Stable and high-power few cycle supercontinuum for 2D ultrabroadband electronic spectroscopy

Ultrabroadband two-dimensional electronic spectroscopy in the pump-probe geometry using conventional optics

We report ultrabroadband two-dimensional electronic spectroscopy (2D ES) measurements obtained in the pump-probe geometry using conventional optics. A phase-stabilized Michelson interferometer provides the pump-pulse delay interval, τ1, necessary to obtain the excitation-frequency dimension. Spectral resolution of the probe beam provides the detection-frequency dimension, ω3. The interferometer incorporates active phase stabilization via a piezo stage and feedback from interference of a continuous-wave reference laser detected in quadrature. To demonstrate the method, we measured a well-characterized laser dye sample and obtained the known peak structure. The vibronic peaks are modulated as a function of the waiting time, τ2, by vibrational wave packets. The interferometer simplifies ultrabroadband 2D ES measurements and analysis.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements

Knowledge of relative displacements between potential energy surfaces (PES) is critical in spectroscopy and photochemistry. Information on displacements is encoded in vibrational coherences. Here we apply ultrafast two-dimensional electronic spectroscopy in a pump-probe half-broadband (HB2DES) geometry to probe the ground- and excited-state potential landscapes of cresyl violet. 2D coherence maps reveal that while the coherence amplitude of the dominant 585 cm-1 Raman-active mode is mainly localized in the ground-state bleach and stimulated emission regions, a 338 cm-1 mode is enhanced in excited-state absorption. Modeling these data with a three-level displaced harmonic oscillator model using the hierarchical equation of motion-phase matching approach (HEOM-PMA) shows that the S1 ← S0 PES displacement is greater along the 585 cm-1 coordinate than the 338 cm-1 coordinate, while Sn ← S1 displacements are similar along both coordinates. HB2DES is thus a powerful tool for exploiting nuclear wavepackets to extract quantitative multidimensional, vibrational coordinate information across multiple PESs.

Full visible range two-dimensional electronic spectroscopy with high time resolution

Two-dimensional electronic spectroscopy (2DES) is a powerful method to study coherent and incoherent interactions and dynamics in complex quantum systems by correlating excitation and detection energies in a nonlinear spectroscopy experiment. Such dynamics can be probed with a time resolution limited only by the duration of the employed laser pulses and in a spectral range defined by the pulse spectrum. In the blue spectral range (<500 nm), the generation of sufficiently broadband ultrashort pulses with pulse durations of 10 fs or less has been challenging so far. Here, we present a 2DES setup based on a hollow-core fiber supercontinuum covering the full visible range (400-700 nm). Pulse compression via custom-made chirped mirrors yields a time resolution of <10 fs. The broad spectral coverage, in particular the extension of the pulse spectra into the blue spectral range, unlocks new possibilities for coherent investigations of blue-light absorbing and multichromophoric compounds, as demonstrated by a 2DES measurement of chlorophyll a.

Rapid scan white light two-dimensional electronic spectroscopy with 100 kHz shot-to-shot detection

We demonstrate an approach to two-dimensional electronic spectroscopy (2DES) that combines the benefits of shot-to-shot detection at high-repetition rates with the simplicity of a broadband white light continuum input and conventional optical elements to generate phase-locked pump pulse pairs. We demonstrate this through mutual synchronization between the laser repetition rate, the acousto-optical deflector, the pump delay stage, and the CCD line camera, which allows for rapid scanning of pump optical delay synchronously with the laser repetition rate, while the delay stage is moved at a constant velocity. The resulting shot-to-shot detection scheme is repetition rate scalable and only limited by the CCD line rate and the maximum stage velocity. Using this approach, we demonstrate the measurement of an averaged 2DES absorptive spectrum in as much as 1.2 s of continuous sample exposure per 2D spectrum. We achieve a signal-to-noise ratio of 6.8 for optical densities down to 0.05 with 11.6 s of averaging at 100 kHz laser repetition rate. Combining rapid scanning of mechanical delay lines with shot-to-shot detection as demonstrated here provides a viable alternative to acousto-optic pulse shaping approaches that is repetition-rate scalable, has comparable throughput and sensitivity, and minimizes sample exposure per 2D spectrum with promising micro-spectroscopy applications.

Parameter estimation in ultrafast spectroscopy using probability theory

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

OPA-driven hollow-core fiber as a tunable, broadband source for coherent multidimensional spectroscopy

Despite the impressive abilities of coherent multi-dimensional spectroscopy (CMDS), its' implementation is limited due to the complexity of continuum generation and required phase stability between the pump pulse pair. In light of this, we have implemented a system producing sub-10 fs pulses with tunable central wavelength. Using a commercial OPA to drive a hollow-core fiber, the system is extremely simple. Output pulse energies lie in the 40-80 μJ range, more than sufficient for transmission through the pulse shaping optics and beam splitters necessary for CMDS. Power fluctuations are minimal, mode quality is excellent, and spectral phase is well behaved at the output. To demonstrate the strength of this source, we measure the two-dimensional spectrum of CdSe quantum dots over a range of population times and find clean signals and clear phonon vibrations. This combination of OPA and hollow-core fiber provides a substantial extension to the capabilities of CMDS.

Broadband visible two-dimensional spectroscopy of molecular dyes

Two-dimensional Fourier transform spectroscopy is a promising technique to study ultrafast molecular dynamics. Similar to transient absorption spectroscopy, a more complete picture of the dynamics requires broadband laser pulses to observe transient changes over a large enough bandwidth, exceeding the inhomogeneous width of electronic transitions, as well as the separation between the electronic or vibronic transitions of interest. Here, we present visible broadband 2D spectra of a series of dye molecules and report vibrational coherences with frequencies up to ∼1400 cm^-1 that were obtained after improvements to our existing two-dimensional Fourier transform setup [Al Haddad et al., Opt. Lett. 40, 312-315 (2015)]. The experiment uses white light from a hollow core fiber, allowing us to acquire 2D spectra with a bandwidth of 200 nm, in a range between 500 and 800 nm, and with a temporal resolution of 10-15 fs. 2D spectra of nile blue, rhodamine 800, terylene diimide, and pinacyanol iodide show vibronic spectral features with at least one vibrational mode and reveal information about structural motion via coherent oscillations of the 2D signals during the population time. For the case of pinacyanol iodide, these observations are complemented by its Raman spectrum, as well as the calculated Raman activity at the ground- and excited-state geometry.

Ultrashort visible energetic pulses generated by nonlinear propagation of necklace beams in capillaries

The generation of ultrashort visible energetic pulses is investigated numerically by the nonlinear propagation of infrared necklace beams in capillaries. We have developed a (3+1)D model that solves the nonlinear propagation equation, including the complete spatio-temporal dynamics and the azimuthal dependence of these structured beams. Due to their singular nonlinear propagation, the spectrum broadening inside the capillary extends to the visible region in a controlled way, despite the high nonlinearity, avoiding self-focusing. The results indicate that the features of these necklace beams enable the formation of visible pulses with pulse duration below 10 fs and energies of 50 μJ by soliton self-compression dynamics for different gas pressures inside the capillary.

Addition of a Carbonyl End Group Increases the Rate of Excited-State Decay in a Carotenoid via Conjugation Extension and Symmetry Breaking

Steady-state absorption, transient absorption, and transient grating spectroscopies were employed to elucidate the role of a conjugated carbonyl group in the photophysics of carotenoids. Spheroidenone and spheroidene have similar molecular structures and differ only in an additional carbonyl group in spheroidenone. Comparison of the optical responses of these two molecules under similar experimental conditions was used to understand the role of this carbonyl group in the structure. It was found that the carbonyl group has two main effects: first, it dramatically increases the depopulation rate of the excited states of the molecule. The lifetimes of all the excited states of spheroidenone were found to be almost half of the ones for spheroidene. Second, the presence of the carbonyl group in the chain alters the decay mechanism to the symmetry-forbidden S₁ state of the molecule, so that the higher vibrational levels of the S₁ state are populated much more effectively. It was also revealed that for both molecules, the S₂/S _x → S₁(hot) → S₁ decay process is not purely sequential and follows a branched model.

Zooming in on vibronic structure by lowest-value projection reconstructed 4D coherent spectroscopy

A fundamental goal of chemical physics is an understanding of microscopic interactions in liquids at and away from equilibrium. In principle, this microscopic information is accessible by high-order and high-dimensionality nonlinear optical measurements. Unfortunately, the time required to execute such experiments increases exponentially with the dimensionality, while the signal decreases exponentially with the order of the nonlinearity. Recently, we demonstrated a non-uniform acquisition method based on radial sampling of the time-domain signal [W. O. Hutson et al., J. Phys. Chem. Lett. 9, 1034 (2018)]. The four-dimensional spectrum was then reconstructed by filtered back-projection using an inverse Radon transform. Here, we demonstrate an alternative reconstruction method based on the statistical analysis of different back-projected spectra which results in a dramatic increase in sensitivity and at least a 100-fold increase in dynamic range compared to conventional uniform sampling and Fourier reconstruction. These results demonstrate that alternative sampling and reconstruction methods enable applications of increasingly high-order and high-dimensionality methods toward deeper insights into the vibronic structure of liquids.

Stability and interaction of few-cycle pulses in a Kerr medium

The different aspects of few-cycle pulse dynamics governed by the regularized short pulse equation (RSPE) are reported. It is shown that the RSPE provides an accurate description of the dynamics of the few-cycle pulse whose duration is larger than a single optical period when the few-cycle pulse's spectrum is in the medium's anomalous dispersion regime. The approximate solutions of the RSPE are constructed from the soliton solutions of the nonlinear Schrödinger (NLS) equation. We demonstrate numerically that the stability of these few-cycle pulses strongly depends on their pulse duration. Furthermore, the interactions of the two and three few-cycle pulses are studied. When pulse parameters are suitably chosen, we show the elastic collision, inelastic collision and repulsive interaction between these multi few-cycle pulses. It is revealed that the interactions of the multi few-cycle pulses rely heavily on their pulse duration.

Impact of the lipid bilayer on energy transfer kinetics in the photosynthetic protein LH2

Photosynthetic purple bacteria convert solar energy to chemical energy with near unity quantum efficiency. The light-harvesting process begins with absorption of solar energy by an antenna protein called Light-Harvesting Complex 2 (LH2). Energy is subsequently transferred within LH2 and then through a network of additional light-harvesting proteins to a central location, termed the reaction center, where charge separation occurs. The energy transfer dynamics of LH2 are highly sensitive to intermolecular distances and relative organizations. As a result, minor structural perturbations can cause significant changes in these dynamics. Previous experiments have primarily been performed in two ways. One uses non-native samples where LH2 is solubilized in detergent, which can alter protein structure. The other uses complex membranes that contain multiple proteins within a large lipid area, which make it difficult to identify and distinguish perturbations caused by protein-protein interactions and lipid-protein interactions. Here, we introduce the use of the biochemical platform of model membrane discs to study the energy transfer dynamics of photosynthetic light-harvesting complexes in a near-native environment. We incorporate a single LH2 from Rhodobacter sphaeroides into membrane discs that provide a spectroscopically amenable sample in an environment more physiological than detergent but less complex than traditional membranes. This provides a simplified system to understand an individual protein and how the lipid-protein interaction affects energy transfer dynamics. We compare the energy transfer rates of detergent-solubilized LH2 with those of LH2 in membrane discs using transient absorption spectroscopy and transient absorption anisotropy. For one key energy transfer step in LH2, we observe a 30% enhancement of the rate for LH2 in membrane discs compared to that in detergent. Based on experimental results and theoretical modeling, we attribute this difference to tilting of the peripheral bacteriochlorophyll in the B800 band. These results highlight the importance of well-defined systems with near-native membrane conditions for physiologically-relevant measurements.

Ultrafast Four-Dimensional Coherent Spectroscopy by Projection Reconstruction

Multidimensional coherent spectroscopy provides insights into the vibronic structure and dynamics of complex systems. In general, the higher the dimensionality, the better the spectral discrimination and the more information that may be extracted about the system. A major impediment to widespread implementation of these methods, however, is that the acquisition time generally increases exponentially with dimensionality, prohibiting practical implementation. We demonstrate the use of nonuniform sampling based on the projection-slice theorem and inverse Radon transform within the context of a fifth-order, 4D technique (GAMERS) designed to correlate the vibrational contributions to different electronic states. Projection-reconstruction (PRO GAMERS) greatly reduces the data sampling requirements without sacrificing frequency resolution. The sensitivity of this technique is demonstrated to surpass conventional uniform sampling by orders of magnitude. The incorporation of projection-reconstruction into multidimensional coherent spectroscopy opens up the possibility to study the structure of complex chemical, biological, and physical systems with unprecedented detail.

Broadband two-dimensional electronic spectroscopy in an actively phase stabilized pump-probe configuration

We introduce a novel configuration for two-dimensional electronic spectroscopy (2DES) that combines the partially collinear pump-probe geometry with active phase locking. We demonstrate the method on a solution sample of CdSe/ZnS nanocrystals by employing two non-collinear optical parametric amplifiers as the pump and probe sources. The two collinear pump pulse replicas are created using a Mach-Zehnder interferometer phase stabilized by active feedback electronics. Taking the advantage of separated paths of the two pump pulses in the interferometer, we improve the signal-to-noise ratio with double modulation of the individual pump beams. In addition, a quartz wedge pair manipulates the phase difference between the two pump pulses, enabling the recovery of the rephasing and non-rephasing signals. Our setup integrates many advantages of available 2DES techniques with robust phase stabilization, ultrafast time resolution, two-color operation, long delay scan, individual polarization manipulation and the ease of implementation.

Ultrabroadband 2D electronic spectroscopy with high-speed, shot-to-shot detection

Two-dimensional electronic spectroscopy (2DES) is an incisive tool for disentangling excited state energies and dynamics in the condensed phase by directly mapping out the correlation between excitation and emission frequencies as a function of time. Despite its enhanced frequency resolution, the spectral window of detection is limited to the laser bandwidth, which has often hindered the visualization of full electronic energy relaxation pathways spread over the entire visible region. Here, we describe a high-sensitivity, ultrabroadband 2DES apparatus. We report a new combination of a simple and robust setup for increased spectral bandwidth and shot-to-shot detection. We utilize 8-fs supercontinuum pulses generated by gas filamentation spanning the entire visible region (450 - 800 nm), which allows for a simultaneous interrogation of electronic transitions over a 200-nm bandwidth, and an all-reflective interferometric delay system with angled nanopositioner stages achieves interferometric precision in coherence time control without introducing wavelength-dependent dispersion to the ultrabroadband spectrum. To address deterioration of detection sensitivity due to the inherent instability of ultrabroadband sources, we introduce a 5-kHz shot-to-shot, dual chopping acquisition scheme by combining a high-speed line-scan camera and two optical choppers to remove scatter contributions from the signal. Comparison of 2D spectra acquired by shot-to-shot detection and averaged detection shows a 15-fold improvement in the signal-to-noise ratio. This is the first direct quantification of detection sensitivity on a filamentation-based ultrabroadband 2DES apparatus.

Broadband 2D electronic spectrometer using white light and pulse shaping: noise and signal evaluation at 1 and 100 kHz

We have developed a broad bandwidth two-dimensional electronic spectrometer that operates shot-to-shot at repetition rates up to 100 kHz using an acousto-optic pulse shaper. It is called a two-dimensional white-light (2D-WL) spectrometer because the input is white-light supercontinuum. Methods for 100 kHz data collection are studied to understand how laser noise is incorporated into 2D spectra during measurement. At 100 kHz, shot-to-shot scanning of the delays and phases of the pulses in the pulse sequence produces a 2D spectrum 13-times faster and with the same signal-to-noise as using mechanical stages and a chopper. Comparing 100 to 1 kHz repetition rates, data acquisition time is decreased by a factor of 200, which is beyond the improvement expected by the repetition rates alone due to reduction in 1/f noise. These improvements arise because shot-to-shot readout and modulation of the pulse train at 100 kHz enables the electronic coherences to be measured faster than the decay in correlation between laser intensities. Using white light supercontinuum for the pump and probe pulses produces high signal-to-noise spectra on samples with optical densities <0.1 within a few minutes of averaging and an instrument response time of <46 fs thereby demonstrating that that simple broadband continuum sources, although weak, are sufficient to create high quality 2D spectra with >200 nm bandwidth.

Rapid-scan coherent 2D fluorescence spectroscopy

We developed pulse-shaper-assisted coherent two-dimensional (2D) electronic spectroscopy in liquids using fluorescence detection. A customized pulse shaper facilitates shot-to-shot modulation at 1 kHz and is employed for rapid scanning over all time delays. A full 2D spectrum with 15 × 15 pixels is obtained in approximately 6 s of measurement time (plus further averaging if needed). Coherent information is extracted from the incoherent fluorescence signal via 27-step phase cycling. We exemplify the technique on cresyl violet in ethanol and recover literature-known oscillations as a function of population time. Signal-to-noise behavior is analyzed as a function of the amount of averaging. Rapid scanning provides a 2D spectrum with a root-mean-square error of < 0.05 after 1 min of measurement time.

Simple fiber-based solution for coherent multidimensional spectroscopy in the visible regime

We report on a setup for coherent multidimensional spectroscopy based on visible continuum generation obtained by propagating 130 fs, <600  μJ pulses centered at 800 nm in a 2.5 m long hollow-core fiber. We find that with these modest input pulse requirements, the fiber can produce a stable, high brightness continuum spanning the 520-900 nm region, moreover in a single propagation step. The fiber exhibits 80% transmission, and the continuum features excellent spatial mode quality. In addition, spectral phase measurements suggest the possibility of a significantly self-compressed output in the visible, which simplifies aspects of the 2D spectrometer. The applicability of this simple, low-requirement source for 2D spectroscopy is demonstrated by performing a control experiment on the molecular dye Nile Blue.

Broadband 7-fs diffractive-optic-based 2D electronic spectroscopy using hollow-core fiber compression

We demonstrate noncollinear coherent two-dimensional (2D) electronic spectroscopy for which broadband pulses are generated in an argon-filled hollow-core fiber pumped by a 1-kHz Ti:Sapphire laser. Compression is achieved to 7 fs duration (TG-FROG) using dispersive mirrors. The hollow fiber provides a clean spatial profile and smooth spectral shape in the 500-700 nm region. The diffractive-optic-based design of the 2D spectrometer avoids directional filtering distortions and temporal broadening from time smearing. For demonstration we record data of cresyl-violet perchlorate in ethanol and use phasing to obtain broadband absorptive 2D spectra. The resulting quantum beating as a function of population time is consistent with literature data.

Multidimensional Electronic Spectroscopy of Photochemical Reactions

Coherent multidimensional electronic spectroscopy can be employed to unravel various channels in molecular chemical reactions. This approach is thus not limited to analysis of energy transfer or charge transfer (i.e. processes from photophysics), but can also be employed in situations where the investigated system undergoes permanent structural changes (i.e. in photochemistry). Photochemical model reactions are discussed by using the example of merocyanine/spiropyran-based molecular switches, which show a rich variety of reaction channels, in particular ring opening and ring closing, cis-trans isomerization, coherent vibrational wave-packet motion, radical ion formation, and population relaxation. Using pump-probe, pump-repump-probe, coherent two-dimensional and three-dimensional, triggered-exchange 2D, and quantum-control spectroscopy, we gain intuitive pictures on which product emerges from which reactant and which reactive molecular modes are associated.