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.     

Fourier Series in Weighted Lorentz Spaces

The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given for the map to be bounded. In addition, new direct analogues are given for known weighted Lorentz space inequalities for the Fourier transform. Applications are given that involve Fourier coefficients of functions in LogL and more general Lorentz–Zygmund spaces.     

Detection of acetylene by electronic resonance-enhanced coherent anti-Stokes Raman scattering

We report the detection of acetylene (C₂H₂) at low concentrations by electronic resonance-enhanced coherent anti-Stokes Raman scattering (ERE-CARS). Visible pump and Stokes beams are tuned into resonance with Q-branch transitions in the v₂ Raman band of acetylene. An ultraviolet probe beam is tuned into resonance with the – electronic transition of C₂H₂, resulting in significant electronic resonance enhancement of the CARS signal. The signal is found to increase significantly with rising pressure for the pressure range 0.1–8 bar at 300 K. Collisional narrowing of the spectra appears to be important at 2 bar and above. A detection limit of approximately 25 ppm at 300 K and 1 bar is achieved for our experimental conditions. The signal magnitudes and the shape of the C₂H₂ spectrum are essentially constant for UV probe wavelengths from 233.0 to 238.5 nm, thus indicating that significant resonant enhancement is achieved even without tuning the probe beam into resonance with a specific electronic resonance transition. PACS 42.65.Dr; 42.62.Fi; 42.65.-k     

Photolytic-interference-free, femtosecond two-photon fluorescence imaging of atomic hydrogen

We discuss photolytic-interference-free, high-repetition-rate imaging of reaction intermediates in flames and plasmas using femtosecond (fs) multiphoton excitation. The high peak power of fs pulses enables efficient nonlinear excitation, while the low energy nearly eliminates interfering single-photon photodissociation processes. We demonstrate proof-of-principle, interference-free, two-photon laser-induced fluorescence line imaging of atomic hydrogen in hydrocarbon flames and discuss the method's implications for certain other atomic and molecular species.     

Measurement of nitric oxide concentrations in flames by using electronic-resonance-enhanced coherent anti-Stokes Raman scattering

We have measured nitric oxide (NO) concentrations in flames by using electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy (ERE-CARS). Visible pump and Stokes beams were tuned to a Q-branch vibrational Raman resonance of NO. A UV probe beam was tuned into resonance with specific rotational transitions in the (v"=1,v'=0) vibrational band in the A(2)Sigma(+)-X(2)Pi electronic transition, thus providing a substantial electronic-resonance enhancement of the resulting CARS signal. NO concentrations were measured at levels down to 50 parts in 10(6) in H(2)/air flames at atmospheric pressure. NO was also detected in heavily sooting C(2)H(2)/air flames at atmospheric pressure with minimal background interference.     

Ballistic imaging in the near-field of an effervescent spray

We have investigated liquid breakup mechanisms in the near nozzle region of a high-pressure effervescent atomizer using ballistic imaging. This technique has revealed various breakup regimes depending upon total flow rate and the gas-to-liquid ratio (GLR). At low total speeds, the jet does not exhibit the wide spread angle and rapid breakup for which effervescent sprays are known, even at high GLR. Above a distinct threshold value for total flow rate, the jet passes through several recognizable flow regimes depending on GLR and it does achieve the expected wide spread angle and rapid breakup. Intermediate GLR’s produce interesting flow patterns that seem to be generated by surging at the nozzle exit, and this surging can probably be attributed to the flow pattern just at the nozzle exit. Indeed, specific interior flows seem to generate the most rapid breakup and should be investigated further.     

Efficiency and scaling of an ultrashort-pulse high-repetition-rate laser-driven X-ray source

Technical issues and performance of a high-repetition-rate ultrafast-laser-based X-ray source have been studied experimentally in the context of developing a dedicated laboratory-based tool for combustion diagnostics. X-ray emission from numerous elemental materials have been investigated to compare with analytical based expectations for yield and efficiency, as well as to evaluate advantages of some materials for operational issues such as debris production and degree of efficiency enhancement utilizing various illumination configurations. A weak inverse scaling of conversion efficiency with atomic number was observed. Broadband energy conversion efficiency of approximately 10^?5 and yield greater than 10¹⁰ photons/s have been measured with numerous target elements. Application of a pre-pulse significantly enhances conversion efficiency, and the enhancement factor depends on material. Thus, previous optimizations must be performed in the atomic number variation as well. Additionally, the efficiency enhancement associated with p-polarization incidence (relative to s-polarization) is observed to depend on base material reflectivity.     

Single-Shot Gas-Phase Thermometry by Time-to-Frequency Mapping of Coherence Dephasing

We demonstrate a single-beam coherent anti-Stokes Raman scattering (CARS) technique for gas-phase thermometry that assesses the species-specific local gas temperature by single-shot time-to-frequency mapping of Raman-coherence dephasing. The proof-of-principle experiments are performed with air in a temperature-controlled gas cell. Impulsive excitation of molecular vibrations by an ultrashort pump/Stokes pulse is followed by multipulse probing of the 2330 cm(-1) Raman transition of N(2). This sequence of colored probe pulses, delayed in time with respect to each other and corresponding to three isolated spectral bands, imprints the coherence dephasing onto the measured CARS spectrum. For calibration purposes, the dephasing rates are recorded at various gas temperatures, and the relationship is fitted to a linear regression. The calibration data are then used to determine the gas temperature and are shown to provide better than 15 K accuracy. The described approach is insensitive to pulse energy fluctuations and can, in principle, gauge the temperature of multiple chemical species in a single laser shot, which is deemed particularly valuable for temperature profiling of reacting flows in gas-turbine combustors.     

An equivalence theorem for some integral conditions with general measures related to Hardy's inequality II

Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 0<q<p<∞, p>1. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures.     

Modeling thermodynamic properties of natural gas mixtures using perturbed-chain statistical associating fluid theory

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was employed for predicting thermodynamic properties of natural gas mixture. Thermodynamic properties like density, isobaric and isochoric heat capacity, enthalpy, entropy, and internal energy were calculated with the PC-SAFT. Results are validated against experimental data for natural gas and mixtures similar to natural gas. The validation show that the Average Absolute Deviation (AAD) for density is 1.10% for binary mixture and 1.08% for mixtures similar to natural gas. Also AAD value for enthalpy is 1.42%, for internal energy, 0.77, for entropy, 0.43, for isochoric heat capacity, 1.26%, and for isobaric heat capacity, 2.66%. Results show PC-SAFT to be able to predict all the thermodynamics properties of natural gas and mixtures similar to natural gas with high accuracy in a wide range of temperature and pressure.