Larry A. Rahn

Stochastic spectral methods for efficient Bayesian solution of inverse problems

We present a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos (PC) expansions to represent random variables. Evaluation of integrals over the unknown parameter space is recast, more efficiently, as Monte Carlo sampling of the random variables underlying the PC expansion. We evaluate the utility of this technique on a transient diffusion problem arising in contaminant source inversion. The accuracy of posterior estimates is examined with respect to the order of the PC representation, the choice of PC basis, and the decomposition of the support of the prior. The computational cost of the new scheme shows significant gains over direct sampling.

Background-free cars studies of carbon monoxide in a flame

Abstract Background-free coherent anti-Stokes Raman spectra (CARS) of carbon monoxide have been obtained in a rich methane-air flat flame. Use of this background rejection method, requiring only two laser frequencies, results in an increase in signal-to-noise of over 200 in the |x (3) | 2 spectrum in comparison with normal CARS. In addition, this technique provides a means for determining the symmetry of observed Raman transitions. The principles of background-free CARS are derived, and the capabilities are demonstrated with experimental data.

Reduction of degenerate four‐wave mixing spectra to relative populations II. Strong‐field limit

Diagrammatic perturbation theory combined with a spherical tensor treatment allows the degenerate four‐wave mixing (DFWM) signal resulting from an isotropic molecular sample to be decomposed into a sum of three multipole moments in the weak‐field (no saturation) limit. The zeroth moment gives the relative internal‐state population contribution, the first moment the orientation contribution, and the second moment the alignment contribution to the DFWM spectra. This treatment makes explicit how the magnitude of the DFWM signal depends on the polarizations of the other three beams and the collisional relaxation caused by the environment. A general expression is derived for the DFWM signal for an arbitrary geometric configuration of the beams (arbitrary phase matching geometry). Under the assumption that the rates of collisional relaxation of the population, the orientation, and the alignment are the same, simple analytic expressions are found for the most commonly used experimental configurations, which shou...

Comparison between CARS and corrected thermocouple temperature measurements in a diffusion flame.

Coherent anti-Stokes Raman spectroscopy (CARS) has been used to obtain radial temperature profiles in an axisymmetric methane diffusion flame. Temperatures were obtained from analysis of background-free nitrogen Q- and O-branch spectra. The spectra were analyzed with a nonlinear least-squares CARS fitting program and compared to measurements from radiation- and conduction-corrected thermocouples. Excellent agreement was obtained in regions of relatively constant temperature, whereas improved CARS spatial resolution was required to obtain agreement near steep temperature gradients.

Diode-laser-pumped Nd:YAG laser injection seeding system

We have designed and tested a compact injection seeding system consisting of a diode-laser-pumped Nd:YAG master oscillator and a permanent-magnet Faraday isolator. With active resonator frequency stabilization, this system permits highly reliable single-axial-mode operation of a Q-switched Nd:YAG laser over a period of hours. The system is capable of injection seeding both stable and unstable resonator designs and is suitable for injection seeding commercial lasers with only minor modifications.

Laser-induced thermal grating effects in flames

Light scattering from a laser-induced thermal grating produced in an atmospheric-pressure H(2)/O(2) flame is observed with a phase-matching geometry commonly used in resonant four-wave mixing and laser-induced grating spectroscopy. The presence of thermal gratings is confirmed in both the time and the frequency domains in two distinct experiments. Diluting the flame with helium decreases the thermal grating signal intensity. Experimental results agree well with calculations based on a solution of the linearized hydrodynamic equations.

A collaborative informatics infrastructure for multi-scale science

The Collaboratory for Multi-scale Chemical Science (CMCS) is developing a powerful informatics-based approach to synthesizing multi-scale information in support of systems-based research and is applying it within combustion science. An open source multi-scale informatics toolkit is being developed that addresses a number of issues core to the emerging concept of knowledge grids including provenance tracking and lightweight federation of data and application resources into cross-scale information flows. The CMCS portal is currently in use by a number of high-profile pilot groups and is playing a significant role in enabling their efforts to improve and extend community maintained chemical reference information.

Effects of laser field statistics on coherent anti-Stokes Raman spectroscopy intensities

The effects of intensity fluctuations in the frequency-doubled output of a multimode Nd:YAG pump laser on coheren anti-Stokes Raman spectroscopy (CARS) signal generation have been investigated in a crossed-beam, twocolor CARS experiment. Measurements of signal intensity as a function of time delay (small compared with pulse length) in one pump beam show a maximum at zero delay. In measurements on a single unresolved transition, however, the nonresonant signal is enhanced by almost a factor of 2 more than the resonant signal. Our results demonstrate the non-Gaussian nature of the laser field statistics and introduce new considerations into the analysis of experimental CARS spectra.

Gain switching of a monolithic single-frequency laser-diode-excited Nd:YAG laser

We report the use of gain switching to obtain 60 mW of single-longitudinal-mode peak output power from a laser-diode-excited monolithic Nd:YAG laser. The device is demonstrated to operate at repetition rates in excess of 1 kHz and exhibits a spectral linewidth of less than 8 MHz. This oscillator provides an ideal source for injection seeding of laboratory Nd:YAG laser systems.

Two-color resonant four-wave mixing: Analytical expressions for signal intensity

We present analytical signal expressions for each two-color resonant four-wave mixing (TC-RFWM) scheme that can be used for double-resonance molecular spectroscopy in the limit of weak fields (no saturation). The theoretical approach employs time-independent, diagrammatic perturbation theory and a spherical tensor analysis in an extension of recent treatments of degenerate four-wave mixing [S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 101, 1072 (1994)] and TC-RFWM for the specific case of stimulated emission pumping [S. Williams et al., J. Chem. Phys. 102, 8342 (1995)]. Under the assumption that the relaxation of the population, the orientation, and the alignment are the same, simple analytic expressions are derived for commonly used experimental configurations. The TC-RFWM signal is found to be a product of a concentration term, a one-photon molecular term, a line shape function, and a laboratory-frame geometric factor. These expressions are intended to facilitate the practical analysis of TC-...