct accumulation of signal with scattering contributions. The spectrum in Fig. 3(b) is obtained from the data accumulated with the beam 3 blocked, i. e. only the scattering contributions from beams 1 and 2. It is clear that there is little difference between the spectra in Figs. 3(a) and 3(b). Due to strong scattering overwhelming weak signal, the dominant features in the 2D spectrum (Fig. 3(a)) are scatter related artifacts. When the scatter related components are subtracted from the total signal, a significant improvement is achieved (Fig. 3(c)). However, the complete removal of artifacts is not possible due to rapidly changing amplitude and shape of the scatter related components; note the resemblance of diagonal features in Figs. 3(b) and 3(c). A result obtained by double modulation lock-in method is shown in Fig. 3(d). The spectrum contains no noticeable scatter related artifacts (no resemblance with Fig. 3(b)); the noise pattern of the spectrum looks random and uniform, rather than resembling certain spectroscopic features. When comparing the spectra in Figs. 3(c) and 3(d), it is clearly seen that some “ghost” features (e. g. just below and to the left of the main positive peak in Fig. 3(c) are remarkably similar to the cross peaks in 2D spectra. Misinterpretation of these features can seriously compromise interpretation of experimental results.

 

Fig. 3 The illustration of scatter induced distortions of 2D spectrum of a scattering sample (TPPS₄ J-aggregates) at t ₂ = 20 fs, (a) 2D spectrum obtained directly from untreated data. (b) Spectrum extracted solely from scattering data measured with beam 3 blocked. (c) 2D spectrum obtained by subtracting the scattering signal (b) from the untreated data (a). (d) 2D spectrum obtained by the double modulation lock-in method. The measurement durations for obtaining spectra (c) and (d) are approximately the same.

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4. Remarks and conclusions

In addition to its advantages, the double modulation technique has several minor shortcomings. First, the signal is generated only during a quarter of the acquisition time. Single modulation (of beam 3, for example) would double the acquisition efficiency, but the signal-to-noise ratio achieved with the double modulation technique is far superior. Second, the amount of light reaching the detector has to be rather high, since the readout rate is on the order of 1 kHz. Slowing down the readout rate results in longer experiments and usually increases the noise in the data due to 1/f nature of the scattering noise in flowing samples. Using high laser repetition rates (>50 kHz) enables experiments with low excitation pulse energies (<200 pJ). However, in some cases when high repetition rate is used, relatively long-lived species (with lifetimes on the order of microseconds), such as triplets, accumulate in the sample. The modulation technique does not separate their contributions from the signal, since their lifetimes are still too short. In the case of static scattering in solid state or frozen samples, when scatter subtraction can be successfully applied, the benefits of the proposed technique are not as prominent, though it still provides superior signal-to-noise ratio, especially when the scattering is relatively high and the laser system is not perfectly stable.

In conclusion, the double modulation technique is an efficient way to tackle scatter and accumulation related problems in 2D spectroscopy, especially in cases of relatively strong scattering and weak signals. It enables acquisition of artifact free 2D spectra under dynamic scattering conditions, when simple subtraction of scattering contributions fails. Due to the use of mechanical choppers it can be implemented in almost any non collinear four wave mixing experiment, regardless the excitation spectrum, laser repetition rate, and other parameters. For example, in addition to conventional 2D spectroscopy, the technique could be used to improve signal-to-noise ratio in, for example, three-dimensional electronic (3D) spectroscopy [13] or two-dimensional electronic double-quantum coherence spectroscopy [14,15].