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Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy Franklin D. Fuller and Jennifer P. Ogilvie Department of Physics, University of Michigan, Ann Arbor, Michigan 48109; email: [email protected]
Annu. Rev. Phys. Chem. 2015. 66:667–90
Keywords
The Annual Review of Physical Chemistry is online at physchem.annualreviews.org
two-dimensional spectroscopy, Fourier transform spectroscopy, electronic spectroscopy
This article’s doi: 10.1146/annurev-physchem-040513-103623 c 2015 by Annual Reviews. Copyright All rights reserved
Abstract Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as crosspeak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the underlying system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.
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INTRODUCTION Insight into molecular processes requires spectroscopic probes with high time resolution and wavelengths ranging from the ultraviolet (UV) to the far infrared (IR). Since the earliest pump-probe spectroscopy measurements (1, 2), a vast array of spectroscopic approaches has been developed and applied to a wide range of systems (3–5). Time resolution has progressed from milliseconds to attoseconds, and the development of stable broadband sources within the UV, visible, and IR regimes continues. The current state of the art of optical spectroscopy of molecular processes in the condensed phase aims to extract the greatest possible spectral information with ultrafast time resolution. Since the first experimental demonstrations (6–9), multidimensional optical (visible and IR) spectroscopy has been applied to address many fundamental questions in condensed phase dynamics. Many excellent reviews and texts discuss the principles and recent applications of multidimensional spectroscopy (4, 5, 10–16). It has been performed over a wide range of wavelengths, from the UV (17–23), through the visible (8, 14, 21, 24–46) and mid-IR (9, 47–57), to terahertz frequencies (58, 59). Most multidimensional spectroscopic measurements to date have been restricted to studies of one or a small number of transitions found in a narrow range within visible or mid-IR regimes. The ability to uncover correlations between multiple distant transitions may offer unique information that permits a richer understanding of the system. Frontiers of multidimensional spectroscopy include mixing frequency regimes and measurement modalities and the expansion of the various frequency axes of multidimensional spectra to the broadest possible extent. Here we briefly review the principles of two-dimensional Fourier transform (2D FT) spectroscopy. We discuss the basics of 2D FT implementation, with an emphasis on particular challenges at visible (and higher) frequencies. We outline the main experimental approaches that have been utilized for two-dimensional Fourier transform electronic spectroscopy (2DES), comparing and contrasting the benefits and drawbacks of the various methods. We discuss efforts to implement broadband 2DES measurements and conclude with some thoughts about current frontiers in 2DES.
2D FT: two-dimensional Fourier transform
Annu. Rev. Phys. Chem. 2015.66. Downloaded from www.annualreviews.org Access provided by Michigan State University Library on 02/12/15. For personal use only.
2DES: two-dimensional Fourier transform electronic spectroscopy
From Pump-Probe to Two-Dimensional Fourier Transform Spectroscopy: Adding a Dimension In many ways, 2D FT is an extension of pump-probe spectroscopy, offering similar information, but remedying some shortcomings of the pump-probe experiment. In a frequency-resolved pumpprobe experiment, an initial pump pulse excites the system of interest. The system is then probed by a second pulse, and the resulting signal is recorded as a function of the waiting-time delay between pump and probe pulses (see Figure 1a). When the transitions involved are well separated, it is possible to visualize processes such as energy transfer or the formation of intermediate photoproducts by observing the transient evolution of the detected peaks. A continuum probe is often used in pump-probe spectroscopy (60, 61) to obtain spectral information over a broad range of the detected frequencies, which can help resolve the dynamics of overlapping features by looking at distant and related peaks in the detection energy. Two-dimensional spectroscopy solves the problem of untangling overlapping signals more generally by also resolving the detected signal as a function of excitation energy, giving a direct view of the potentially multiple transitions that contribute to a given detected signal. The time resolution of dynamics over the waiting time, in both a pump-probe and 2D experiment, is determined by the duration of the pump pulse, with shorter pulses giving higher time resolution. The commensurately larger bandwidth of a shorter pulse leads to a trade-off between time and frequency resolution in a pump-probe experiment: the shorter the pump pulse, the higher the 668
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Figure 1 (a) Pulse sequence for pump-probe spectroscopy. (b) Pulse sequence for transient-grating (TG) spectroscopy. The hashed pump pulse indicates the presence of two time-coincident pump pulses that are crossed at an angle. (c) Pulse sequence for two-dimensional Fourier transform (2D FT) spectroscopy. (d ) Pulse sequence for fluorescence-detected two-dimensional spectroscopy. (e–i ) Phase-matching condition for (e) 2D FT in the pump-probe geometry, ( f ) the rephasing 2D FT signal in the BOXCARS geometry, ( g) the nonrephasing 2D FT signal in the BOXCARS geometry, (h) the TG signal in the BOXCARS geometry, and (i ) the rephasing, nonrephasing, and TG signals for a hybrid pulse-shaping diffractive optics–based approach that employs two time-delayed pulses along k1 and k2 (63).
time resolution and the lower the certainty of the excitation frequency as determined by the timebandwidth product of the pulse. This trade-off is circumvented in 2D spectroscopy using the Fourier transform methodology (10). Instead of scanning a single narrowband pulse in frequency (often called a double-resonance experiment), one resolves the excitation axis by scanning a delay between a pair of broadband pulses. The signal generated by the system oscillates as a function of the interpulse pump delay τ , allowing the excitation axis to be recovered by Fourier transforming the signal along the τ axis. The result has both high temporal and spectral resolution, limited only by the signal-to-noise ratio. Figure 1c shows the pulse sequence for 2D FT spectroscopy. The most commonly used form of 2D FT spectroscopy employs three identical pulses, effectively splitting the pump pulse of a pumpprobe experiment into two time-delayed interactions with the sample. The signal is then recorded as a function of all three time delays. For a given waiting time T, the Fourier transform of the signal with respect to the τ and t delays provides the 2D FT spectrum. 3D FT spectroscopy additionally Fourier transforms the signal with respect to T, producing a 3D frequency solid. Other collection www.annualreviews.org • 2D FT Electronic Spectroscopy
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FD-2D: fluorescence-detected two-dimensional Fourier transform
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BOXCARS: a geometry commonly used in four-pulse experiments in which the wave vectors of the four pulses each point to one corner of a box TG: transient grating
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modalities exist. For example, in a fluorescence-detected version of the experiment [fluorescencedetected two-dimensional Fourier transform (FD-2D) spectroscopy] (see Figure 1d ), a fourth pulse places the system in an excited state population from which the spontaneous fluorescence emission is measured (62). In 2D FT spectroscopy, two different phase-matched signals are typically recorded: the rephasing and nonrephasing signals in the k2 − k1 + k3 and k1 − k2 + k3 directions, respectively. When summed, these signals yield the absorptive 2D FT spectrum, free from broadening refractive contributions. Another signal, with the phase-matching direction k1 + k2 − k3 , yields information about double-quantum coherences (10). Depending on the experimental geometry of the incident pulses, the phase-matching condition for the various signals determines the direction of their emission. A range of geometries has been employed for 2D FT measurements, including fully collinear (not shown in the figure) and a partially noncollinear pump-probe geometry in which the first two pulses are collinear, followed by a probe pulse at a small angle, as depicted in Figure 1e. A fully noncollinear BOXCARS setup is frequently used, and Figure 1f,g shows the phase-matching conditions for the rephasing and nonrephasing signals, respectively. Phase matching for transient-grating (TG) signals in the BOXCARS geometry is shown in Figure 1h, whereas Figure 1i shows the phase-matching conditions for a recently employed hybrid pump-probe-BOXCARS geometry (described in further detail in the Pump-Probe Geometry section and in Reference 63).
What Is in a Two-Dimensional Fourier Transform Spectrum? The typical information available from absorptive 2D FT spectra is summarized in Figure 2. The T = 0 correlation spectrum (Figure 2a) contains valuable information about the fundamental lineshapes of the transitions under study, in which the ratio of the diagonal to antidiagonal width reflects the degree of inhomogeneous versus homogeneous broadening (8, 10). At longer T delays, the diagonal elongation of an inhomogeneously broadened transition is lost as the system loses memory (correlation) of the initial excitation frequency. The timescale of this memory loss provides the timescale of spectral diffusion and has found applications in understanding liquid dynamics and solvation (8, 52, 64). The dynamic Stokes shift is also directly observable by the shift of a transition from being centered along the diagonal (65). Excitonic coupling between transitions is manifested by cross peaks in the T = 0 spectrum, whereas the growth of cross peaks at later waiting times reflects energy transfer (24). Waiting-time-dependent oscillations of the diagonal and cross peaks reflect vibrational, vibronic, and electronic coherences. The physical origin of such oscillations and their possible importance for photosynthetic energy and charge transfer continue to be subjects of intense debate (27, 29, 43, 46, 66–76). Excited state absorption is also evident in 2D FT spectra, often showing up above the diagonal in electronic spectra and below the diagonal in vibrational spectra (providing a measure of anharmonicity).
CHALLENGES OF IMPLEMENTING TWO-DIMENSIONAL FOURIER TRANSFORM SPECTROSCOPY The principal technical challenge in implementing a multidimensional Fourier transform experiment is creating and delivering the appropriate pulse sequence with variable, yet phase-stable time delays between them. Phase stability refers to the variation of the phase of one optical pulse with respect to the other for a given time delay. To first order, phase stability is equivalent to a timing jitter between the pulses—the relevant timescale of which is given by the oscillation period of the optical field (proportional to the wavelength). As a consequence, the shorter the wavelength 670
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Figure 2 Schematic illustration of the information contained in absorptive two-dimensional Fourier transform spectra. The observed spectral range shown in the unshaded region is determined by the excitation and detection laser bandwidths. (a) The T = 0 correlation spectrum reveals homogeneous and inhomogeneous line widths, excitonic coupling, and excited state absorption features. (b) At T > 0, the broadening of peaks in the antidiagonal direction reflects spectral diffusion. The growth of cross peaks indicates energy transfer. The emergence of an entirely new peak at later waiting times, such as the B D cross peak in panel b, represents the formation of a new product species, populated upon excitation of B , that absorbs at D. An example of such a process is the generation of a charge-separated state in the photosystem II reaction center (data shown in Figure 4).
becomes, the more phase stability becomes a demanding instrumentation consideration. In the most common 2D FT measurements, phase stability and precise timing are required only over the time delays that will be Fourier transformed: typically the τ and t delay. During these time intervals, the system is in a coherence between the ground and excited state, while it is in a population during the waiting-time period. In some cases, the first two pulse interactions may produce a coherence between vibrational, vibronic, or electronic excited or ground states, and Fourier transforming over the T delay yields a 3D FT spectrum that reveals the waiting-time coherence frequencies. These frequencies are typically orders of magnitude lower than optical frequencies and do not require the high degree of phase stability that an optical frequency coherence requires. For two-quantum (2Q) measurements, a fully phase-stable setup is desired because the system in is a coherence between the ground and 2Q excited state during the T period, requiring a high degree of phase stability over that time interval. In typical 2D FT experiments, the τ delay is scanned in the time domain, and the excitation frequency axis is obtained via Fourier transform. To convert time delays to accurate Fourier transform frequencies, one requires an interferometric precision of ∼λ/100, corresponding to timing errors of ∼0.017 fs at 500 nm (10). At long wavelengths, this requirement is considerably easier to meet, and many two-dimensional Fourier transform infrared (2D IR) implementations use conventional delay stages without any form of active or passive phase stabilization, although scanning artifacts from imperfect translation stages have been shown to degrade the quality of 2D IR spectra (77). In a well-constructed interferometer, optical path-length fluctuations and mechanical instabilities have been found to introduce root-mean-square timing errors of ∼0.1 fs www.annualreviews.org • 2D FT Electronic Spectroscopy
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2D IR: two-dimensional Fourier transform infrared
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over a 20-min period (10). Because many 2DES experiments require a timescale on the order of minutes for the collection of a single 2D spectrum, mechanisms for both stabilizing the phase and precisely measuring time delays are needed. In 2D FT spectroscopy, the detection frequency axis is typically obtained via a heterodynedetected frequency-domain measurement of the signal, in which a spectrometer effectively performs the Fourier transform. In heterodyne detection, the signal field is interfered with a local oscillator field to amplify the signal and enable the extraction of the complex signal field (78). In the fully noncollinear geometry, the complex field is extracted via spectral interferometry (79). A stable relative time delay and phase between the signal and local oscillator are critical to obtaining high signal-to-noise ratios. Another challenge of 2D FT spectroscopy, common to many scientific measurements, is that the desired 2D signal is typically small and must be isolated from a large background field and from other spurious signals, such as scatter or other undesirable nonlinear signals. Three techniques are commonly used in the literature to tackle this broad problem: amplitude modulation, phase modulation or cycling, and phase matching. Quite often, combinations of some or all of these methods are used, depending on the ease with which they can be applied in different experimental implementations. Fully noncollinear 2D FT experiments face an additional challenge of phasing the 2D spectra. To obtain the maximum information from 2D measurements, it is often desirable to have absorptive spectra, which are obtained by adding rephasing and nonrephasing signals with the appropriate phase relationship. Absorptive 2D spectra are free from broadening refractive contributions and provide information about the absolute sign of different spectral features, facilitating their physical identification (10). Although frequency-domain (79) or time-domain (80) heterodyne detection allows one to measure the complex signal, in some experimental implementations of 2D FT spectroscopy, the detected signal is phase shifted from a purely absorptive or dispersive signal by a polynomial function of the frequency. The unknown phase shift can be found by measuring the spectrally resolved pump-probe signal and invoking the projection-slice theorem (10). The pump-probe represents the real part of the third-order signal, and when compared to the absolute value of the signal recovered by spectral interferometry, it is possible to find a polynomial phase that connects the two. One disadvantage of this approach is that the signal-to-noise ratio of the pump-probe data is often poor, making precise phasing difficult. An equivalent phasing problem arises in heterodyne-detected TG spectroscopy, where the absorptive component of the TG signal is equivalent to the pump-probe signal but can be measured with a higher signal-tonoise ratio with optimized heterodyne detection (81–83). Other approaches to solving the phasing problem have employed a balanced detection scheme to obtain absorptive TG data (83) and then used higher signal-to-noise TG data for phasing 2D spectra (84). Alternatively, precise phasing without the need to invoke the projection-slice theorem has also been demonstrated (84–86).
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Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy The challenges of implementing 2DES have been met using a variety of approaches. Here we briefly discuss the main methods that have been used. We summarize their advantages and disadvantages and their inherent bandwidth limitations. Interferometer-based setups. Many of the first multidimensional Fourier transform experiments employed interferometers to generate the time-delayed pulse pairs and spectral interferometry to detect the complex signal (6, 8). In pioneering work to map out the χ (2) response of a 672
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nonlinear crystal, the Joffre group (6) utilized spectral interferometry between a reference pulse and both exciting pulses and between the reference pulse and signal to record the relative time delay and determine the full complex signal field in two dimensions. In the first third-order 2DES measurements, the Jonas group (8) used a fully noncollinear beam geometry generated by a fourbeam interferometer. They calibrated their translation stages using spectral interferometry, with a tracer beam that followed the signal path to determine the absolute signal phase (8, 87), enabling phasing of the obtained spectra. The Cundiff group has developed an actively phase-stabilized approach, in which two interferometers generate the required excitation and local oscillator pulses and a third interferometer is used to lock their relative phases. The setup utilizes a continuous-wave laser that copropagates through the interferometers to control the relative delays and phases via path-length adjustments made by mirrors mounted on piezoelectric transducers (88). This setup enables standard onequantum as well as 2Q and 3D measurements and phase-cycling capabilities that can be used to reduce scatter signals. This group has demonstrated an all-optical method for phasing their data (85). In general, interferometer-based approaches enable broadband measurements and are typically limited by the optical coatings on the beam splitters and mirrors.
DO: diffractive optics
Passive phase stabilization. Although the component technology to accomplish active stabilization schemes exists commercially, the coordination of motion control, electronics, and auxillary optical measurements makes such instruments nontrivial to construct. For this reason, passively phase-stable implementations, requiring only optical elements, have been widely pursued, and several methods have emerged. In general, passively phase-stable instruments are easy to construct and maintain but may have some bandwidth limitations due to their optical components. Diffractive optics–based methods. A simple solution to implementing 2DES with passive phase stabilization is to use diffractive optics (DO) to generate the required pulse sequence and phasematched geometry. DO have been employed in TG spectroscopy (81, 89) and fifth-order Raman spectroscopy (90, 91), in which they have been used for passively phase-stable heterodyne detection. To extend the use of DO to 2D spectroscopy, investigators needed to be able to control time delays between pulse pairs. Refractive delays using rotating cover slides (92, 93) or the translation of wedges (94, 95) have been used for this purpose. DO-based approaches are background-free and fully noncollinear, offering the ability to optimize the signal-to-noise ratio and implement polarization-dependent measurements. As a consequence of being fully noncollinear, however, they do require phasing of the data to obtain absorptive 2D spectra. For extremely broadband 2DES, the use of DO imposes a limit of an octave of bandwidth owing to overlapping diffraction orders produced by the DO. The use of refractive elements to produce the τ delay also poses a problem for large bandwidths if the pulse broadening is too large over the τ range that is scanned. For room-temperature measurements of condensed phase systems, a scan range of ∼300 fs is typical. For an ∼10-fs pulse at a 600-nm center wavelength, this produces an ∼6% pulse broadening. Another approach to achieving passive phase stability is to have the optical paths of the relevant pulse pairs in the experiment experience similar path-length fluctuations, whose correlated noise cancels in the total signal phase. The Miller group (92) implemented this idea using stacked retroreflectors, obviating the need for a refractive delay line. They also developed an approach that incorporates pulse shaping of the pump pulses with a DO-based, fully noncollinear BOXCARS geometry (96). Their method features an improved scanning protocol that decouples the τ and T delays that were previously coupled in the original design (92). It also improved on the phase stability by using hollow retroreflectors rather than roof mirrors. The use of a pulse shaper prior www.annualreviews.org • 2D FT Electronic Spectroscopy
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to the DO setup enables coherent control experiments in which both pump pulses are shaped equivalently. The Miller group (97) demonstrated that the method supports broadband 2D FT spectroscopy over the 500–690-nm range and recorded 2D FT spectra with shaped pulses that they had previously found to control population transfer in rhodamine 101. A variation on the DO setup was developed to enable 2Q measurements with the use of DO consisting of two perpendicularly oriented transmission gratings to generate all four beams for a BOXCARS geometry from a single input beam, ensuring high phase stability between all four pulses. In this arrangement, three wedge pairs were employed to scan the relative delays (98). The use of wedges in this implementation restricts the achievable delays for broadband pulses, a drawback if the evolution along T is of interest but quite sufficient for 2Q measurements. A novel DO-based approach was recently demonstrated by the Hauer group (84). They employed two DO elements and a modified phase-matching geometry. A distinct advantage of their method is that it uses a balanced detection approach to simultaneously collect rephasing and nonrephasing signals. This also enables them to obtain absorptive TG instead of pump-probe signals to phase the data. For low signal-to-noise experiments, this avoids the need to use noisy pumpprobe data. The Zigmantas group (99) demonstrated high signal-to-noise ratio measurements in highly scattering samples combining a DO-based approach with double modulation with optical choppers. In general, DO-based approaches enable broadband measurements, although they are ultimately limited to an octave of bandwidth owing to overlapping diffraction orders from the DO. If refractive delays are used, pulse broadening may be a limiting factor.
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Other passively phase-stable approaches. Several approaches that employ passive phase stability without DO have also been developed. The Brixner group (100) demonstrated an all-reflective BOXCARS setup that uses beam splitters rather than DO, enabling broader bandwidth applications. It utilizes the concept of correlated pulse pairs demonstrated by the Miller group (92) to achieve passive phase stability. The Meech group (101) expanded on this design, adding a double chopping scheme along with a high-speed, single-line CCD (charge-coupled device) to permit rapid spectral acquisition and improved scatter removal. Aiming at broad-bandwidth applications, several other all-reflective approaches have been demonstrated recently. Rather than generating the four beams for a BOXCARS setup from DO, the Pfeifer group (102) utilized a spatial mask, as previously used by the Nelson group (103) in a pulse-shaping-based setup. The four beams then hit common optics, with the exception of a quadrant mirror with four independent piezoelectric stages to scan the required delays. An all-reflective setup was also recently developed by the Engel group (104). They generated the four beams for their BOXCARS experiment using beam splitters and employed independent mirrors mounted to slightly angled stages to achieve fine control of the τ delay. They reported phase stability of λ/75 at 800 nm between pulse pairs. Pulse-shaping methods. Pulse shapers for 2DES were first employed by the Warren group (62) in a fully collinear geometry, using FD-2D. Fully collinear measurements contain many spatially overlapping signals and utilize phase cycling rather than phase matching to separate out the desired signal components. Optical 2D spectroscopy with phase cycling was first proposed by Ernst and colleagues (105) and is readily implemented with pulse-shaping technology. The use of a pulse shaper enables phase-cycling methods that are commonly used in nuclear magnetic resonance spectroscopy (106). Phase-cycling approaches are less restricted by sample size than fully noncollinear implementations that require coherent buildup of the signal, making them more amenable to studies of smaller numbers of molecules, particularly in combination with fluorescence detection. In FD-2D, a fourth interaction with the sample converts the third-order coherence into a population that is detected via spontaneous fluorescence (see Figure 1d ). 674
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Fully noncollinear 2D FT spectroscopy with a pulse shaper has been pioneered by the Nelson group (103, 107–109). Their approach has full passive phase stability of all four beams used in the experiment and has no moving parts. The basis of their approach is to employ a spatiotemporal pulse shaper to vary the relative timing and phase of the different pulses. This approach is very versatile and can easily switch between different phase-matching conditions for different measurements. The passive phase stability of all pulses enables the measurement of 2Q and higher signals (107). Because the pulse shaper generates all the time delays, this limits the spectral resolution of any Fourier-transformed dimension and the maximum waiting time in standard 2D experiments. The optical design of the spatiotemporal pulse shaper causes some issues with variable chirp for the different pulses and intensity-dependent delays that can be largely corrected (107). The bandwidth of pulse-shaper-based 2DES methods is likely limited by the pulse shaper itself. For spatial light modulators, the coatings may be the limiting factor, whereas diffraction efficiency and dispersion may be limiting for acousto-optic devices.
AOM: acousto-optic modulator
Phase-modulation two-dimensional spectroscopy. Rather than employing phase cycling to enable the isolation of particular signals of interest in collinear FD-2D experiments, the Marcus group (37) has pioneered a related phase-modulation approach. The close relationship between phase-cycling and phase-modulation approaches has been discussed by Nardin et al. (110). The phase-modulation approach uses acousto-optic modulators (AOMs) in each arm of two MachZender interferometers to generate the four collinear pulses used in the experiment. The AOMs impart a radio-frequency shift individually to the four pulses, tagging each with a unique frequency. The frequency shifts are measured using the interference of a narrowband selection of the excitation pulse itself (37) or a continuous-wave reference passing through the same interferometer (110). Signals are isolated and demodulated via lock-in amplification using a reference signal constructed from the observed frequency shifts. This phase-modulation scheme effectively removes time-delay jitter introduced by mechanical instabilities of the interferometers, and the use of lock-in detection enables the suppression of low-frequency noise (37). The Marcus group (36) has shown that the information content in FD-2D experiments is complimentary but distinct from 2DES experiments. Their method has few limitations on bandwidth, with the AOMs likely the limiting factor. In the IR, in which AOMs are highly inefficient, a wobbling Brewster window, or a photoelastic modulator, has been used to achieve subcycle delays that approximate pure phase shifts in noncollinear 2D IR experiments (111). This approach has been used to enable quasi-phasecycling schemes for scatter removal and to avoid the duty-cycle loss incurred by optical chopping. Subcycle delays approximate pure phase shifts only over a narrow bandwidth, however. Pump-probe geometry. Although the fully noncollinear geometry has been the most common approach to 2D FT spectroscopy, Faeder & Jonas (112) suggested that a pump-probe geometry could ease some of the technical demands. This type of geometry was previously used in timedomain photon-echo measurements (80, 113). In the pump-probe geometry, the two pump pulses are collinear, and the probe is crossed at a small angle, as in pump-probe spectroscopy. This approach was first implemented by Shim et al. (114) in the IR using a pulse shaper and later by DeFlores et al. (115) using a Mach-Zehnder interferometer. It was also implemented by Gumstrup et al. (116) using pulse shapers in the near IR and by our group in the visible range (117). In the pump-probe geometry, both the rephasing and nonrephasing signals are emitted along the probe direction (k1 = k2 ), allowing them to be collected simultaneously. This has the advantage of removing timing errors that can be introduced in separate rephasing and nonrephasing scans. As in pump-probe spectroscopy, the probe acts as a heterodyning field with a well-defined zero phase www.annualreviews.org • 2D FT Electronic Spectroscopy
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TWINS: Translating-WedgeBased Identical Pulses eNcoding System
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relative to the signal. Because the probe enters the detector, the method is not background-free and may therefore suffer from a reduced signal-to-noise ratio, depending on the detailed noise characteristics of the setup. Polarization schemes can remove this difficulty for recording some of the tensor elements of the χ (3) response (117, 118). We have recently compared pulse-shaping-based measurements in the pump-probe and fully noncollinear geometries, finding an improvement of ∼20× in the fully noncollinear geometry (63). Rock et al. (119) recently compared a pump-probe pulse-shaping-based 2D IR setup to a conventional fully noncollinear 2D IR spectrometer with no passive or active phase stabilization. They found that the pulse-shaping-based pump-probe configuration offered an enhanced signal-to-noise ratio, attributed to the higher phase stability of the pulse-shaping-based approach. Recently, the Jonas group (120) used the pump-probe geometry with the sample embedded in a Sagnac interferometer. This approach permits optimization of the heterodyne detection via interference between the probe and reference to control the signal-to-local oscillator ratio. When the pump-probe geometry is used in combination with a pulse shaper, the τ delay can be generated with high precision, removing timing errors and uncertainty in the location of τ = 0. Furthermore, because the heterodyning probe field is known to have zero phase offset from the signal, the phasing problem is eliminated and absorptive spectra are obtained automatically. The use of a pulse shaper also enables phase-cycling methods to remove scatter signals (114) and separate rephasing and nonrephasing contributions (117) and TG signals (63). An important practical implementation for phase cycling is the speed with which it can be performed. Pulse shapers that can be updated on a shot-to-shot basis can more effectively remove laser power fluctuations that often dominate the noise in 2DES measurements. Phase-cycling schemes for both 2DES (121) and fifth-order 3D spectroscopy (122) in the pump-probe geometry have recently been detailed by the Tan group. The latter is analogous to fifth-order measurements that have been made in the IR regime (123, 124). An alternate scheme for generating phase-stable collinear pulses for 2D spectroscopy in the pump-probe geometry is the TWINS (Translating-Wedge-Based Identical Pulses eNcoding System) method of Cerullo and colleagues (125). Inspired by the Babinet-Soleil compensator, this approach uses pairs of birefringent wedges to generate pulse delays with high precision and phase stability. The method can readily produce pulse pairs with parallel or orthogonal relative polarization to enable polarization-based signal selective and background suppression methods (118). Although the method introduces material dispersion, TWINS has been demonstrated with 13-fs pulses, and with the appropriate choice of materials, it is thought to be useable with sub-10-fs pulses (125). TWINS has recently been extended to 2D IR spectroscopy using a different choice of wedge material (126). Although considerably cheaper and with broader bandwidth than pulse shapers, the TWINS approach does not readily enable phase cycling for separation of rephasing and nonrephasing signals and reduction of scatter contributions. We recently developed a hybrid pulse-shaper-DO approach (63) that borrows the time precision and simultaneous rephasing and nonrephasing acquisition of the pulse-shaping pump-probe method and combines it with the background-free properties of traditional DO-based setups. In this setup, two beams of the usual BOXCARS geometry are each supplied with two collinear pump pulses generated from a pulse shaper (Figure 1i). The probe beam and local oscillator beams are brought into the other two beams of the BOXCARS geometry. The result is that background-free TG, rephasing, and nonrephasing signals simultaneously enter the spectrometer and can then be separated from each other via phase cycling. The concept is less clean than other setup designs, but the implementation and alignment are quite simple owing to the lack of moving wedge pairs or stages. We find that the signal-to-noise ratio is more than an order of magnitude improved from a pump-probe geometry setup, principally because of the background-free design permits Fuller
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Figure 3 Setup illustrating (a) two-dimensional Fourier transform electronic spectroscopy (2DES) in the pump-probe geometry with a pulse shaper (116, 117), (b) diffractive optics (DO-)based 2DES (93, 95), and (c) a hybrid pulse-shaper-DO setup with drop-in modification (63). In all three setups, lenses are shown for convenience only; imaging is typically done with reflective optics to reduce dispersion. Abbreviation: LO, local oscillator.
larger probe energies and the adjustment of the local oscillator to the signal intensity ratio. Finally, the simultaneous collection of rephasing and nonrephasing signals and the excellent time zero certainty of the pulse-shaped delay allow for phasing of data without the systematic noise or distortion usually encountered in traditional DO setups (63). A schematic comparison of a selection of the passively stable instruments discussed above is depicted in Figure 3.
Single-shot approaches. A problem that plagues all higher-dimensional spectroscopies is that the acquisition time increases exponentially for each dimension added. As with pulse characterization techniques (127), there are a few groups that have sought to solve this problem by measuring two dimensions simultaneously—producing a 2D spectrum in a single laser shot. The fact that the entire spectrum is collected in a single laser shot reduces systematic noise due to laser fluctuations between measurements. To detect two dimensions simultaneously, one encodes the second dimension over an extended spatial region, which necessitates higher powers and more stringent spatial mode quality from the laser source. www.annualreviews.org • 2D FT Electronic Spectroscopy
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Gradient-assisted photon-echo spectroscopy (GRAPES) uses this approach, encoding the pump delay spatially in a background-free BOXCARS geometry (128), as has been done previously for single-shot pulse characterization methods (127). To accomplish this, the two noncollinear pump beams are brought to a cylindrical focus such that one side of the focus intersects before the other, producing a spatially varying time delay across the focus. The spatially encoded time delays are then imaged into a spectrally dispersive spectrometer in which the detection axis is resolved by angular dispersion into an orthogonal direction onto a 2D detector. In its first implementation, GRAPES was used to collect rephasing spectra. The Engel group (129) has since demonstrated the acquisition of absorptive 2D spectra with GRAPES. The single-shot nature of GRAPES makes it more amenable to noisier light sources than other 2D implementations. The Engel group (130) has also demonstrated broadband (750–850 nm) GRAPES with a supercontinuum in argon gas. Although not strictly a 2DES measurement, angle-resolved coherent spectroscopy is a related single-shot method. Rather than encoding time delays spatially, it examines both the excitation energy and detection energy in k-space rather than frequency or time (131). The 2D spectrum is collected by detecting changes between the signal wave front and the input wave fronts.
GRAPES: gradient-assisted photon-echo spectroscopy
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PSII RC: photosystem II reaction center
Toward Broadband Two-Dimensional Electronic Spectroscopy The various implementations of 2DES have benefits and drawbacks from the standpoint of ease of implementation and bandwidth limitations. Table 1 summarizes some important considerations for many of the different methods discussed and notes the typical bandwidths that have been achieved to date with each approach. Many of the broadest-bandwidth approaches are limited by the bandwidth of the laser source itself. To span multiple broad electronic transitions while also attaining high temporal resolution, one needs to produce very short (
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Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy Franklin D. Fuller and Jennifer P. Ogilvie Department of Physics, University of Michigan, Ann Arbor, Michigan 48109; email: [email protected]
Annu. Rev. Phys. Chem. 2015. 66:667–90
Keywords
The Annual Review of Physical Chemistry is online at physchem.annualreviews.org
two-dimensional spectroscopy, Fourier transform spectroscopy, electronic spectroscopy
This article’s doi: 10.1146/annurev-physchem-040513-103623 c 2015 by Annual Reviews. Copyright All rights reserved
Abstract Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as crosspeak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the underlying system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.
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INTRODUCTION Insight into molecular processes requires spectroscopic probes with high time resolution and wavelengths ranging from the ultraviolet (UV) to the far infrared (IR). Since the earliest pump-probe spectroscopy measurements (1, 2), a vast array of spectroscopic approaches has been developed and applied to a wide range of systems (3–5). Time resolution has progressed from milliseconds to attoseconds, and the development of stable broadband sources within the UV, visible, and IR regimes continues. The current state of the art of optical spectroscopy of molecular processes in the condensed phase aims to extract the greatest possible spectral information with ultrafast time resolution. Since the first experimental demonstrations (6–9), multidimensional optical (visible and IR) spectroscopy has been applied to address many fundamental questions in condensed phase dynamics. Many excellent reviews and texts discuss the principles and recent applications of multidimensional spectroscopy (4, 5, 10–16). It has been performed over a wide range of wavelengths, from the UV (17–23), through the visible (8, 14, 21, 24–46) and mid-IR (9, 47–57), to terahertz frequencies (58, 59). Most multidimensional spectroscopic measurements to date have been restricted to studies of one or a small number of transitions found in a narrow range within visible or mid-IR regimes. The ability to uncover correlations between multiple distant transitions may offer unique information that permits a richer understanding of the system. Frontiers of multidimensional spectroscopy include mixing frequency regimes and measurement modalities and the expansion of the various frequency axes of multidimensional spectra to the broadest possible extent. Here we briefly review the principles of two-dimensional Fourier transform (2D FT) spectroscopy. We discuss the basics of 2D FT implementation, with an emphasis on particular challenges at visible (and higher) frequencies. We outline the main experimental approaches that have been utilized for two-dimensional Fourier transform electronic spectroscopy (2DES), comparing and contrasting the benefits and drawbacks of the various methods. We discuss efforts to implement broadband 2DES measurements and conclude with some thoughts about current frontiers in 2DES.
2D FT: two-dimensional Fourier transform
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2DES: two-dimensional Fourier transform electronic spectroscopy
From Pump-Probe to Two-Dimensional Fourier Transform Spectroscopy: Adding a Dimension In many ways, 2D FT is an extension of pump-probe spectroscopy, offering similar information, but remedying some shortcomings of the pump-probe experiment. In a frequency-resolved pumpprobe experiment, an initial pump pulse excites the system of interest. The system is then probed by a second pulse, and the resulting signal is recorded as a function of the waiting-time delay between pump and probe pulses (see Figure 1a). When the transitions involved are well separated, it is possible to visualize processes such as energy transfer or the formation of intermediate photoproducts by observing the transient evolution of the detected peaks. A continuum probe is often used in pump-probe spectroscopy (60, 61) to obtain spectral information over a broad range of the detected frequencies, which can help resolve the dynamics of overlapping features by looking at distant and related peaks in the detection energy. Two-dimensional spectroscopy solves the problem of untangling overlapping signals more generally by also resolving the detected signal as a function of excitation energy, giving a direct view of the potentially multiple transitions that contribute to a given detected signal. The time resolution of dynamics over the waiting time, in both a pump-probe and 2D experiment, is determined by the duration of the pump pulse, with shorter pulses giving higher time resolution. The commensurately larger bandwidth of a shorter pulse leads to a trade-off between time and frequency resolution in a pump-probe experiment: the shorter the pump pulse, the higher the 668
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Figure 1 (a) Pulse sequence for pump-probe spectroscopy. (b) Pulse sequence for transient-grating (TG) spectroscopy. The hashed pump pulse indicates the presence of two time-coincident pump pulses that are crossed at an angle. (c) Pulse sequence for two-dimensional Fourier transform (2D FT) spectroscopy. (d ) Pulse sequence for fluorescence-detected two-dimensional spectroscopy. (e–i ) Phase-matching condition for (e) 2D FT in the pump-probe geometry, ( f ) the rephasing 2D FT signal in the BOXCARS geometry, ( g) the nonrephasing 2D FT signal in the BOXCARS geometry, (h) the TG signal in the BOXCARS geometry, and (i ) the rephasing, nonrephasing, and TG signals for a hybrid pulse-shaping diffractive optics–based approach that employs two time-delayed pulses along k1 and k2 (63).
time resolution and the lower the certainty of the excitation frequency as determined by the timebandwidth product of the pulse. This trade-off is circumvented in 2D spectroscopy using the Fourier transform methodology (10). Instead of scanning a single narrowband pulse in frequency (often called a double-resonance experiment), one resolves the excitation axis by scanning a delay between a pair of broadband pulses. The signal generated by the system oscillates as a function of the interpulse pump delay τ , allowing the excitation axis to be recovered by Fourier transforming the signal along the τ axis. The result has both high temporal and spectral resolution, limited only by the signal-to-noise ratio. Figure 1c shows the pulse sequence for 2D FT spectroscopy. The most commonly used form of 2D FT spectroscopy employs three identical pulses, effectively splitting the pump pulse of a pumpprobe experiment into two time-delayed interactions with the sample. The signal is then recorded as a function of all three time delays. For a given waiting time T, the Fourier transform of the signal with respect to the τ and t delays provides the 2D FT spectrum. 3D FT spectroscopy additionally Fourier transforms the signal with respect to T, producing a 3D frequency solid. Other collection www.annualreviews.org • 2D FT Electronic Spectroscopy
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FD-2D: fluorescence-detected two-dimensional Fourier transform
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BOXCARS: a geometry commonly used in four-pulse experiments in which the wave vectors of the four pulses each point to one corner of a box TG: transient grating
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modalities exist. For example, in a fluorescence-detected version of the experiment [fluorescencedetected two-dimensional Fourier transform (FD-2D) spectroscopy] (see Figure 1d ), a fourth pulse places the system in an excited state population from which the spontaneous fluorescence emission is measured (62). In 2D FT spectroscopy, two different phase-matched signals are typically recorded: the rephasing and nonrephasing signals in the k2 − k1 + k3 and k1 − k2 + k3 directions, respectively. When summed, these signals yield the absorptive 2D FT spectrum, free from broadening refractive contributions. Another signal, with the phase-matching direction k1 + k2 − k3 , yields information about double-quantum coherences (10). Depending on the experimental geometry of the incident pulses, the phase-matching condition for the various signals determines the direction of their emission. A range of geometries has been employed for 2D FT measurements, including fully collinear (not shown in the figure) and a partially noncollinear pump-probe geometry in which the first two pulses are collinear, followed by a probe pulse at a small angle, as depicted in Figure 1e. A fully noncollinear BOXCARS setup is frequently used, and Figure 1f,g shows the phase-matching conditions for the rephasing and nonrephasing signals, respectively. Phase matching for transient-grating (TG) signals in the BOXCARS geometry is shown in Figure 1h, whereas Figure 1i shows the phase-matching conditions for a recently employed hybrid pump-probe-BOXCARS geometry (described in further detail in the Pump-Probe Geometry section and in Reference 63).
What Is in a Two-Dimensional Fourier Transform Spectrum? The typical information available from absorptive 2D FT spectra is summarized in Figure 2. The T = 0 correlation spectrum (Figure 2a) contains valuable information about the fundamental lineshapes of the transitions under study, in which the ratio of the diagonal to antidiagonal width reflects the degree of inhomogeneous versus homogeneous broadening (8, 10). At longer T delays, the diagonal elongation of an inhomogeneously broadened transition is lost as the system loses memory (correlation) of the initial excitation frequency. The timescale of this memory loss provides the timescale of spectral diffusion and has found applications in understanding liquid dynamics and solvation (8, 52, 64). The dynamic Stokes shift is also directly observable by the shift of a transition from being centered along the diagonal (65). Excitonic coupling between transitions is manifested by cross peaks in the T = 0 spectrum, whereas the growth of cross peaks at later waiting times reflects energy transfer (24). Waiting-time-dependent oscillations of the diagonal and cross peaks reflect vibrational, vibronic, and electronic coherences. The physical origin of such oscillations and their possible importance for photosynthetic energy and charge transfer continue to be subjects of intense debate (27, 29, 43, 46, 66–76). Excited state absorption is also evident in 2D FT spectra, often showing up above the diagonal in electronic spectra and below the diagonal in vibrational spectra (providing a measure of anharmonicity).
CHALLENGES OF IMPLEMENTING TWO-DIMENSIONAL FOURIER TRANSFORM SPECTROSCOPY The principal technical challenge in implementing a multidimensional Fourier transform experiment is creating and delivering the appropriate pulse sequence with variable, yet phase-stable time delays between them. Phase stability refers to the variation of the phase of one optical pulse with respect to the other for a given time delay. To first order, phase stability is equivalent to a timing jitter between the pulses—the relevant timescale of which is given by the oscillation period of the optical field (proportional to the wavelength). As a consequence, the shorter the wavelength 670
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Figure 2 Schematic illustration of the information contained in absorptive two-dimensional Fourier transform spectra. The observed spectral range shown in the unshaded region is determined by the excitation and detection laser bandwidths. (a) The T = 0 correlation spectrum reveals homogeneous and inhomogeneous line widths, excitonic coupling, and excited state absorption features. (b) At T > 0, the broadening of peaks in the antidiagonal direction reflects spectral diffusion. The growth of cross peaks indicates energy transfer. The emergence of an entirely new peak at later waiting times, such as the B D cross peak in panel b, represents the formation of a new product species, populated upon excitation of B , that absorbs at D. An example of such a process is the generation of a charge-separated state in the photosystem II reaction center (data shown in Figure 4).
becomes, the more phase stability becomes a demanding instrumentation consideration. In the most common 2D FT measurements, phase stability and precise timing are required only over the time delays that will be Fourier transformed: typically the τ and t delay. During these time intervals, the system is in a coherence between the ground and excited state, while it is in a population during the waiting-time period. In some cases, the first two pulse interactions may produce a coherence between vibrational, vibronic, or electronic excited or ground states, and Fourier transforming over the T delay yields a 3D FT spectrum that reveals the waiting-time coherence frequencies. These frequencies are typically orders of magnitude lower than optical frequencies and do not require the high degree of phase stability that an optical frequency coherence requires. For two-quantum (2Q) measurements, a fully phase-stable setup is desired because the system in is a coherence between the ground and 2Q excited state during the T period, requiring a high degree of phase stability over that time interval. In typical 2D FT experiments, the τ delay is scanned in the time domain, and the excitation frequency axis is obtained via Fourier transform. To convert time delays to accurate Fourier transform frequencies, one requires an interferometric precision of ∼λ/100, corresponding to timing errors of ∼0.017 fs at 500 nm (10). At long wavelengths, this requirement is considerably easier to meet, and many two-dimensional Fourier transform infrared (2D IR) implementations use conventional delay stages without any form of active or passive phase stabilization, although scanning artifacts from imperfect translation stages have been shown to degrade the quality of 2D IR spectra (77). In a well-constructed interferometer, optical path-length fluctuations and mechanical instabilities have been found to introduce root-mean-square timing errors of ∼0.1 fs www.annualreviews.org • 2D FT Electronic Spectroscopy
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2D IR: two-dimensional Fourier transform infrared
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over a 20-min period (10). Because many 2DES experiments require a timescale on the order of minutes for the collection of a single 2D spectrum, mechanisms for both stabilizing the phase and precisely measuring time delays are needed. In 2D FT spectroscopy, the detection frequency axis is typically obtained via a heterodynedetected frequency-domain measurement of the signal, in which a spectrometer effectively performs the Fourier transform. In heterodyne detection, the signal field is interfered with a local oscillator field to amplify the signal and enable the extraction of the complex signal field (78). In the fully noncollinear geometry, the complex field is extracted via spectral interferometry (79). A stable relative time delay and phase between the signal and local oscillator are critical to obtaining high signal-to-noise ratios. Another challenge of 2D FT spectroscopy, common to many scientific measurements, is that the desired 2D signal is typically small and must be isolated from a large background field and from other spurious signals, such as scatter or other undesirable nonlinear signals. Three techniques are commonly used in the literature to tackle this broad problem: amplitude modulation, phase modulation or cycling, and phase matching. Quite often, combinations of some or all of these methods are used, depending on the ease with which they can be applied in different experimental implementations. Fully noncollinear 2D FT experiments face an additional challenge of phasing the 2D spectra. To obtain the maximum information from 2D measurements, it is often desirable to have absorptive spectra, which are obtained by adding rephasing and nonrephasing signals with the appropriate phase relationship. Absorptive 2D spectra are free from broadening refractive contributions and provide information about the absolute sign of different spectral features, facilitating their physical identification (10). Although frequency-domain (79) or time-domain (80) heterodyne detection allows one to measure the complex signal, in some experimental implementations of 2D FT spectroscopy, the detected signal is phase shifted from a purely absorptive or dispersive signal by a polynomial function of the frequency. The unknown phase shift can be found by measuring the spectrally resolved pump-probe signal and invoking the projection-slice theorem (10). The pump-probe represents the real part of the third-order signal, and when compared to the absolute value of the signal recovered by spectral interferometry, it is possible to find a polynomial phase that connects the two. One disadvantage of this approach is that the signal-to-noise ratio of the pump-probe data is often poor, making precise phasing difficult. An equivalent phasing problem arises in heterodyne-detected TG spectroscopy, where the absorptive component of the TG signal is equivalent to the pump-probe signal but can be measured with a higher signal-tonoise ratio with optimized heterodyne detection (81–83). Other approaches to solving the phasing problem have employed a balanced detection scheme to obtain absorptive TG data (83) and then used higher signal-to-noise TG data for phasing 2D spectra (84). Alternatively, precise phasing without the need to invoke the projection-slice theorem has also been demonstrated (84–86).
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Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy The challenges of implementing 2DES have been met using a variety of approaches. Here we briefly discuss the main methods that have been used. We summarize their advantages and disadvantages and their inherent bandwidth limitations. Interferometer-based setups. Many of the first multidimensional Fourier transform experiments employed interferometers to generate the time-delayed pulse pairs and spectral interferometry to detect the complex signal (6, 8). In pioneering work to map out the χ (2) response of a 672
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nonlinear crystal, the Joffre group (6) utilized spectral interferometry between a reference pulse and both exciting pulses and between the reference pulse and signal to record the relative time delay and determine the full complex signal field in two dimensions. In the first third-order 2DES measurements, the Jonas group (8) used a fully noncollinear beam geometry generated by a fourbeam interferometer. They calibrated their translation stages using spectral interferometry, with a tracer beam that followed the signal path to determine the absolute signal phase (8, 87), enabling phasing of the obtained spectra. The Cundiff group has developed an actively phase-stabilized approach, in which two interferometers generate the required excitation and local oscillator pulses and a third interferometer is used to lock their relative phases. The setup utilizes a continuous-wave laser that copropagates through the interferometers to control the relative delays and phases via path-length adjustments made by mirrors mounted on piezoelectric transducers (88). This setup enables standard onequantum as well as 2Q and 3D measurements and phase-cycling capabilities that can be used to reduce scatter signals. This group has demonstrated an all-optical method for phasing their data (85). In general, interferometer-based approaches enable broadband measurements and are typically limited by the optical coatings on the beam splitters and mirrors.
DO: diffractive optics
Passive phase stabilization. Although the component technology to accomplish active stabilization schemes exists commercially, the coordination of motion control, electronics, and auxillary optical measurements makes such instruments nontrivial to construct. For this reason, passively phase-stable implementations, requiring only optical elements, have been widely pursued, and several methods have emerged. In general, passively phase-stable instruments are easy to construct and maintain but may have some bandwidth limitations due to their optical components. Diffractive optics–based methods. A simple solution to implementing 2DES with passive phase stabilization is to use diffractive optics (DO) to generate the required pulse sequence and phasematched geometry. DO have been employed in TG spectroscopy (81, 89) and fifth-order Raman spectroscopy (90, 91), in which they have been used for passively phase-stable heterodyne detection. To extend the use of DO to 2D spectroscopy, investigators needed to be able to control time delays between pulse pairs. Refractive delays using rotating cover slides (92, 93) or the translation of wedges (94, 95) have been used for this purpose. DO-based approaches are background-free and fully noncollinear, offering the ability to optimize the signal-to-noise ratio and implement polarization-dependent measurements. As a consequence of being fully noncollinear, however, they do require phasing of the data to obtain absorptive 2D spectra. For extremely broadband 2DES, the use of DO imposes a limit of an octave of bandwidth owing to overlapping diffraction orders produced by the DO. The use of refractive elements to produce the τ delay also poses a problem for large bandwidths if the pulse broadening is too large over the τ range that is scanned. For room-temperature measurements of condensed phase systems, a scan range of ∼300 fs is typical. For an ∼10-fs pulse at a 600-nm center wavelength, this produces an ∼6% pulse broadening. Another approach to achieving passive phase stability is to have the optical paths of the relevant pulse pairs in the experiment experience similar path-length fluctuations, whose correlated noise cancels in the total signal phase. The Miller group (92) implemented this idea using stacked retroreflectors, obviating the need for a refractive delay line. They also developed an approach that incorporates pulse shaping of the pump pulses with a DO-based, fully noncollinear BOXCARS geometry (96). Their method features an improved scanning protocol that decouples the τ and T delays that were previously coupled in the original design (92). It also improved on the phase stability by using hollow retroreflectors rather than roof mirrors. The use of a pulse shaper prior www.annualreviews.org • 2D FT Electronic Spectroscopy
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to the DO setup enables coherent control experiments in which both pump pulses are shaped equivalently. The Miller group (97) demonstrated that the method supports broadband 2D FT spectroscopy over the 500–690-nm range and recorded 2D FT spectra with shaped pulses that they had previously found to control population transfer in rhodamine 101. A variation on the DO setup was developed to enable 2Q measurements with the use of DO consisting of two perpendicularly oriented transmission gratings to generate all four beams for a BOXCARS geometry from a single input beam, ensuring high phase stability between all four pulses. In this arrangement, three wedge pairs were employed to scan the relative delays (98). The use of wedges in this implementation restricts the achievable delays for broadband pulses, a drawback if the evolution along T is of interest but quite sufficient for 2Q measurements. A novel DO-based approach was recently demonstrated by the Hauer group (84). They employed two DO elements and a modified phase-matching geometry. A distinct advantage of their method is that it uses a balanced detection approach to simultaneously collect rephasing and nonrephasing signals. This also enables them to obtain absorptive TG instead of pump-probe signals to phase the data. For low signal-to-noise experiments, this avoids the need to use noisy pumpprobe data. The Zigmantas group (99) demonstrated high signal-to-noise ratio measurements in highly scattering samples combining a DO-based approach with double modulation with optical choppers. In general, DO-based approaches enable broadband measurements, although they are ultimately limited to an octave of bandwidth owing to overlapping diffraction orders from the DO. If refractive delays are used, pulse broadening may be a limiting factor.
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Other passively phase-stable approaches. Several approaches that employ passive phase stability without DO have also been developed. The Brixner group (100) demonstrated an all-reflective BOXCARS setup that uses beam splitters rather than DO, enabling broader bandwidth applications. It utilizes the concept of correlated pulse pairs demonstrated by the Miller group (92) to achieve passive phase stability. The Meech group (101) expanded on this design, adding a double chopping scheme along with a high-speed, single-line CCD (charge-coupled device) to permit rapid spectral acquisition and improved scatter removal. Aiming at broad-bandwidth applications, several other all-reflective approaches have been demonstrated recently. Rather than generating the four beams for a BOXCARS setup from DO, the Pfeifer group (102) utilized a spatial mask, as previously used by the Nelson group (103) in a pulse-shaping-based setup. The four beams then hit common optics, with the exception of a quadrant mirror with four independent piezoelectric stages to scan the required delays. An all-reflective setup was also recently developed by the Engel group (104). They generated the four beams for their BOXCARS experiment using beam splitters and employed independent mirrors mounted to slightly angled stages to achieve fine control of the τ delay. They reported phase stability of λ/75 at 800 nm between pulse pairs. Pulse-shaping methods. Pulse shapers for 2DES were first employed by the Warren group (62) in a fully collinear geometry, using FD-2D. Fully collinear measurements contain many spatially overlapping signals and utilize phase cycling rather than phase matching to separate out the desired signal components. Optical 2D spectroscopy with phase cycling was first proposed by Ernst and colleagues (105) and is readily implemented with pulse-shaping technology. The use of a pulse shaper enables phase-cycling methods that are commonly used in nuclear magnetic resonance spectroscopy (106). Phase-cycling approaches are less restricted by sample size than fully noncollinear implementations that require coherent buildup of the signal, making them more amenable to studies of smaller numbers of molecules, particularly in combination with fluorescence detection. In FD-2D, a fourth interaction with the sample converts the third-order coherence into a population that is detected via spontaneous fluorescence (see Figure 1d ). 674
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Fully noncollinear 2D FT spectroscopy with a pulse shaper has been pioneered by the Nelson group (103, 107–109). Their approach has full passive phase stability of all four beams used in the experiment and has no moving parts. The basis of their approach is to employ a spatiotemporal pulse shaper to vary the relative timing and phase of the different pulses. This approach is very versatile and can easily switch between different phase-matching conditions for different measurements. The passive phase stability of all pulses enables the measurement of 2Q and higher signals (107). Because the pulse shaper generates all the time delays, this limits the spectral resolution of any Fourier-transformed dimension and the maximum waiting time in standard 2D experiments. The optical design of the spatiotemporal pulse shaper causes some issues with variable chirp for the different pulses and intensity-dependent delays that can be largely corrected (107). The bandwidth of pulse-shaper-based 2DES methods is likely limited by the pulse shaper itself. For spatial light modulators, the coatings may be the limiting factor, whereas diffraction efficiency and dispersion may be limiting for acousto-optic devices.
AOM: acousto-optic modulator
Phase-modulation two-dimensional spectroscopy. Rather than employing phase cycling to enable the isolation of particular signals of interest in collinear FD-2D experiments, the Marcus group (37) has pioneered a related phase-modulation approach. The close relationship between phase-cycling and phase-modulation approaches has been discussed by Nardin et al. (110). The phase-modulation approach uses acousto-optic modulators (AOMs) in each arm of two MachZender interferometers to generate the four collinear pulses used in the experiment. The AOMs impart a radio-frequency shift individually to the four pulses, tagging each with a unique frequency. The frequency shifts are measured using the interference of a narrowband selection of the excitation pulse itself (37) or a continuous-wave reference passing through the same interferometer (110). Signals are isolated and demodulated via lock-in amplification using a reference signal constructed from the observed frequency shifts. This phase-modulation scheme effectively removes time-delay jitter introduced by mechanical instabilities of the interferometers, and the use of lock-in detection enables the suppression of low-frequency noise (37). The Marcus group (36) has shown that the information content in FD-2D experiments is complimentary but distinct from 2DES experiments. Their method has few limitations on bandwidth, with the AOMs likely the limiting factor. In the IR, in which AOMs are highly inefficient, a wobbling Brewster window, or a photoelastic modulator, has been used to achieve subcycle delays that approximate pure phase shifts in noncollinear 2D IR experiments (111). This approach has been used to enable quasi-phasecycling schemes for scatter removal and to avoid the duty-cycle loss incurred by optical chopping. Subcycle delays approximate pure phase shifts only over a narrow bandwidth, however. Pump-probe geometry. Although the fully noncollinear geometry has been the most common approach to 2D FT spectroscopy, Faeder & Jonas (112) suggested that a pump-probe geometry could ease some of the technical demands. This type of geometry was previously used in timedomain photon-echo measurements (80, 113). In the pump-probe geometry, the two pump pulses are collinear, and the probe is crossed at a small angle, as in pump-probe spectroscopy. This approach was first implemented by Shim et al. (114) in the IR using a pulse shaper and later by DeFlores et al. (115) using a Mach-Zehnder interferometer. It was also implemented by Gumstrup et al. (116) using pulse shapers in the near IR and by our group in the visible range (117). In the pump-probe geometry, both the rephasing and nonrephasing signals are emitted along the probe direction (k1 = k2 ), allowing them to be collected simultaneously. This has the advantage of removing timing errors that can be introduced in separate rephasing and nonrephasing scans. As in pump-probe spectroscopy, the probe acts as a heterodyning field with a well-defined zero phase www.annualreviews.org • 2D FT Electronic Spectroscopy
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TWINS: Translating-WedgeBased Identical Pulses eNcoding System
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relative to the signal. Because the probe enters the detector, the method is not background-free and may therefore suffer from a reduced signal-to-noise ratio, depending on the detailed noise characteristics of the setup. Polarization schemes can remove this difficulty for recording some of the tensor elements of the χ (3) response (117, 118). We have recently compared pulse-shaping-based measurements in the pump-probe and fully noncollinear geometries, finding an improvement of ∼20× in the fully noncollinear geometry (63). Rock et al. (119) recently compared a pump-probe pulse-shaping-based 2D IR setup to a conventional fully noncollinear 2D IR spectrometer with no passive or active phase stabilization. They found that the pulse-shaping-based pump-probe configuration offered an enhanced signal-to-noise ratio, attributed to the higher phase stability of the pulse-shaping-based approach. Recently, the Jonas group (120) used the pump-probe geometry with the sample embedded in a Sagnac interferometer. This approach permits optimization of the heterodyne detection via interference between the probe and reference to control the signal-to-local oscillator ratio. When the pump-probe geometry is used in combination with a pulse shaper, the τ delay can be generated with high precision, removing timing errors and uncertainty in the location of τ = 0. Furthermore, because the heterodyning probe field is known to have zero phase offset from the signal, the phasing problem is eliminated and absorptive spectra are obtained automatically. The use of a pulse shaper also enables phase-cycling methods to remove scatter signals (114) and separate rephasing and nonrephasing contributions (117) and TG signals (63). An important practical implementation for phase cycling is the speed with which it can be performed. Pulse shapers that can be updated on a shot-to-shot basis can more effectively remove laser power fluctuations that often dominate the noise in 2DES measurements. Phase-cycling schemes for both 2DES (121) and fifth-order 3D spectroscopy (122) in the pump-probe geometry have recently been detailed by the Tan group. The latter is analogous to fifth-order measurements that have been made in the IR regime (123, 124). An alternate scheme for generating phase-stable collinear pulses for 2D spectroscopy in the pump-probe geometry is the TWINS (Translating-Wedge-Based Identical Pulses eNcoding System) method of Cerullo and colleagues (125). Inspired by the Babinet-Soleil compensator, this approach uses pairs of birefringent wedges to generate pulse delays with high precision and phase stability. The method can readily produce pulse pairs with parallel or orthogonal relative polarization to enable polarization-based signal selective and background suppression methods (118). Although the method introduces material dispersion, TWINS has been demonstrated with 13-fs pulses, and with the appropriate choice of materials, it is thought to be useable with sub-10-fs pulses (125). TWINS has recently been extended to 2D IR spectroscopy using a different choice of wedge material (126). Although considerably cheaper and with broader bandwidth than pulse shapers, the TWINS approach does not readily enable phase cycling for separation of rephasing and nonrephasing signals and reduction of scatter contributions. We recently developed a hybrid pulse-shaper-DO approach (63) that borrows the time precision and simultaneous rephasing and nonrephasing acquisition of the pulse-shaping pump-probe method and combines it with the background-free properties of traditional DO-based setups. In this setup, two beams of the usual BOXCARS geometry are each supplied with two collinear pump pulses generated from a pulse shaper (Figure 1i). The probe beam and local oscillator beams are brought into the other two beams of the BOXCARS geometry. The result is that background-free TG, rephasing, and nonrephasing signals simultaneously enter the spectrometer and can then be separated from each other via phase cycling. The concept is less clean than other setup designs, but the implementation and alignment are quite simple owing to the lack of moving wedge pairs or stages. We find that the signal-to-noise ratio is more than an order of magnitude improved from a pump-probe geometry setup, principally because of the background-free design permits Fuller
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a
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Figure 3 Setup illustrating (a) two-dimensional Fourier transform electronic spectroscopy (2DES) in the pump-probe geometry with a pulse shaper (116, 117), (b) diffractive optics (DO-)based 2DES (93, 95), and (c) a hybrid pulse-shaper-DO setup with drop-in modification (63). In all three setups, lenses are shown for convenience only; imaging is typically done with reflective optics to reduce dispersion. Abbreviation: LO, local oscillator.
larger probe energies and the adjustment of the local oscillator to the signal intensity ratio. Finally, the simultaneous collection of rephasing and nonrephasing signals and the excellent time zero certainty of the pulse-shaped delay allow for phasing of data without the systematic noise or distortion usually encountered in traditional DO setups (63). A schematic comparison of a selection of the passively stable instruments discussed above is depicted in Figure 3.
Single-shot approaches. A problem that plagues all higher-dimensional spectroscopies is that the acquisition time increases exponentially for each dimension added. As with pulse characterization techniques (127), there are a few groups that have sought to solve this problem by measuring two dimensions simultaneously—producing a 2D spectrum in a single laser shot. The fact that the entire spectrum is collected in a single laser shot reduces systematic noise due to laser fluctuations between measurements. To detect two dimensions simultaneously, one encodes the second dimension over an extended spatial region, which necessitates higher powers and more stringent spatial mode quality from the laser source. www.annualreviews.org • 2D FT Electronic Spectroscopy
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Gradient-assisted photon-echo spectroscopy (GRAPES) uses this approach, encoding the pump delay spatially in a background-free BOXCARS geometry (128), as has been done previously for single-shot pulse characterization methods (127). To accomplish this, the two noncollinear pump beams are brought to a cylindrical focus such that one side of the focus intersects before the other, producing a spatially varying time delay across the focus. The spatially encoded time delays are then imaged into a spectrally dispersive spectrometer in which the detection axis is resolved by angular dispersion into an orthogonal direction onto a 2D detector. In its first implementation, GRAPES was used to collect rephasing spectra. The Engel group (129) has since demonstrated the acquisition of absorptive 2D spectra with GRAPES. The single-shot nature of GRAPES makes it more amenable to noisier light sources than other 2D implementations. The Engel group (130) has also demonstrated broadband (750–850 nm) GRAPES with a supercontinuum in argon gas. Although not strictly a 2DES measurement, angle-resolved coherent spectroscopy is a related single-shot method. Rather than encoding time delays spatially, it examines both the excitation energy and detection energy in k-space rather than frequency or time (131). The 2D spectrum is collected by detecting changes between the signal wave front and the input wave fronts.
GRAPES: gradient-assisted photon-echo spectroscopy
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PSII RC: photosystem II reaction center
Toward Broadband Two-Dimensional Electronic Spectroscopy The various implementations of 2DES have benefits and drawbacks from the standpoint of ease of implementation and bandwidth limitations. Table 1 summarizes some important considerations for many of the different methods discussed and notes the typical bandwidths that have been achieved to date with each approach. Many of the broadest-bandwidth approaches are limited by the bandwidth of the laser source itself. To span multiple broad electronic transitions while also attaining high temporal resolution, one needs to produce very short (
