1. Introduction

Two-dimensional electronic spectroscopy (2DES) has recently emerged as a powerful technique for studying energy transfer in photosynthetic and solid-state systems [1–3]. Despite the rich chemical information available from 2DES, the relative difficulty of implementing the experiment has limited the degree to which the method has been utilized. This is particularly true at visible wavelengths where the demand for high phase-stability generally requires diffractive-optics-based [4,5] or actively phase-stabilized approaches [3]. Alternately, collinear experiments combined with phase-cycling [6], phase-modulation [7], or noncollinear, pulse-shaping-based methods [8] have been pursued. An optical analog of 2D NMR spectroscopy, 2DES spreads spectral information along two frequency axes, allowing correlations to be made between excitation and detection frequencies. The cross-peaks of a 2DES spectrum reveal coupling between electronic transitions and allow the monitoring of energy transfer dynamics. In systems such as photosynthetic complexes, energy transfer occurs between electronic transitions that span a broad frequency range, from the visible to the near-IR [9]. To map out the complete energy transfer pathways in such systems requires the ability to span this large frequency range.

The Fourier transform implementation of 2DES provides both maximum time and frequency resolution when heterodyne-detected rephasing and nonrephasing contributions to the third-order response are combined with the proper phase relationship, yielding absorptive and dispersive spectra [10]. In the commonly-used box-car geometry, the rephasing and nonrephasing signals are emitted in different phase-matched directions. To obtain absorptive spectra, the two contributions must be measured separately and “phased” by fitting them to a separate dispersed pump-probe measurement [11,12]. In addition, making the necessary interferometric measurements requires that the phase stability between the pulses be much better than an optical wavelength. It was suggested some time ago that absorptive 2D spectra could be obtained using a combination of a collinear pump pulse pair and noncollinear probe [10]. One of the advantages of this approach is that both the rephasing and nonrephasing contributions are emitted in the phase-matched direction of the probe pulse. Thus both signals can be collected simultaneously without timing errors that can lead to difficulty in extracting the absorptive component. In addition, since the signals are emitted in the same direction as the probe beam, the probe serves as an intrinsically phase stable local oscillator for heterodyne detection. Recently, 2D spectra have been collected in this “pump-probe” geometry at IR [13,14] and near-IR wavelengths [15], employing both conventional optics and pulse-shapers to provide the two excitation pulses. One disadvantage of the pump-probe approach to 2D spectroscopy is that the intrinsic heterodyning scheme does not allow for arbitrary control of the ratio of signal to local oscillator necessary to optimize heterodyne measurements. This limitation has recently been addressed in 2DIR experiments employing alternate polarization schemes [16].

Here we expand on recent advances to demonstrate two-color 2DES in a pump-probe geometry to obtain absorptive spectra at visible wavelengths. The two-color approach allows access to information far from the diagonal, allowing the study of coupling and energy transfer between disparate electronic transitions. Diffractive optics-based 2D spectroscopy employing different pump and probe sources has been demonstrated by Moran et al., though they did not explore off-diagonal regions of the 2D spectrum [17]. As a demonstration of two-color 2DES we present data on the laser dye LDS750 which has a large Stokes shift and thus exhibits spectral evolution far from the diagonal. We employ an acousto-optic pulse-shaper (Dazzler, Fastlite) to create phase-locked pulse pairs and automatically retrieve absorptive 2D spectra. We present phase and amplitude modulation and polarization schemes that improve the signal-to-noise ratio (SNR) of the acquired 2D spectra and show that phase-cycling can be used to separate rephasing and nonrephasing components of 2D spectra. With the simple in-line insertion of a Dazzler pulse-shaper, a standard spectrally-resolved pump-probe experiment can be converted to a Fourier transform 2D spectrometer. This straightforward approach eases the complexity of implementing Fourier transform 2D spectroscopy. While here we expand the application of pump-probe 2D from the near-IR and IR into the visible, the method is easily extended to the ultraviolet regime.

2. Experimental implementation

Our experimental setup is shown in Fig. 1. A titanium sapphire oscillator (Synergy, Femtolasers) seeds a regenerative amplifier (Spitfire Pro, Spectra Physics), producing 800 nm, 1 mJ pulses at 1 kHz. The amplified beam is split and used to pump two home-built non-collinear optical parametric amplifiers (NOPAs) [18]. One NOPA creates the pump beam, and the second NOPA creates an independently tunable probe beam, providing a combination that will permit studies of energy transfer over the visible-near-IR range. For these experiments the pump beam was sent into an acousto-optic pulse-shaper (Dazzler, Fastlite), which created the first two excitation pulses with a variable delay, t ₁. The modulation applied to produce the pulse pair was of the form |E(ω)|(1+exp[i(ω t ₁+ϕ ₁₂)]) where E(ω) is the spectral amplitude of the pulse and ϕ ₁₂ is the relative carrier wave phase shift. Unlike spectral modulations produced by an interferometer, the pulse shaper allows the introduction of an arbitrary carrier wave phase shift that can be useful for phase-cycling schemes analogous to those used in NMR [19]. Pump and probe pulses crossed at the sample cell at a small angle (~2°). Pulse energies of 5 nJ and 1 nJ were used for the pump and probe pulses respectively. The pump pulse was characterized via second order autocorrelation with a GaN photodiode [20] using the Dazzler to scan the necessary delay, indicating pulses of 30 fs duration. Cross-correlation with the probe pulse demonstrated a time resolution of 45 fs for the 2D measurements.

The heterodyne-detected 2D signal was spectrally resolved at 1 kHz using a Horiba Jobin Yvon iHR320 spectrometer and Pixis 100B CCD camera, providing the ν ₃ axis of the 2D spectrum. After scanning the t ₁ delay using the Dazzler, the 2D spectra were computed as detailed in Section 4. All spectra were normalized with respect to the transmitted probe pulse. The data acquisition time was typically ~1.5 minutes, after scanning a delay of 200 fs in 0.6 fs steps, averaging 250 scans at each t ₁ delay. The spectral resolution of the Dazzler at 550 nm is 0.25 nm, and in principle it can create delays of >8 ps. In practice, since we use the Dazzler to compensate itself and the dispersion of our setup, our maximum delay is limited to ~400 fs, which is more than adequate. The acquisition speed of the 2D spectra is limited by a combination of the time required to save spectra throughout the scan, and the time necessary to update the Dazzler waveform. Recent improvements to the Dazzler software would effectively eliminate its contribution to the acquisition time, reducing acquisition to ~1 minute per 2D spectrum. The sample of LDS750 was purchased from Exciton Inc. and mixed with acetonitrile (Sigma Aldrich) to produce a total optical density of 0.3 in a 1 mm pathlength flow-cell.

 

Fig. 1. Experimental setup for two-color 2DES in the pump-probe geometry. Two independently tunable noncollinear optical parametric amplifiers provide pump and probe pulses. The probe pulse is compressed with a prism compressor (PC) and the pump pulses are compressed with the Dazzler pulse-shaper. The Dazzler also creates the first two excitation pulses separated by an arbitrary delay t ₁. The inset shows the pulse sequence at the sample and the different polarization schemes employed.

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While pump-probe spectroscopy generally employs a chopper to detect the difference in transmission induced by the pump pulse, there are several possibilities offered by the use of a pulse-shaper. The pulse-shaper can act as a chopper itself (amplitude modulation) or it can be used in various phase-cycling schemes. Here we employed the Dazzler in several different modalities: as a 500 Hz chopper, and as a 500 Hz phase modulator. One simple phase-cycling scheme used consecutive pump pulses that were given a ϕ ₁₂=180° relative phase shift, producing signals that were opposite in sign at every second laser shot. This scheme has several advantages over chopping. Difference detection between the ϕ ₁₂=0° and ϕ ₁₂=180° signals effectively doubles the duty-cycle of the experiment. Also, since the overall signal will contain pump-probe signals produced by the individual pump pulses, difference detection reduces the unwanted pump-probe component of the signal. While this signal can be separated by the Fourier transform (where it appears near zero frequency), diminishing its amplitude permits undersampling of the signal if desired. An alternate phase cycling approach allows us to separate rephasing and nonrephasing contributions to the 2D spectrum. In this scheme the signal was collected in two separate scans with ϕ ₁₂=0° and ϕ ₁₂=90°, using either the chopping or difference detection method. These signals were then combined as detailed in Section 4.

To optimize the signal-to-noise ratio of the heterodyne-detected 2D spectra, control over the relative amplitude of signal and local oscillator is necessary. In the pump-probe geometry, the probe pulse also acts as the local oscillator, and is generally weak to avoid detector saturation. Using different polarizations for the signal and local oscillator permits both independent adjustment of the local oscillator field strength and a stronger probe intensity to be used, greatly improving the SNR [16,21]. While the Dazzler pulse-shaper does not allow tailoring of the polarization of the individual pulses in the pump pair, polarization can still be used to enhance the SNR using a different polarization scheme than previously demonstrated for 2D IR spectroscopy in the pump-probe geometry [14, 16]. Rather than employing perpendicularly polarized pump pulses, a configuration similar to that used in optical Kerr effect spectroscopy (OKE) can be implemented.

In isotropic media, there are four nonzero components of the third order nonlinear response, three of which are independent [22]. Achieving optimized heterodyne detection via polarization discrimination can be performed for components where the probe and analyzer are orthogonal. Since the Dazzler does not allow independent control of the two pump polarizations, the XYXY and XYYX elements cannot be separately measured. Here we oriented the pump and probe polarizations at 45o relative to each other. An analyzer oriented perpendicular to the probe then detected a signal proportional to XYXY + XYYX. Optimized heterodyne detection can be achieved by rotating the analyzer slightly (~5°) to provide the desired amplitude of the local oscillator field. This procedure adds a small component of the elements XXXX and XXYY to the overall measurement. Both XXXX and XXYY elements can be independently measured, although their SNR will be reduced due to the lack of control over the local oscillator amplitude. For many applications the ability to measure XXXX, XXYY and the combination XYXY + XYYX is sufficient, enabling suppression of diagonal peaks for example [23–25]. To implement the full range of polarization schemes aimed at suppressing diagonal features, enhancing cross peaks and determining angles between transition dipoles, independent control over the pump pulse polarizations may be desirable. In this case pulse-shapers capable of polarization-shaping [26] or a noncollinear geometry can be used.

3. Experimental results

To demonstrate the two-color 2DES method we have studied LDS750 in acetonitrile. This laser dye shows a large Stokes shift due to a combination of solvation and intramolecular relaxation processes [27], making it suitable to demonstrate the two-color capabilities of the experiment. Figure 2 shows the absorptive (real), imaginary and the absolute value 2D spectra at t2=500 fs. The vertical asymmetry of the lineshape is largely attributed to unequal bandwidths of the pump (18 THz, center at 549 THz) and probe (26 THz, center at 436 THz) pulses. Under our experimental conditions peak distortions due to propagation effects may be significant [28–30]. While overall distortions are expected to be reduced in the current pump-probe implementation compared to the box-car geometry, the high signal-to-noise achieved here suggests that reducing the sample thickness and OD will be feasible in future experiments to minimize these effects. In addition, adopting the 2D representation suggested by Yetzbacher et. al. will aid in producing 2D spectra that are less susceptible to distortions [30].

 

Fig. 2. (a) Real (absorptive), (b) Imaginary and (c) Absolute value components of the 2D spectrum of LDS750 in acetonitrile at t ₂=500 fs. Data is taken in using polarization scheme ii).

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Figure 3 shows absorptive 2D spectra of LDS750 taken at t ₂=300 fs for two different polarization schemes. Here the pump excitation was lowered to 1 nJ for both measurements to illustrate the improved SNR obtainable when the ratio of signal to local oscillator can be adjusted. The probe energy was 1 nJ in both cases and the overall signal level at the detector was equalized in the two measurements by applying ND filters to scheme i). The polarizer extinction ratio was measured to be better than 10000:1. Figure 3a) corresponds to the data taken with polarization scheme i), while Fig. 3b) shows the data for scheme ii). Polarization scheme i) probes the parallel (XXXX) component of the response function. In this configuration the signal and local oscillator have the same polarization and their relative amplitudes cannot be adjusted to optimize the SNR of the heterodyne-detected signal. In scheme ii), the pump pulse is oriented at 45° with respect to the probe, and an analyzer is set to be orthogonal to the probe pulse. Tilting the analyzer slightly (~5°) permits an arbitrary amount of local oscillator to enter the detector to optimize the heterodyne detection. Scheme ii) mixes XYXY and XYYX components of the response function but provides an enhanced SNR. The data shown in Fig. 3 shows an enhancement of ~3 in the SNR of the data obtained with scheme ii) compared to scheme i). We note that the overall SNR improvement is closer to ~9 because of the comparatively larger XXXX signal. Further enhancement can be readily made by increasing the probe strength in scheme ii) [16].

 

Fig. 3. Improved SNR achieved with different polarization schemes for LDS750 in acetonitrile at t ₂=300 fs. a) Absorptive 2D spectrum for the parallel polarization configuration (scheme i). b) Absorptive 2D spectrum for the 45° polarization configuration (scheme ii)).

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In Fig. 4 we demonstrate the ability to use the pulse-shaper to separate rephasing and nonrephasing contributions to the 2D spectrum. We acquire two separate 2D signals with phase shifts ϕ ₁₂=ϕ ₂-ϕ ₁=0° and ϕ ₁₂=90° and combine the two scans in the time domain. As will be discussed in Section 4, the sum of the two signals provides the rephasing component while the difference yields the nonrephasing component.

High relative phase stability between the pump pulse pair and the probe/local oscillator pair in 2D spectroscopy is crucial and difficult to achieve at visible wavelengths. In the pump-probe geometry, the fact that the local oscillator is derived from the probe pulse ensures passive phase stability for the probe/local oscillator pair. We used spectral interferometry to characterize the phase stability of the pump pulse pair produced by the Dazzler. Using a fixed delay of 400 fs between the pulses, we acquired spectra every minute over the period of 3 hours and examined the RMS deviation of the spectral phase from the expected linear form. Over this time interval we measured an RMS phase stability of λ/85 at 530 nm, comparable to what has been achieved with diffractive optics [4]. The majority of the phase instability in our setup is thought to come from changes in beam pointing into the Dazzler.

4. Discussion

2D spectroscopy is a third order technique, probing the optical polarization induced in a material by a sequence of three laser pulses. Provided the probe pulse follows the pump pulses at sufficiently large delay to avoid temporal overlap between pump and probe pulses, the system response to the three incident fields can be characterized by a response function R(t ₃, t ₂, t ₁) that consists of a sum of rephasing and nonrephasing contributions [31,32]:

The rephasing and nonrephasing components are each composed of a number of Liouville pathways that enumerate the possible light-material interactions, including excited state absorption, excited state emission and ground state bleaching [31,32].

In the pump-probe geometry, the total signal intensity detected in the phase-matched direction is given by [10]:

where E ₃ is the probe field, P ⁽¹⁾ ₃ is the free-induction decay from pulse 3, P ⁽³⁾ _S2D is the desired polarization induced by interaction with all three pulses, P ⁽¹⁾ _{pp 1} is the pump-probe polarization resulting from pump pulse 1, and P ⁽³⁾ _{pp 2} is the pump-probe polarization from pump pulse 2. The third order polarization P ⁽³⁾ _S2D is given by the triple convolution of the third order response of the system with the three excitation fields. In the impulsive limit this is given by

whereϕ_j is a constant spectral phase due to the j ^th pulse. The desired third order signal P ⁽³⁾ _S2D can be isolated from the other contributions by either the 0°–180° phase subtraction method, or by chopping and Fourier transforming with respect to t ₁. The signal of interest is then:

Because pulses 1 and 2 have the same wavevector and are essentially interchangeable, for ϕ ₁₂=ϕ ₁-ϕ ₂=0° the time domain signal must be symmetric with respect to t ₁=0 and therefore be purely real [10]. Thus the FT with respect to t ₁ should have all its amplitude in the real part. If ϕ ₁₂=90°, the signal becomes anti-symmetric with respect to t ₁=0 and all of the amplitude will be present in the imaginary part. In practice, since we only scan positive t ₁ values, care must be taken when computing and interpreting the final 2D spectrum. We can either symmetrize the data prior to FT along t ₁, or take the Cosine transform (when ϕ ₁₂=0°) or the Sine transform (when ϕ ₁₂=90°) with respect to t ₁. Along the t ₃ dimension, causality requires that there be no 2D signal if pulse 3 interacts with the sample before pulses 1 and 2. This requirement can be enforced by taking the inverse Fourier transform of S(ω ₃,t ₂,t ₁) to obtain a time domain signal S′(t ₃,t ₂,t ₁), and then setting the signal to zero for t ₃<0. Upon applying the symmetry and causality conditions, Fourier transform with respect to t ₁ and t ₃ yields the complex 2D spectrum, the real part of which is purely absorptive. While the imaginary part of the data shown in Fig. 2 resembles a dispersive spectrum, it contains no new information. It is equivalent to a Kramers-Kronig inversion of the absorptive data over a finite frequency range and is therefore not a complete measure of the dispersive susceptibility [19].

As recent work has shown, separating rephasing and nonrephasing spectra can be useful for observing vibronic modulation of 2DES lineshapes [33]. De Boeij et. al. [34,35] suggested a method for recovering the rephasing and nonrephasing components of frequency-resolved phase-locked pump-probe signals. This can be easily applied to the pump-probe implementation of 2D spectroscopy to obtain the rephasing and nonrephasing signals. Briefly, we collect data with the relative phase of the pump pulses at ϕ ₁₂=0° and ϕ ₁₂=90°. After inverse Fourier transformation along ω ₃ and enforcing causality, we obtain respectively:

Combining these gives the separated signals S′₀°(t ₃,t ₂,t ₁)+iS′_90°(t ₃,t ₂,t ₁)∝R ^(R)(t ₃,t ₂,t ₁) and S′₀°(t ₃,t ₂,t ₁)-iS′_90°(t ₃,t ₂,t ₁)∝R ^(NR)(t ₃,t ₂,t ₁). These combinations can then be Fourier transformed along t ₁ and t ₃ to give the 2D rephasing and nonrephasing spectra.

 

Fig. 4. Separation of the rephasing and nonrephasing contributions for LDS750 in acetonitrile at t ₂=500 fs taken using polarization scheme ii). The columns contain real, imaginary and absolute value spectra as indicated. Top row: components of the rephasing signal. Middle row: components of the nonrephasing signal. Bottom row: addition of the rephasing and nonrephasing signals.

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2D spectroscopy in the pump-probe geometry is considerably easier to implement than noncollinear approaches. The great benefit of using a pulse-shaper to generate the t ₁ delay is that it removes any uncertainty as to the location of t ₁=0, allowing easy measurement of the absorptive 2D spectrum [13,15]. The information content of the absorptive component has been shown to be equivalent to that obtained by noncollinear 2D FT [10]. We note that the imaginary component of the 2D spectrum, being equivalent to a finite bandwidth Kramers-Kronig inversion of the absorptive data, provides no new information beyond what is present in the absorptive spectrum. The dispersive spectrum can be obtained by noncollinear 2D implementations, or by an alternate polarization scheme that allows control over the relative signal/local oscillator phase [14]. Use of a pulse-shaper also provides access to phase-cycling procedures that can improve the SNR [13] and isolate signals of interest. For example, we have demonstrated that rephasing and nonrephasing spectra can be separated by acquiring data with ϕ ₁₂=0° and ϕ ₁₂=90°.

While simpler to implement than noncollinear approaches to 2D spectroscopy, the pump-probe geometry is not a background free measurement and as such will have a poorer SNR. For some of the tensor components (where probe and analyzer are orthogonal), polarization schemes can remove this difficulty, allowing optimization of the SNR of the heterodyne-detected signal. Pulse-shapers that lack polarization control will limit the number of independent tensor components that can be measured when used in the pump-probe geometry. Full polarization control, which can be useful for selecting particular contributions to a 2D spectrum, may be desirable for some applications.

5. Conclusions

In summary we have demonstrated a pulse-shaping-based approach for obtaining absorptive 2D spectra in a noncollinear pump-probe geometry at visible frequencies. We have shown that a simple polarization scheme improves the SNR achievable in the pump-probe geometry and have explored several phase-cycling methods to improve the SNR and to separate rephasing and nonrephasing contributions. The ease of the method will make 2D spectroscopy accessible to a wide range of research groups, as well as open up new frequency ranges such as the ultraviolet, where pulse-shapers have recently become available. Finally, while here we have demonstrated two-color 2DES, the pump-probe approach opens up the possibility of using a white-light continuum probe as is often employed in transient absorption spectroscopy.