Degenerate Four-Wave Mixing Spectroscopy: Multistate Resonances and Multimode Laser Effects

The origin band of the Ã1B2-X1A1 (π* ← π) absorption system in monodeuterated tropolone (TrOD) has been probed with near-rotational resolution by applying the frequency-domain techniques of polarization-resolved degenerate four-wave mixing (DFWM) spectroscopy under ambient, bulk-gas conditions. Judicious selection of polarization geometries for the incident and detected electromagnetic waves alleviated intrinsic spectral congestion and facilitated dissection of overlapping transitions, thereby enabling refined rotational-tunneling parameters to be extracted for the Ã1B2(π*π) manifold. A tunneling-induced bifurcation of Δ0Ã = 2.241(14) cm(-1) was measured for the zero-point level of electronically excited TrOD, reflecting the presence of a substantial barrier along the O-D···O ↔ O···D-O reaction coordinate and representing nearly a 10-fold decrease in magnitude over the analogous quantity in the parent (TrOH) isotopologue. Observed trends in hydron-migration rates are discussed in light of the changes in the potential-surface topology sustained from the π* ← π electron promotion and the dynamical effects incurred by selective isotopic modification of the nuclear framework, with similar considerations being applied to interpret rotational constants and inertial defects. Simultaneous analyses performed on an interloping sequence band built upon ν38(b1) gave an excited-state tunneling splitting of Δ(ν38)Ã = 1.217(61) cm(-1), highlighting the ability of this symmetric, out-of-plane normal mode to inhibit the unimolecular tautomerization process.

Degenerate four-wave mixing spectroscopy as a probe of photodissociation dynamics: nascent SH population distributions from the 266 nm photolysis of hydrogen sulfide

Degenerate four-wave mixing spectroscopy has been used to study the photodissociation dynamics of tert-butyl hydroperoxide (t-BuOOH) at 266 nm, long-wavelength tail of the ultraviolet (UV) absorption continuum. The nascent rotational distributions, spin-orbit state ratio, and Λ-doublet population ratio of the OH (X 2Π) fragments have been extracted. No vibrationally excited OH was observed. The rotational distribution peaked at N″=5. The average rotational energy was estimated to be 4.2% of the available energy. A slight preference for the Π− Λ-doublet component and a statistical distribution of the spin-orbit states were observed. The experimental observations are similar to those found for OH from H2O2 photodissociation and are consistent with dissociation via a repulsive excited state.

It is shown that, as a result of the atomic recoil associated with the absorption and emission of radiation, resonances can appear in nonlinear spectroscopy. The theory is illustrated by calculating the line shapes associated with nearly degenerate four-wave mixing and pump-probe spectroscopy when laser fields interact with an ensemble of two-level atoms. The recoil-induced resonances should be observable for atoms cooled below the Doppler limit of laser cooling, and the line shapes may provide a means for measuring the velocity distribution of these cooled atoms.

Femtosecond time‐resolved degenerate four‐wave mixing (DFWM) spectroscopy with ultrashort laser pulses was applied to probe pure rotational Raman transitions of the H2 molecule. Owing to the broad bandwidth of the sub‐20 fs pulse, several pure rotational Stokes and anti‐Stokes transitions are simultaneously excited with the same pulse, making the experiment relevant for thermometry in combustion processes. Simulations of the DFWM signal accurately predict how the change in population distribution due to changes in temperature influences the shape of the transients and the corresponding Fourier transform. The influence of the pulse duration was also investigated. The relative peak intensities in fast Fourier transform spectra were employed for temperature determination. First measurements at room temperature show good agreement with theory. Copyright © 2004 John Wiley & Sons, Ltd.

Double-resonance laser-induced grating spectroscopy of nitric oxide

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

Our research efforts over the last few years have focused on the development of strategies for the quantitative application of DFWM and PS in flame environments. We have developed, validated, and applied a theoretical methodology based on direct numerical integration (DNI) of the time-dependent density matrix equations for analysis of the physics of the DFWM and PS processes. The incorporation of the Zeeman state structure of the energy levels of the radiative transitions has allowed us to investigate the physics of the PS process and polarization effects in DFWM. Our research effort has focused mainly on the moderate saturation regime, with laser pulse lengths significantly greater than characteristic collisional times, and with the assumption of monochromatic lasers. Recently, we have completed a study of multi-axial-mode laser effects of homogeneously broadened PS.

The d 3Πg↔a 3Πu Swan bands of C2 have been recorded with high resolution using DFWM in the nearly Doppler free, phase conjugate geometry. C2 was probed in a standard oxy-acetylene welding flame with excellent signal-to-noise ratio and spectral resolution. Theoretical spectra were simulated and fitted directly to the complex overlapping spectra. The good agreement obtained shows that DFWM holds promise to become a robust and reliable tool for flame thermometry. Current theories of DFWM are reviewed in context of the present work and advantages and disadvantages of the technique are discussed.

The authors studied the exciton spin relaxation of bulk GaN by creating spin polarization gratings using degenerate four-wave mixing spectroscopy. The spectrally resolved analysis achieved with this technique facilitated the direct evaluation of spin polarizations in the individual excitons (A and B excitons). The spin polarizations for each exciton decay very quickly (τs∼1ps) at low temperatures. Moreover the τs is faster than the dephasing time T2 throughout the measured temperature range, suggesting the existence of fast intrinsic spin relaxation processes, which can be attributed to a large exchange constant characterized in GaN.

Recent theoretical predictions of anisotropy-induced polarization components in the signal wave generated from gas-phase degenerate four-wave mixing spectroscopy are verified experimentally by probing optically pumped ensembles of jet-cooled molecules that are characterized by well-defined orientation and/or alignment parameters. Aside from corroborating recent multipole moment analyses, detailed simulation of recorded data sets demonstrates the feasibility of performing a new class of resonant four-wave mixing measurements designed to extract angular momentum anisotropy information from target species in a manner that is both background-free and insensitive to isotropic contributions.

The ring-puckering motion in cyclopentene as well as the hindered internal rotation around the central C–C bond in 1-butene have been studied by high-level quantum chemical calculations. Relevant potential energy surfaces of these molecules along these large-amplitude motions are provided as well as rotational constants are given allowing for thorough comparison with recent results from time-resolved femtosecond degenerate four-wave mixing (fs DFWM) spectroscopy. Emphasis is put on the performance of various post-Hartree Fock methods, the required level of electron correlation as well as the basis set quality.

We investigate the third-order nonlinear-optical susceptibility ${\ensuremath{\chi}}^{(3)}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\ensuremath{\chi}}^{(3)}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\ensuremath{\chi}}^{(3)}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\ensuremath{\chi}}^{(3)}$ contains terms that scale as \ensuremath{\sim}${N}^{2}$ and \ensuremath{\sim}N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear \ensuremath{\sim}N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.

The ring-puckering vibration in cyclopentene was studied by rotational time-resolved femtosecond degenerate four-wave mixing (fs DFWM) spectroscopy. The fs DFWM spectra of cyclopentene were measured both in a supersonic expansion and in a gas cell at room temperature. The room temperature fs DFWM spectrum has been satisfactorily reproduced by a fitted simulation based on a one-dimensional model for the ring-puckering vibration. This has allowed for the determination of energetic parameters of the ring-puckering motion such as the energy barrier to ring inversion of 274(+12/-20) cm(-1) and the equilibrium ring-puckering angle of 24.3 degrees . The derived dependences of the rotational constants A and B on the puckering angle resemble very closely those obtained by microwave spectroscopy. In addition, previous theoretical estimates of the ring inversion barrier of cyclopentene were improved by performing high level ab initio calculations. Zero-point vibrational energy correction was found to be essential for an accurate evaluation of the puckering potential. Altogether, this study provides a proof-of-principle of the applicability of the fs DFWM technique for investigating large amplitude intramolecular motions.

High-resolution investigation of degenerate four-wave mixing in the γ(0, 0) band of nitric oxide