Theory of femtosecond coherent anti-Stokes Raman scattering spectroscopy of gas-phase transitions

A theoretical analysis of coherent anti-Stokes Raman scattering (CARS) spectroscopy of gas-phase resonances using femtosecond lasers is performed. The time-dependent density matrix equations for the femtosecond CARS process are formulated and manipulated into a form suitable for solution by direct numerical integration (DNI). The temporal shapes of the pump, Stokes, and probe laser pulses are specified as an input to the DNI calculations. It is assumed that the laser pulse shapes are 70 fs Gaussians and that the pulses are Fourier-transform limited. A single excited electronic level is defined as an effective intermediate level in the Raman process, and transition strengths are adjusted to match the experimental Raman polarizability. The excitation of the Raman coherence is investigated for different Q-branch rotational transitions in the fundamental 2330 cm(-1) band of diatomic nitrogen, assuming that the pump and Stokes pulses are temporally overlapped. The excitation process is shown to be virtually identical for transitions ranging from Q2 to Q20. The excitation of the Raman coherences is also very efficient; for laser irradiances of 5x10(17) W/m2, corresponding approximately to a 100 microJ, 70 fs pulse focused to 50 microm, approximately 10% of the population of the ground Raman level is pumped to the excited Raman level during the impulsive pump-Stokes excitation, and the magnitude of the induced Raman coherence reaches 40% of its maximum possible value. The theoretical results are compared with the results of experiments where the femtosecond CARS signal is recorded as a function of probe delay with respect to the impulsive pump-Stokes excitation.     

Communication: hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering thermometry using a narrowband time-asymmetric probe pulse

A narrowband, time-asymmetric probe pulse is introduced into the hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering (fs/ps RCARS) technique to provide accurate and precise single-shot, high-repetition-rate gas-phase thermometric measurements. This narrowband pulse-generated by inserting a Fabry-Pe?rot e?talon into the probe-pulse beam path-enables frequency-domain detection of pure-rotational transitions. The unique time-asymmetric nature of this pulse, in turn, allows for detection of resonant Raman-active rotational transitions free of signal contamination by nonresonant four-wave-mixing processes while still allowing detection at short probe-pulse delays, where collisional dephasing processes are negligible. We demonstrate that this approach provides excellent single-shot thermometric accuracy (<1% error) and precision (~2.5%) in gas-phase environments.     

Optimal coherent control of coherent anti-Stokes Raman scattering: signal enhancement and background elimination

The ability to enhance resonant signals and eliminate the non-resonant background is analyzed for coherent anti-Stokes Raman scattering (CARS). The analysis is done at a specific frequency as well as for broadband excitation using femtosecond pulse-shaping techniques. An appropriate objective functional is employed to balance resonant signal enhancement against non-resonant background suppression. Optimal enhancement of the signal and minimization of the background can be achieved by shaping the probe pulse alone while keeping the pump and Stokes pulses unshaped. In some cases analytical forms for the probe pulse can be found, and numerical simulations are carried out for other circumstances. It is found that a good approximate optimal solution for resonant signal enhancement in two-pulse CARS is a superposition of linear and arctangent-type phases for the pump. The well-known probe delay method is shown to be a quasi-optimal scheme for broadband background suppression. The results should provide a basis to improve the performance of CARS spectroscopy and microscopy.     

Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra

The development of a time-resolved coherent anti-Stokes Raman scattering (CARS) variant for use as a probe of excited electronic state Raman-active modes following excitation with an ultrafast pump pulse is detailed. Application of this technique involves a combination of broadband fs-time scale pulses and a narrowband pulse of ps duration that allows multiplexed detection of the CARS signal, permitting direct observation of molecular Raman frequencies and intensities with time resolution dictated by the broadband pulses. Thus, this nonlinear optical probe, designated fs/ps CARS, is suitable for observation of Raman spectral evolution following excitation with a pump pulse. Because of the spatial separation of the CARS output signal relative to the three input beams inherent in a folded BOXCARS arrangement, this technique is particularly amenable to probing low-frequency vibrational modes, which play a significant role in accepting vibrational energy during intramolecular vibrational energy redistribution within electronically excited states. Additionally, this spatial separation allows discrimination against strong fluorescence signal, as demonstrated in the case of rhodamine 6G.     

Perturbative theory and modeling of electronic-resonance-enhanced coherent anti-Stokes Raman scattering spectroscopy of nitric oxide

A theory is developed for three-laser electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) spectroscopy of nitric oxide (NO). A vibrational Q-branch Raman polarization is excited in the NO molecule by the frequency difference between visible Raman pump and Stokes beams. An ultraviolet probe beam is scattered from the induced Raman polarization to produce an ultraviolet ERE-CARS signal. The frequency of the ultraviolet probe beam is selected to be in electronic resonance with rotational transitions in the A (2)Sigma(+)<--X (2)Pi (1,0) band of NO. This choice results in a resonance between the frequency of the ERE-CARS signal and transitions in the (0,0) band. The theoretical model for ERE-CARS NO spectra has been developed in the perturbative limit. Comparisons to experimental spectra are presented where either the probe laser was scanned with fixed Stokes frequency or the Stokes laser was scanned with fixed probe frequency. At atmospheric pressure and an NO concentration of 100 ppm, good agreement is found between theoretical and experimental spectral peak locations and relative intensities for both types of spectra. Factors relating to saturation in the experiments are discussed, including implications for the theoretical predictions.     

Analysis of time resolved femtosecond and femtosecond/picosecond coherent anti-Stokes Raman spectroscopy: application to toluene and Rhodamine 6G

The third-order polarization for coherent anti-Stokes Raman scattering (CARS) from a pure state is described by 48 terms in perturbation theory, but only 4 terms satisfy the rotating wave approximation. They are represented by Feynman dual time-line diagrams and four-wave mixing energy level diagrams. In time-resolved (tr) fs and fs/ps CARS from the ground vibrational state, one resonant diagram, which is the typical CARS term, with three field interactions-pump, Stokes, followed by probe-on the ket is dominant. Using the separable, displaced harmonic oscillators approximation, an analytic result is obtained for the four-time correlation function in the CARS third-order polarization. Dlott's phenomenological expression for off-resonance CARS from the ground vibrational state is derived using a three-state model. We calculated the tr fs and fs/ps CARS for toluene and Rhodamine 6G (R6G), initially in the ground vibrational state, to compare with experimental results. The observed vibrational features and major peaks for both tr fs and fs/ps CARS, from off-resonance (for toluene) to resonance (for R6G) pump wavelengths, can be well reproduced by the calculations. The connections between fs/ps CARS, fs stimulated Raman spectroscopy, and impulsive stimulated scattering for toluene and R6G are discussed.     

Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The direct measurement of self-broadened linewidths using the time decay of pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) signals is demonstrated in gas-phase N(2) and O(2) from 1-20 atm. Using fs pump and Stokes pulses and a spectrally narrowed ps probe pulse, collisional dephasing rates with time constants as short as 2.5 ps are captured with high accuracy for individual rotational transitions. S-branch linewidths of N(2) and O(2) from ~0.06 to 2.2 cm(-1) and the line separation of O(2) triplet states are obtained from the measured dephasing rates and compared with high-resolution, frequency-domain measurements and S-branch approximations using the modified exponential gap model. The accuracy of the current measurements suggests that the fs/ps RCARS approach is well suited for tracking the collisional dynamics of gas-phase mixtures over a wide range of pressures.     

Elucidating the spectral and temporal contributions from the resonant and nonresonant response to femtosecond coherent anti-Stokes Raman scattering

A theoretical expression is developed for femtosecond coherent anti-Stokes Raman scattering (CARS) to quantitatively account for the vibrational line shape in the presence of nonresonant signal. The contributions of the resonant and nonresonant components are extracted from the emitted signal line shape as a function of Stokes wavelength and as a function of the temporal overlap of the two pump pulses (for spectrally resolved femtosecond CARS). The theory is compared to the measured spectra of the oxygen vibrational transition DeltaG(01)=1556.4 cm(-1) for temporal detunings of 0 and 700 fs.     

Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X(2)Σ and B(2)Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment.     

Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control

Sequences of carefully timed and shaped optical pulses provide femtosecond snapshots of molecular structure as well as electronic and vibrational dynamical processes, in analogy with multidimensional NMR. We apply a genetic learning algorithm towards the design of pulse sequences which simplify the multidimensional signals by controlling the relative intensities of various peaks. Numerical simulations demonstrate how poorly resolved weak features may be amplified and observed by using optimized optical pulses, specifically shaped to achieve a desired spectroscopic target.     

Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.     

Simulation protocols for coherent femtosecond vibrational spectra of peptides

Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D(2)O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.     

Direct measurement of S-branch N(2)-H(2) Raman linewidths using time-resolved pure rotational coherent anti-Stokes Raman spectroscopy

S-branch N(2)-H(2) Raman linewidths have been measured in the temperature region 294-1466 K using time-resolved dual-broadband picosecond pure rotational coherent anti-Stokes Raman spectroscopy (RCARS). Data are extracted by mapping the dephasing rates of the CARS signal temporal decay. The J-dependent coherence decays are detected in the time domain by following the individual spectral lines as a function of probe delay. The linewidth data set was employed in spectral fits of N(2) RCARS spectra recorded in binary mixtures of N(2) and H(2) at calibrated temperature conditions up to 661 K using a standard nanosecond RCARS setup. In this region, the set shows a deviation of less than 2% in comparison with thermocouples. The results provide useful knowledge for the applicability of N(2) CARS thermometry on the fuel-side of H(2) diffusion flames.     

Microchip HPLC separations monitored simultaneously by coherent anti-Stokes Raman scattering and fluorescence detection

Microchimica Acta - Coherent anti-Stokes Raman scattering (CARS) was evaluated and applied to process monitoring in chip-based high-performance liquid chromatography (HPLC). By stimulating the...     

Origin of negative and dispersive features in anti-Stokes and resonance femtosecond stimulated Raman spectroscopy

Femtosecond stimulated Raman spectroscopy is extended to probe ground state anti-Stokes vibrational features. Off resonance, negative anti-Stokes features are seen that are the mirror image of the positive Stokes side spectra. On resonance, the observed dispersive lineshapes are dramatically dependent on the frequencies of the picosecond pump and femtosecond probe pulses used to generate the stimulated Raman spectra. These observations are explained by the contributions of the inverse Raman and hot luminescence four-wave mixing processes discussed by Sun et al. [J. Chem. Phys. 128, 144114 (2008)], which contribute to the overall femtosecond stimulated Raman signal.     

Time- and frequency-resolved coherent anti-Stokes Raman scattering spectroscopy with sub-25 fs laser pulses

In general, many different diagrams can contribute to the signal measured in broadband four-wave mixing experiments. Care must therefore be taken when designing an experiment to be sensitive to only the desired diagram by taking advantage of phase matching, pulse timing, sequence, and the wavelengths employed. We use sub-25 fs pulses to create and monitor vibrational wavepackets in gaseous iodine, bromine, and iodine bromide through time- and frequency-resolved femtosecond coherent anti-Stokes Raman scattering (CARS) spectroscopy. We experimentally illustrate this using iodine, where the broad bandwidths of our pulses, and Boltzmann population in the lower three vibrational levels conspire to make a single diagram dominant in one spectral region of the signal spectrum. In another spectral region, however, the signal is the sum of two almost equally contributing diagrams, making it difficult to directly extract information about the molecular dynamics. We derive simple analytical expressions for the time- and frequency-resolved CARS signal to study the interplay of different diagrams. Expressions are given for all five diagrams which can contribute to the CARS signal in our case.     

Sum frequency generation and coherent anti-Stokes Raman spectroscopic studies on plasma-treated plasticized polyvinyl chloride films

Polyvinyl chloride (PVC) is a widely used polymer to which various phthalates are extensively applied as plasticizers. PVC materials are often treated with plasma to vary the hydrophobicity or for cleaning purposes, but little is known of the nature of the surface molecular structures after treatment. This research characterizes molecular surface structures of PVC and bis-2-ethylhexyl phthalate (DEHP)-plasticized PVC films in air before annealing, after annealing, and after exposure to air-generated glow discharge plasma using sum frequency generation (SFG) vibrational spectroscopy. In addition, we compare the vibrational molecular signatures on the surfaces of PVC with DEHP (at a variety of percent loadings) to those of the bulk detected using coherent anti-Stokes Raman scattering (CARS). X-ray photoelectron spectroscopy (XPS) and contact angle measurements have been used to analyze PVC surfaces to supplement SFG data. Our results indicate that DEHP was found on the surfaces of PVC films even at low weight percentages (5 wt %) and that DEHP segregates on surfaces after annealing. The treatment of these films with glow discharge plasma resulted in surface-sensitive reactions involving the removal of chlorine atoms, the addition of oxygen atoms, and C-H bond rearrangement. CARS data demonstrate that the bulk of our films remained undisturbed during the plasma treatment. For the first time, we probed the molecular structure of the surface and the bulk of a PVC material using combined SFG and CARS studies on the same sample in exactly the same environment. In addition, the methodology used in this research can be applied to characterize various plasticizers in a wide variety of polymer systems to understand their surface and bulk structures before and after systematic applications of heat, plasma, or other treatments.     

Nanosecond rapid freezing of liquid benzene under shock compression studied by time-resolved coherent anti-Stokes Raman spectroscopy

Nanosecond time-resolved coherent anti-Stokes Raman spectroscopy is used to investigate the shock-induced liquid-solid phase transition and crystallization of liquid benzene. Temporal evolution of the Raman shift of the ring-breathing and C-H stretching modes is investigated. A metastable supercompressed state and a liquid-solid phase transition are observed under shock compression. Time-resolved Raman spectra reveal that the liquid state is initially a metastable state and rapidly transforms to the solid state within 25 ns under shock compression at 4.2 GPa.     

Quantum theory of (femtosecond) time-resolved stimulated Raman scattering

We present a complete perturbation theory of stimulated Raman scattering (SRS), which includes the new experimental technique of femtosecond stimulated Raman scattering (FSRS), where a picosecond Raman pump pulse and a femtosecond probe pulse simultaneously act on a stationary or nonstationary vibrational state. It is shown that eight terms in perturbation theory are required to account for SRS, with observation along the probe pulse direction, and they can be grouped into four nonlinear processes which are labeled as stimulated Raman scattering or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). Previous FSRS theories have used only the SRS(I) process or only the "resonance Raman scattering" term in SRS(I). Each process can be represented by an overlap between a wave packet in the initial electronic state and a wave packet in the excited Raman electronic state. Calculations were performed with Gaussian Raman pump and probe pulses on displaced harmonic potentials to illustrate various features of FSRS, such as high time and frequency resolution; Raman gain for the Stokes line, Raman loss for the anti-Stokes line, and absence of the Rayleigh line in off-resonance FSRS from a stationary or decaying v=0 state; dispersive line shapes in resonance FSRS; and the possibility of observing vibrational wave packet motion with off-resonance FSRS.