Nitric oxide concentration measurements in atmospheric pressure flames using electronic-resonance-enhanced coherent anti-Stokes Raman scattering

We report the application of electronic-resonance-enhanced coherent anti-Stokes Raman scattering (ERE-CARS) for measurements of nitric oxide concentration ([NO]) in three different atmospheric pressure flames. Visible pump (532 nm) and Stokes (591 nm) beams are used to probe the Q-branch of the Raman transition. A significant resonance enhancement is obtained by tuning an ultraviolet probe beam (236 nm) into resonance with specific rotational transitions in the (v’=0, v”=1) vibrational band of the A²Σ⁺–X²Π electronic system of NO. ERE-CARS spectra are recorded at various heights within a hydrogen-air flame producing relatively low concentrations of NO over a Hencken burner. Good agreement is obtained between NO ERE-CARS measurements and the results of flame computations using UNICORN, a two-dimensional flame code. Excellent agreement between measured and calculated NO spectra is also obtained when using a modified version of the Sandia CARSFT code for heavily sooting acetylene-air flames (φ=0.8 to φ=1.6) on the same Hencken burner. Finally, NO concentration profiles are measured using ERE-CARS in a laminar, counter-flow, non-premixed hydrogen-air flame. Spectral scans are recorded by probing the Q₁ (9.5), Q₁ (13.5) and Q₁ (17.5) Raman transitions. The measured shape of the [NO] profile is in good agreement with that predicted using the OPPDIF code, even without correcting for collisional effects. These comparisons between [NO] measurements and predictions establish the utility of ERE-CARS for detection of NO in flames with large temperature and concentration gradients as well as in sooting environments. PACS 07.88.+y; 42.62.Fi; 42.65.Dr     

Über trigonometrische Reihen mit zahlentheoretischen Koeffizienten

Ohne Zusammenfassung     

Nonperturbative modeling of two-photon absorption in a three-state system

The physics of the two-photon absorption process is investigated for a three-state system. The density-matrix equations for the two-photon interaction are solved in the steady-state limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the two-photon resonance are investigated in detail by numerical solution of the steady-state density-matrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the single-photon transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipole-moment matrix elements for the single-photon transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the single-photon transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.     

Aufeinanderfolgende Elemente in multiplikativen Zahlenmengen

LetM be a multiplicative set with 1M andmnM if and only ifmM,nM for (m,n)=1. It is shown by elementary means that there exists the asymptotic density of the setM(M–1) for every multiplicative setM. The density is positive if and only ifM possesses a positive density and 2M for some . This result is slightly generalized to sums over multiplicative functionsf with |f|1.     

Photoaddressable polymers for liquid crystal alignment

We demonstrate reversible photoinduced in situ reorientation of low molecular mass liquid crystals (LCs) by means of photoaddressable polymers (PAPs). These polymers contain mesogenic azobenzene side chains optimized to reorient cooperatively and effectively upon illumination with polarized light. Various low molecular mass LCs were introduced between two PAP layers and these sandwich devices were tested with respect to stability and reversibility of photoinduced orientation. Dissolution of the PAP layer by the low molecular mass LC was observed for several material combinations and systematically investigated. Different anisotropic dyes were added as fluorescence markers in order to monitor the photoinduced LC orientation. With an optimized material combination, more than 10 reversible reorientation processes could be realized with polarized light of either 514 or 405 nm wavelength, without any reduction in alignment quality. Further, microscopic polarized fluorescence patterns could be produced and erased within short exposure times.     

Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations

Linear partial differential algebraic equations (PDAEs) of the form Au _t(t, x) + Bu _xx(t, x) + Cu(t, x) = f(t, x) are studied where at least one of the matrices A, B R ^n×n is singular. For these systems we introduce a uniform differential time index and a differential space index. We show that in contrast to problems with regular matrices A and B the initial conditions and/or boundary conditions for problems with singular matrices A and B have to fulfill certain consistency conditions. Furthermore, two numerical methods for solving PDAEs are considered. In two theorems it is shown that there is a strong dependence of the order of convergence on these indexes. We present examples for the calculation of the order of convergence and give results of numerical calculations for several aspects encountered in the numerical solution of PDAEs.     

10 kHz detection of CO2 at 4.5 microm by using tunable diode-laser-based difference-frequency generation

A compact, high-speed tunable, diode-laser-based mid-infrared (MIR) laser source has been developed for absorption spectroscopy of CO2 at rates up to 10 kHz. Radiation at 4.5 microm with a mode-hop-free tuning range of 80 GHz is generated by difference-frequency mixing the 860 nm output of a distributed-feedback diode laser with the 1064 nm output of a diode-pumped Nd:YAG laser in a periodically poled lithium niobate crystal. MIR absorption spectroscopy of CO2 with a detection limit of 44 ppm m at 10 kHz is demonstrated in a C2H4-air laminar diffusion flame and in the exhaust of a liquid-fueled model gas-turbine combustor.     

OH sensor based on ultraviolet, continuous-wave absorption spectroscopy utilizing a frequency-quadrupled, fiber-amplified external-cavity diode laser

The development of an all-solid-state cw laser system for optical absorption measurements of the OH radical in the UV spectral range is described. The tunable output of a 1064-nm external-cavity diode laser is amplified by use of a Nd:doped, double-clad fiber amplifier. The amplified near-IR radiation is frequency doubled by a periodically poled lithium niobate crystal and then quadrupled in a beta-barium borate crystal. The design and operation of the system and measurements of OH absorption in the (2, 0) band of the A(2)?(+)- X(2)? electronic transition are discussed.     

Spectral measurements of incipient plasma temperature and electron number density during laser ablation of aluminum in air

Plasmas generated during incipient laser ablation of aluminum in air were studied using emission spectroscopy. A plasma emission model was developed, invoking one-dimensional radiative transfer, to describe the observed emission spectra, while taking into account the effects of continuum radiation. Theoretical spectra were calculated and compared to experimental spectra in the range 387–406 nm. Satisfactory agreement was found between the experimental and predicted spectra, especially at delay times of 30–200 ns, thus providing plasma temperatures and electron number densities as functions of delay time and laser irradiance (1.8–8.0 GW/cm²). In general, both the plasma temperature and electron number density rise at greater laser irradiances but drop at increasing delay times, with a more rapid drop for delay times less than 60 ns. PACS 42.62.Fi; 52.25.-b