Visible-infrared two-dimensional Fourier-transform spectroscopy

Broadband rapid-scanning phase-modulated Fourier transform electronic spectroscopy

We present a phase-modulated approach for ultrabroadband Fourier transform electronic spectroscopy. To overcome the bandwidth limitations and spatial chirp introduced by acousto-optic modulators (AOMs), pulses from a 1 µm laser are modulated using AOMs prior to continuum generation. This phase modulation is transferred to the continuum generated in a yttrium aluminum garnet crystal. Separately generated phase-modulated continua in two arms of a Mach-Zehnder interferometer interfere with the difference of their modulation frequencies, enabling physical under-sampling of the signal and the suppression of low-frequency noise. By interferometrically tracking the relative time delay of the continua, we perform continuous, rapid-scanning Fourier transform electronic spectroscopy with a high signal-to-noise ratio and spectral resolution. As proof of principle, we measure the linear absorption and fluorescence excitation spectra of a laser dye and various biological samples.

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.

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.

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.

Broadband near UV to visible optical activity measurement using self-heterodyned method

We demonstrate that broadband electronic optical activity can be measured with supercontinuum light pulse generated by a femtosecond pump (800 nm). It is the self-heterodyned detection technique that enables us to selectively measure the real (optical rotatory dispersion, ORD) or imaginary (circular dichroism, CD) part of the chiroptical susceptibility by controlling the incident polarization state. The single-shot-based measurement that is capable of correcting power fluctuations of the continuum light is realized by using a fast CCD detector and a polarizing beam splitter. Particularly, non-differential scheme used does not rely on any polarization-switching components. We anticipate that this broadband CD/ORD spectrometry with intrinsically ultrafast time-resolution will be applied to a variety of ultrafast chiroptical dynamics studies.

Femtosecond spectroscopy from the perspective of a global multidimensional response function

At the microscopic level, multidimensional response functions, such as the nonlinear optical susceptibility or the time-ordered response function, are commonly used tools in nonlinear optical spectroscopy for determining the nonlinear polarization resulting from an arbitrary excitation. In this Account, we point out that the approach successfully developed for the nonlinear polarization can also be used in the case of a directly observable macroscopic quantity. This observable can be, for example, the electric field radiated in a nonlinear mixing experiment, the rate of fluorescence resulting from one- or two-photon absorption, or the rate of a photochemical reaction. For each of these physical processes, perturbation theory can be used to expand the measured quantity in a power series of the exciting field, and an appropriate global response function can be introduced for each order of perturbation. At order n, the multidimensional response function will depend on n variables (either time or frequency) and have the same general properties as the nonlinear susceptibility resulting, for example, from time invariance or causality. The global response function is introduced in this Account in close analogy with the nonlinear susceptibility or the time-ordered microscopic response. We discuss various applications of the global response function formalism. For example, it can be shown that in the weak field limit, a stationary signal induced in a time-invariant system is independent of the spectral phase of the exciting field. Although this result had been demonstrated previously, the global response function enables its derivation in a more general way because no specific microscopic model is needed. Multidimensional spectroscopy is obviously ideally suited to measure the global multidimensional response function. It is shown that the second (or third)-order response can be exactly measured with 2D (or 3D) spectroscopy by taking into account the exact shape of the exciting pulses. In the case of a 2D measurement of the third-order response, a particular projection of the complete 3D response function is actually measured. This projection can be related to a mixed time and frequency representation of the response function when the pulses are assumed to be infinitely short. We thus show that the global response function is a useful tool for deriving general results and that it should help in designing future experimental schemes for femtosecond spectroscopy.

Unobtrusive interferometer tracking by path length oscillation for multidimensional spectroscopy

We track the path difference between interferometer arms with few-nanometer accuracy without adding optics to the beam path. We measure the interference of a helium-neon beam that copropagates through the interferometer with midinfrared pulses used for multidimensional spectroscopy. This can indicate motion, but not direction. By oscillating the path length of one arm with a mirror on a piezoelectric stack and monitoring the oscillations of the recombined helium-neon beam, the direction can be calculated, and the path delay can be continuously tracked.

All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy

A combination of spatial interference patterns and spectral interferometry are used to find the global phase for non-collinear two-dimensional Fourier-transform (2DFT) spectra. Results are compared with those using the spectrally resolved transient absorption (STRA) method to find the global phase when excitation is with co-linear polarization. Additionally cross-linear polarized 2DFT spectra are correctly "phased" using the all-optical technique, where the SRTA is not applicable.

Chirality-induced signals in coherent multidimensional spectroscopy of excitons

The nonlocal second- and third-order susceptibilities of an isotropic ensemble of aggregates are calculated by solving the nonlinear exciton equations which map the system into coupled anharmonic oscillators. Both electric and magnetic contributions are included using the minimal-coupling Hamiltonian. The various tensor components are evaluated to first order in the optical wave vector k. Additional structural information about the interchromophore distances, which is not accessible through zeroth-order contributions (the dipole approximation), is contained to the first order in k. New resonant second- and third-order signals predicted for chiral molecules provide multidimensional extensions of circular dichroism spectroscopy. Numerical simulations demonstrate the sensitivity of third-order signals to the secondary structural motiffs of peptides.

Two-dimensional infrared surface spectroscopy for CO on Cu(100): Detection of intermolecular coupling of adsorbates

Surface-specific infrared signals obtained by subjecting the system to two infrared laser pulses are calculated for an admixture of CO and isotopic CO on Cu(100) by using molecular dynamics simulation based on a stability matrix formalism. The two-dimensional profiles of the signals in the frequency domain show both diagonal and cross peaks. The former peaks mainly arise from the overtones of the CO and isotopic CO, while the latter represent the couplings between those. As temperature is increased, the phases of cross peaks in a second-order infrared response function change significantly, while those of diagonal peaks are unchanged. The authors show that the phase shifts are originated from the potential anharmonicities due to the electronic interaction between adsorbates. Using a model with two dipole moments, they find that the frustrated rotational mode activated with temperature has effects on the anharmonicity. These results indicate that two-dimensional infrared surface spectroscopy reveals the anharmonic couplings between adsorbates and surface atoms or between adsorbates which cannot be observed in first-order spectroscopy.

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].

Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy

A scheme for active phase stabilization and absolute positioning in Fourier-transform two-dimensional (2D) IR spectroscopy is presented. The position accuracy is better than 20 nm(rms) corresponding to lambda/250 at 5 microm, which significantly improves the quality of Fourier-transform 2D IR spectra. Phase stabilization is added to a standard photon echo setup in a way that does not impair the flexibility of the experiment and the control over IR pulse parameters.

Mid-infrared electric field characterization using a visible charge-coupled-device-based spectrometer

We characterize ultrashort mid-infrared pulses through upconversion by using the stretched pulses obtained from the uncompressed output of a chirped-pulse amplifier. The power spectrum thus translated into the visible region can be readily measured with a standard silicon CCD camera-based spectrometer. The spectral phase is also characterized by a variant of zero-added-phase spectral phase interferometry for direct electric field reconstruction. This is a general method that provides a multiplex advantage over conventional infrared detector array-based methods.

Dephasing-Induced Vibronic Resonances in Difference Frequency Generation Spectroscopy

The difference frequency generation (DFG) signal from a two electronic level system with vibrational modes coupled to a Brownian oscillator bath is computed. Interference effects between two Liouville space pathways result in pure-dephasing-induced, excited-state resonances provided the two excitation pulses overlap and time ordering is not enforced. Numerical simulations of two-dimensional DFG signals illustrate how the ground and excited electronic state resonances may be distinguished.

Phase-stabilized two-dimensional electronic spectroscopy

Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.

Tunable two-dimensional femtosecond spectroscopy

We have developed a two-dimensional (2D) Fourier-transform femtosecond spectroscopy technique for the visible spectral region. Three-pulse photon echo signals are generated in a phase-matched noncollinear four-wave mixing box geometry that employs a 3-kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized in amplitude and phase by spectral interferometry. Unlike for previous setups, we achieve long-term phase stability by employing diffractive optics and interferometric accuracy of excitation-pulse time delays by using movable glass wedges. As an example of this technique, 2D correlation and relaxation spectra at 600 nm are shown for a solution of Nile Blue dye in acetonitrile.

Two-dimensional femtosecond spectroscopy

The simplest two-dimensional (2D) spectra show how excitation with one (variable) frequency affects the spectrum at all other frequencies, thus revealing the molecular connections between transitions. Femtosecond 2D Fourier transform (2D FT) spectra are more flexible and share some of the remarkable properties of their conceptual parent, 2D FT nuclear magnetic resonance. When 2D FT spectra are experimentally separated into real absorptive and imaginary refractive parts, the time resolution and frequency resolution can both reach the uncertainty limit set for each resonance by the sample itself. Coherent four-level contributions to the signal provide new molecular phase information, such as relative signs of transition dipoles. The nonlinear response can be picked apart by selecting a single coherence pathway (e.g., specifying the relative signs of energy level difference frequencies during different time intervals as in the photon echo). Because molecules are frozen on the femtosecond timescale, femtosecond 2D FT experiments can separate a distribution of instantaneous molecular environments and intramolecular geometries as inhomogeneous broadening. This review provides an introduction to two-dimensional Fourier transform experiments exploiting second- and third-order vibrational and electronic nonlinearities.