Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions

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.

Generalized central slice theorem perspective on Fourier-transform spectral imaging at a sub-Nyquist sampling rate

Fourier-transform spectral imaging captures frequency-resolved images with high spectral resolution, broad spectral range, high photon flux, and low stray light. In this technique, spectral information is resolved by taking Fourier transformation of the interference signals of two copies of the incident light at different time delays. The time delay should be scanned at a high sampling rate beyond the Nyquist limit to avoid aliasing, at the price of low measurement efficiency and stringent requirements on motion control for time delay scan. Here we propose, what we believe to be, a new perspective on Fourier-transform spectral imaging based on a generalized central slice theorem analogous to computerized tomography, using an angularly dispersive optics decouples measurements of the spectral envelope and the central frequency. Thus, as the central frequency is directly determined by the angular dispersion, the smooth spectral-spatial intensity envelope is reconstructed from interferograms measured at a sub-Nyquist time delay sampling rate. This perspective enables high-efficiency hyperspectral imaging and even spatiotemporal optical field characterization of femtosecond laser pulses without a loss of spectral and spatial resolutions.

Coherent 2D electronic spectroscopy with complete characterization of excitation pulses during all scanning steps

Coherent two-dimensional (2D) electronic spectroscopy has become a standard tool in ultrafast science. Thus it is relevant to consider the accuracy of data considering both experimental imperfections and theoretical assumptions about idealized conditions. It is already known that chirped excitation pulses can affect 2D line shapes. In the present work, we demonstrate performance-efficient, automated characterization of the full electric field of each individual multipulse sequence employed during a 2D scanning procedure. Using Fourier-transform spectral interferometry, we analyze how the temporal intensity and phase profile varies from scanning step to scanning step and extract relevant pulse-sequence parameters. This takes into account both random and systematic variations during the scan that may be caused, for example, by femtosecond pulse-shaping artifacts. Using the characterized fields, we simulate and compare 2D spectra obtained with idealized and real shapes obtained from an LCD-based pulse shaper. Exemplarily, we consider fluorescence of a molecular dimer and multiphoton photoemission of a plasmonic nanoslit. The deviations from pulse-shaper artifacts in our specific case do not distort strongly the population-based multidimensional data. The characterization procedure is applicable to other pulses-shaping technologies or excitation geometries, including also pump-probe geometry with multipulse excitation and coherent detection, and allows for accurate consideration of realistic optical excitation fields at all inter-pulse time-delays.

Leveraging scatter in two-dimensional spectroscopy: passive phase drift correction enables a global phasing protocol

Phase stability between pulse pairs defining Fourier-transform time delays can limit resolution and complicates development and adoption of multidimensional coherent spectroscopies. We demonstrate a data processing procedure to correct the long-term phase drift of the nonlinear signal during two-dimensional (2D) experiments based on the relative phase between scattered excitation pulses and a global phasing procedure to generate fully absorptive 2D electronic spectra of wafer-scale monolayer MoS₂. Our correction results in a ∼30-fold increase in effective long-term signal phase stability, from ∼λ/2 to ∼λ/70 with negligible extra experimental time and no additional optical components. This scatter-based drift correction should be applicable to other interferometric techniques as well, significantly lowering the practical experimental requirements for this class of measurements.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Phase-modulated harmonic light spectroscopy

By combining phase-modulated nonlinear spectroscopy with second harmonic generation, the concept of phase-modulated harmonic light spectroscopy is introduced. Simultaneous spectroscopy with different harmonics of the light is demonstrated and linear and nonlinear excitation of the spectroscopic sample is investigated. Sum frequency generation and stray light effects during temporal pulse overlap have been evaluated in detail, accompanied by simulations. The presented work provides a promising concept to facilitate coherent nonlinear time-domain spectroscopy in the extreme ultraviolet wavelength regime and contributes valuable insights for future studies in this direction.

Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. I. Weak-field regime

We present a theoretical description of double-pump femtosecond single-molecule signals with fluorescence detection.

Optical resonance imaging: An optical analog to MRI with sub-diffraction-limited capabilities

We propose here optical resonance imaging (ORI), a direct optical analog to magnetic resonance imaging (MRI). The proposed pulse sequence for ORI maps space to time and recovers an image from a heterodyne-detected third-order nonlinear photon echo measurement. As opposed to traditional photon echo measurements, the third pulse in the ORI pulse sequence has significant pulse-front tilt that acts as a temporal gradient. This gradient couples space to time by stimulating the emission of a photon echo signal from different lateral spatial locations of a sample at different times, providing a widefield ultrafast microscopy. We circumvent the diffraction limit of the optics by mapping the lateral spatial coordinate of the sample with the emission time of the signal, which can be measured to high precision using interferometric heterodyne detection. This technique is thus an optical analog of MRI, where magnetic-field gradients are used to localize the spin-echo emission to a point below the diffraction limit of the radio-frequency wave used. We calculate the expected ORI signal using 15 fs pulses and 87° of pulse-front tilt, collected using f/2 optics and find a two-point resolution 275 nm using 800 nm light that satisfies the Rayleigh criterion. We also derive a general equation for resolution in optical resonance imaging that indicates that there is a possibility of superresolution imaging using this technique. The photon echo sequence also enables spectroscopic determination of the input and output energy. The technique thus correlates the input energy with the final position and energy of the exciton.

Precise phase determination with the built-in spectral interferometry in two-dimensional electronic spectroscopy

A new method determining the precise phase of pulse sequences in two-dimensional electronic spectroscopy (2DES) is proposed merely using the already built-in spectral interferometry. The approach is easily implemented without the supplementary instrumental construction, only at the expense of a few additional scanning and data-fitting processes. This method is executed with the sample in place, effectively avoiding the phase ambiguities of the beam propagation in samples, thus calibrating the absolute phase at the exact interaction region. The new proposed method is expected to improve the phasing procedure in 2DES in a more convenient way.

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Two-dimensional vibrational-electronic spectroscopy

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([Fe(III)(CN)6](3-) dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5Fe(II)CNRu(III)(NH3)5](-) dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

Real-Time Quantum Dynamics Reveals Complex, Many-Body Interactions in Solvated Nanodroplets

Electronic excitations in the liquid phase are surprisingly rich and considerably more complex than either gas-phase or solid-state systems. While the majority of physical and biological processes take place in solvent, our understanding of nonequilibrium excited-state processes in these condensed phase environments remains far from complete. A central and long-standing issue in these solvated environments is the assessment of many-body interactions, particularly when the entire system is out of equilibrium and many quantum states participate in the overall process. Here we present a microscopic picture of solute-solvent electron dynamics and solvatochromic effects, which we uncover using a new real-time quantum dynamics approach for extremely large solvated nanodroplets. In particular, we find that a complex interplay of quantum interactions underlies our observations of solute-solvent effects, and simple macroscopic solvatochromic shifts can even be qualitatively different at the microscopic molecular level in these systems. By treating both the solvent and the solute on the same footing at a quantum-mechanical level, we demonstrate that the electron dynamics in these systems are surprisingly complex, and the emergence of many-body interactions underlies the dynamics in these solvated systems.

Carrier envelope phase shifter for broadband terahertz pulses

We demonstrated controlled shifting of the internal phase of broadband terahertz (THz) pulses. The internal phase of an ultrashort pulse is called the carrier envelope phase (CEP), which is an important parameter in the interaction of few-cycle light pulses and matter. Our CEP shifter utilizes the ultra-broadband feature of prism wave plates. We analytically derived the amount of CEP shift achievable by the CEP shifter using Jones matrixes. THz time-domain measurements clearly showed the shift of the CEP, and the results agreed well with the calculated values. The CEP shift was as high as 2π, indicating that any CEP values can be chosen using our CEP shifter.

Shaped and Feedback-Controlled Excitation of Single Molecules in the Weak-Field Limit

Coherent control uses tailored femtosecond pulse shapes to influence quantum pathways and drive a light-induced process toward a specific outcome. There has been a long-standing debate whether the absorption properties or the probability for population to remain in an excited state of a molecule can be influenced by the pulse shape, even if only a single photon is absorbed. Most such experiments are performed on many molecules simultaneously, so that ensemble averaging reduces the access to quantum effects. Here, we demonstrate systematic coherent control experiments on the fluorescence intensity of a single molecule in the weak-field limit. We demonstrate that a delay scan of interfering pulses reproduces the excitation spectrum of the molecule upon Fourier transformation, but that the spectral phase of a pulse sequence does not affect the transition probability. We generalize this result to arbitrary pulse shapes by performing the first closed-loop coherent control experiments on a single molecule.

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.

Enhanced-Resolution Single-Shot 2DFT Spectroscopy by Spatial Spectral Interferometry

We demonstrate use of spatial interference for the complete electric field reconstruction of two-dimensional (2D) coherent spectroscopic signals generated through four-wave mixing (4WM) in a single laser shot. Until now, the amplitude and phase characterization of 4WM signals has relied primarily on Fourier transform spectral interferometry (FTSI), which limits the measurement's sensitivity and resolution. We show that spatial spectral interferometry (SSI) is a generalized approach to 4WM signal detection that eliminates these inherent limitations of FTSI without introducing additional experimental complexity. SSI is used to measure the 2D photon echo spectra of two systems with dramatically different line widths, the coupled D line transitions in rubidium vapor and the energy-transfer dynamics in the light-harvesting protein LH2.

Two-dimensional electronic spectroscopy with birefringent wedges

We present a simple experimental setup for performing two-dimensional (2D) electronic spectroscopy in the partially collinear pump-probe geometry. The setup uses a sequence of birefringent wedges to create and delay a pair of phase-locked, collinear pump pulses, with extremely high phase stability and reproducibility. Continuous delay scanning is possible without any active stabilization or position tracking, and allows to record rapidly and easily 2D spectra. The setup works over a broad spectral range from the ultraviolet to the near-IR, it is compatible with few-optical-cycle pulses and can be easily reconfigured to two-colour operation. A simple method for scattering suppression is also introduced. As a proof of principle, we present degenerate and two-color 2D spectra of the light-harvesting complex 1 of purple bacteria.

Measurement of energy contrast of amplified ultrashort pulses using cross-polarized wave generation and spectral interferometry

We present a method using spectral interferometry (SI) to characterize a pulse in the presence of an incoherent background such as amplified spontaneous emission (ASE). The output of a regenerative amplifier is interfered with a copy of the pulse that has been converted using third-order cross-polarized wave generation (XPW). The ASE shows as a pedestal background in the interference pattern. The energy contrast between the short-pulse component and the ASE is retrieved. The spectra of the interacting beams are obtained through an improvement to the self-referenced spectral interferometry (SRSI) analysis.

Probing energy transfer events in the light harvesting complex 2 (LH2) of Rhodobacter sphaeroides with two-dimensional spectroscopy

Excitation energy transfer events in the photosynthetic light harvesting complex 2 (LH2) of Rhodobacter sphaeroides are investigated with polarization controlled two-dimensional electronic spectroscopy. A spectrally broadened pulse allows simultaneous measurement of the energy transfer within and between the two absorption bands at 800 nm and 850 nm. The phased all-parallel polarization two-dimensional spectra resolve the initial events of energy transfer by separating the intra-band and inter-band relaxation processes across the two-dimensional map. The internal dynamics of the 800 nm region of the spectra are resolved as a cross peak that grows in on an ultrafast time scale, reflecting energy transfer between higher lying excitations of the B850 chromophores into the B800 states. We utilize a polarization sequence designed to highlight the initial excited state dynamics which uncovers an ultrafast transfer component between the two bands that was not observed in the all-parallel polarization data. We attribute the ultrafast transfer component to energy transfer from higher energy exciton states to lower energy states of the strongly coupled B850 chromophores. Connecting the spectroscopic signature to the molecular structure, we reveal multiple relaxation pathways including a cyclic transfer of energy between the two rings of the complex.

Independent phasing of rephasing and non-rephasing 2D electronic spectra

Assigning absolute phase to two-dimensional (2D) third-order nonlinear optical signals generally requires acquiring both the rephasing and the non-rephasing signals and comparing the sum of the two to spectrally resolved pump-probe spectra. To date, however, Gradient Assisted Photon Echo Spectroscopy (GRAPES) has only been able to acquire rephasing spectra. Such a constraint requires a new phasing protocol. Here, we analytically prove that the rephasing and non-rephasing spectra can be phased independently using pump-probe signal. We verify this result holds even for finite duration pulses by simulation. This relationship holds for all 2D spectroscopies, not only GRAPES. In addition, we present improvements to GRAPES that enable acquisition of rephasing and non-rephasing signals in different phase-matched directions. We employ our phasing protocol to phase the data for laser dye IR-144, leading to reconstruction of purely absorptive 2D spectrum.

Fifth-order three-dimensional electronic spectroscopy using a pump-probe configuration

We present the theoretical details and experimental demonstration of fifth-order three-dimensional (3D) electronic spectroscopy using a pump-probe beam geometry. This is achieved using a pulse shaper and appropriate phase cycling schemes. We show how 8-step and 27-step phase cycling schemes can measure purely absorptive 3D spectra as well as 3D spectra for the individual fifth-order processes that contribute to the purely absorptive spectrum. 3D spectra as a function of two separate controllable waiting time periods can be obtained. The peak shapes and positions of the peaks in the experimental measurement correspond well to theory.

Angle determination and scattering suppression in polarization-enhanced two-dimensional infrared spectroscopy in the pump-probe geometry

The signal to noise in two-dimensional spectra recorded in the pump-probe geometry can be significantly improved with a quasi-crossed polarizer configuration, often employed in linear dichroism measurements. Here we examine this method in detail and demonstrate how to analyse and interpret the amplified signals. The angle between transition dipole moments can be determined with better accuracy than in conventional anisotropy measurements, and the method can be used to selectively suppress individual peaks and to efficiently remove scattering contributions. We present spectra of the coupled CO-stretch modes of a Ruthenium-carbonyl complex in DMSO for experimental illustration.

Modeling and correction of distorted two-dimensional Fourier transform spectra from pixelated pulse shaping devices

Two-dimensional Fourier transform spectra of a three level model system are simulated using a non-perturbative density matrix formalism. The electric field distortions resultant from using pixelated pulse shaping devices to produce phase-locked pulse pairs are modeled and the effects on the recovered spectra are examined. To minimize spectral distortions, a temporal filtering scheme is employed which eliminates contributions from spurious sample polarizations.

Structure, Dynamics, and Function in the Major Light-Harvesting Complex of Photosystem II

In natural light-harvesting systems, pigment-protein complexes (PPC) convert sunlight to chemical energy with near unity quantum efficiency. PPCs exhibit emergent properties that cannot be simply extrapolated from knowledge of their component parts. In this Perspective, we examine the design principles of PPCs, focussing on the major light-harvesting complex of Photosystem II (LHCII), the most abundant PPC in green plants. Studies using two-dimensional electronic spectroscopy (2DES) provide an incisive tool to probe the electronic, energetic, and spatial landscapes that enable the efficiency observed in photosynthetic light-harvesting. Using the information about energy transfer pathways, quantum effects, and excited state geometry contained within 2D spectra, the excited state properties can be linked back to the molecular structure. This understanding of the structure-function relationships of natural systems constitutes a step towards a blueprint for the construction of artificial light-harvesting devices that can reproduce the efficacy of natural systems.

Invited article: The coherent optical laser beam recombination technique (COLBERT) spectrometer: coherent multidimensional spectroscopy made easier

We have developed an efficient spectrometer capable of performing a wide variety of coherent multidimensional measurements at optical wavelengths. The two major components of the largely automated device are a spatial beam shaper which controls the beam geometry and a spatiotemporal pulse shaper which controls the temporal waveform of the femtosecond pulse in each beam. We describe how to construct, calibrate, and operate the device, and we discuss its limitations. We use the exciton states of a semiconductor nanostructure as a working example. A series of complex multidimensional spectra-displayed in amplitude and real parts-reveals increasingly intricate correlations among the excitons.

Zeptosecond precision pulse shaping

We investigate the temporal precision in the generation of ultrashort laser pulse pairs by pulse shaping techniques. To this end, we combine a femtosecond polarization pulse shaper with a polarizer and employ two linear spectral phase masks to mimic an ultrastable common-path interferometer. In an all-optical experiment we study the interference signal resulting from two temporally delayed pulses. Our results show a 2σ-precision of 300 zs = 300 × 10(-21) s in pulse-to-pulse delay. The standard deviation of the mean is 11 zs. The obtained precision corresponds to a variation of the arm's length in conventional delay stage based interferometers of 0.45 Å. We apply these precisely generated pulse pairs to a strong-field quantum control experiment. Coherent control of ultrafast electron dynamics via photon locking by temporal phase discontinuities on a few attosecond timescale is demonstrated.

Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments

We demonstrate how quasi-phase-cycling achieved by sub-cycle delay modulation can be used to replace optical chopping in a box-CARS 2D IR experiment in order to enhance the signal size, and, at the same time, completely eliminate any scattering contamination. Two optical devices are described that can be used for this purpose, a wobbling Brewster window and a photoelastic modulator. They are simple to construct, easy to incorporate into any existing 2D IR setup, and have attractive features such as a high optical throughput and a fast modulation frequency needed to phase cycle on a shot-to-shot basis.

Three-dimensional electronic spectroscopy of excitons in GaAs quantum wells

We demonstrate three-dimensional (3D) electronic Fourier transform spectroscopy of GaAs quantum wells using four fully phase-coherent, noncollinear optical fields. Since the full complex signal field is measured as a function of all three time intervals, nearly every peak in the resulting 3D spectral solid arises from a distinguishable sequence of transitions represented by a single Feynman pathway. We use the 3D spectral peaks to separate two pathways involving weakly bound mixed biexcitons generated in different time orders. In the process, we reveal a peak that was previously obscured by a correlated but unbound exciton pair coherence. We also demonstrate a calibration procedure for the carrier frequency which yields biexciton binding energy values with high accuracy.

Simulation of four-wave mixing signals by a perturbative approach: application to ultrafast two-dimensional infrared spectroscopy

We propose an alternative method for the calculation of the phase-matched contributions, which are responsible for the third-order optical signals measured in four-wave mixing experiments. In particular, we extend the strong field dissipation theory of Meier and Tannor [J. Chem. Phys. 111, 3365 (1999)] to the case of a perturbative treatment with respect to the exciting laser fields. Our approach is based on an analytical expression of the third-order density matrix and hence it does not require to verify numerically the irrelevance of higher order terms or the calculation of a spatial Fourier transform. In order to illustrate this method, we simulate the experimental signal measured in femtosecond two-dimensional infrared (2D-IR) vibrational spectroscopy. We consider an intramolecular anharmonic vibrational mode modeled by a Morse potential and coupled to a dissipative bath of harmonic oscillators. We calculate the 2D-IR correlation spectrum and we discuss the influence of the population decay on the line shapes. In particular, we compare two situations, one where only pure dephasing processes are considered, and another one where phase losses due to population relaxation are also taken into account. We show that the shape of the peaks observed in a 2D-IR correlation spectrum differs in these two cases, and therefore this difference appears as a signature of population decay and gives information on the importance of pure dephasing processes in phase loss mechanisms.

Removing cross-phase modulation from midinfrared chirped-pulse upconversion spectra

We observe that narrow spectral features in mid-infrared spectra obtained by chirped-pulse up-conversion are strongly distorted by cross-phase modulation between the mid-infrared field and the chirped pulse. We discuss the consequences of this effect on spectral resolution, and introduce a correction method that recovers masked lines. This simple correction can be applied either when the upconverted field is fully characterized, such as in multidimensional spectroscopy, or when causality can be used, such as in absorption spectroscopy, which we demonstrate experimentally.

Mechanism of phase-energy coupling in f-to-2f interferometry

White-light generation has been used widely in single-shot f-to-2f interferometers for stabilizing the carrier-envelope (CE) phase of laser amplifiers. The accuracy of the relative phase values measured by such an interferometer is affected by fluctuations in the laser pulse energy. A simple two-step model is proposed to explain the mechanism that couples the laser energy and the CE phase. The model explains the experimentally observed dependence of the group delay between the f and the 2f pulses on the laser energy, as well as the CE phase shift caused by the pulse energy variation.

How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping

We have recently developed a new and simple way of collecting 2D infrared and visible spectra that utilizes a pulse shaper and a partly collinear beam geometry. 2D IR and Vis spectroscopies are powerful tools for studying molecular structures and their dynamics. They can be used to correlate vibrational or electronic eigenstates, measure energy transfer rates, and quantify the dynamics of lineshapes, for instance, all with femtosecond time-resolution. As a result, they are finding use in systems that exhibit fast dynamics, such as sub-millisecond chemical and biological dynamics, and in hard-to-study environments, such as in membranes. While powerful, these techniques have been difficult to implement because they require a series of femtosecond pulses to be spatially and temporally overlapped with precise time-resolution and interferometric phase stability. However, many of the difficulties associated with implementing 2D spectroscopies are eliminated by using a pulse shaper and a simple beam geometry, which substantially lowers the technical barriers required for researchers to enter this exciting field while simultaneously providing many new capabilities. The aim of this paper is to provide an overview of the methods for collecting 2D spectra so that an outsider considering using 2D spectroscopy in their own research can judge which approach would be most suitable for their research aims. This paper focuses primarily on 2D IR spectroscopy, but also includes our recent work on adapting this technology to collecting 2D Vis spectra. We review work that has already been published as well as cover several topics that we have not reported previously, including phase cycling methods to remove background signals, eliminate unwanted scatter, and shift data collection into the rotating frame.

Theory and phase-cycling scheme selection principles of collinear phase coherent multi-dimensional optical spectroscopy

We present the theory and the selection procedure of phase-cycling schemes for phase coherent multidimension optical spectroscopy. We apply our selection procedure to determine the phase-cycling schemes with the least number of steps needed to measure the two-dimensional spectra of various time resolved four wave mixing optical processes. The phase-cycling scheme selection procedure presented in this paper can be applied to higher order nonlinear optical experiments involving more optical pulses that measure higher dimensional optical spectra.

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Coherent control of pump-probe signals of helical structures by adaptive pulse polarizations

The simplification of the pump-probe spectrum of excitons by pure-phase-polarization pulse shaping is investigated by a simulation study. The state of light is manipulated by varying the phases of two perpendicular polarization components of the pump, holding its total spectral and temporal intensity profiles fixed. Genetic and iterative Fourier transform algorithms are used to search for pulse phase functions that optimize the ratio of the signal at two frequencies. New features are extracted from the congested pump-probe spectrum of a helical pentamer by selecting a combination of Liouville space pathways. Tensor components which dominate the optimized spectra are identified.