Development of a tunable mid-IR difference frequency laser source for highly sensitive airborne trace gas detection

The development of a compact tunable mid-IR laser system at 3.5 μm for quantitative airborne spectroscopic trace gas absorption measurements is reported. The mid-IR laser system is based on difference frequency generation (DFG) in periodically poled LiNbO₃ and utilizes optical fiber amplified near-IR diode and fiber lasers as pump sources operating at 1083 nm and 1562 nm, respectively. This paper describes the optical sensor architecture, performance characteristics of individual pump lasers and DFG, as well as its application to wavelength modulation spectroscopy employing an astigmatic Herriott multi-pass gas absorption cell. This compact system permits detection of formaldehyde with a minimal detectable concentration (1σ replicate precision) of 74 parts-per-trillion by volume (pptv) for 1 min of averaging time and was achieved using calibrated gas standards, zero air background and rapid dual-beam subtraction. This corresponds to a pathlength-normalized replicate fractional absorption sensitivity of 2.5×10^-10 cm^-1. Received: 29 April 2002 / Published online: 21 August 2002 RID="*" ID="*"Corresponding author. Fax: +1-303/497-1492, E-mail: dr@ucar.edu     

Two-dimensional asymptotic expansions for large deviations of spherically distributed random vectors if the dominating point degenerates asymptotically

A geometric approach to asymptotic expansions for large-deviation probabilities, developed for the Gaussian law by Breitung and Richter [J. Multivariate Anal.,58, 1–20 (1996)], will be extended in the present paper to the class of spherical measures by utilizing their common geometric properties. This approach consists of rewriting the probabilities under consideration as large parameter values of the Laplace transform of a suitably defined function, expanding this function in a power series, and then applying Watson’s lemma. A geometric representation of the Laplace transform allows one to combine the global and local properties of both the underlying measure and the large-deviation domain. A special new type of difficulty is to be dealt with because the so-called dominating points of the large-deviation domain degenerate asymptotically. As is shown in Richter and Schumacher (in print), the typical statistical applications of large-deviation theory lead to such situations. In the present paper, consideration is restricted to a certain two-dimensional domain of large-deviations having asymptotically degenerating dominating points. The key assumption is a parametrized expansion for the inverse $\bar g^{ - 1} $ of the negative logarithm of the density-generating function of the two-dimensional spherical law under consideration.     

On the parity of crossing numbers

For an integer n ? 1, a graph G has an n-constant crossing number if, for any two good drawings ? and ?′ of G in the plane, μ(?) ≡ μ(?′) (mod n), where μ(?) is the number of crossings in ?. We prove that, except for trivial cases, a graph G has n-constant crossing number if and only if n = 2 and G is either K_p or K_q,r, where p, q, and r are odd.     

X-ray absorption and X-ray photoelectron spectroscopy of a rhodium colloid

Transition metal colloids are potential precursors of heterogeneous catalysts with application to selective chemical reactions. Sample preparation techniques are described. Experimental details are given of the characterization of these often air-sensitive particles by X-ray photoelectron and X-ray absorption spectroscopy. First results obtained with both techniques for a Rh-colloid show that the metal is mainly present in the zerovalent chemical state. But the spectra indicate further chemical states of Rh which can be assigned to the outermost metal atoms of the colloid interacting with organic ligands or to the educt Rh-halides.     

Electroexcitation of 208Pb,distribution of electric dipole and quadrupole strength and fragmentation of the isoscalar quadrupole giant resonance

Low momentum transfer, high-resolution inelastic electron scattering on ²⁰⁸Pb has been used to study the distribution of E1 and E2 strength in the region of excitation energy E_x = 8?12MeV. The E1 and E2 strength is very fragmented and the EWSR strength amounts to (10⁺⁷_?6)% and (29⁺¹¹_?8)% in the investigated energy region, respectively. The E2 strength found is less than most current theoretical predictions but agrees qualitatively with a 1p - 1h +2p - 2h model calculation presented in this paper. The E2 strength is also smaller than what is known from hadron scattering and the shape of the strength distribution is also markedly different in electron and hadron scattering.     

Search for M1 strength in 51V and the difference in 51V(e,e′) and 51V(p,p′) spectra

Following the studies of the distribution of M1 strength in the even-even N = 28 isotones ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe by inelastic electron scattering, the result of a search for M1 transitions in the odd-even N = 28 nucleus ⁵¹V is reported. No strong M1 excitation has been detected, in contrast to a recent (p, p') experiment. There is no immediate explanation for this discrepancy. Shell-model calculations indicate that a part of it might be accounted for by an interference between the spin and orbital term of the electromagnetic transition operator in the (e, e') experiment.     

Elastic scattering of 40Ar on 40Ca at Elab = 191, 236 and 272 MeV

Cross sections for elastic scattering of ⁴⁰Ar on ⁴⁰Ca have been measured at energies E_lab = 191, 236 and 272 MeV employing position-sensitive detectors and the method of kinematical coincidences. The experimental data are first compared with the ordinary and the generalized Fresnel models. Only the generalized Fresnel model describes the experimental data well. An optical model analysis with a Woods-Saxon potential yields an energy independent set of parameters (V_R = ?21.76 MeV, r_OR = 1.37 fm, a_R = 0.45 fm; W₁ = ?13.69 MeV, r₀₁ = 1.40 fm, a₁ = 0.36 fm) very similar to the one found in ⁴⁰Ca-⁴⁰Ca scattering at corresponding energies. Values deduced for the total reaction cross sections for the three energies are in good agreement with those predicted by the generalized Fresnel model. The data are also compared with optical model calculations with the real part of the potential replaced by various microscopically determined potentials. The proximity, Fleckner-Mosel and the Krappe-Nix-Sierk potentials like the phenomenological optical model potential reproduce the measured data fairly well over several orders of magnitude.     

On automorphisms of the degrees that preserve jumps

IfF is an automorphism of the degrees of unsolvability that preserves the jump operator, thenF leaves fixed all the degreesc that satisfyc≧0 ⁽³⁾. The results of this paper were part of the author’s PhD thesis (Illinois 1977), supervised by Carl G. Jockusch, Jr.     

Electrical analogy of transient heat flow in laser rods

An analog circuit is presented for the determination of the transient thermal profile in optically pumped laser rods. The model can be used to simulate the behavior of solid and hollow cylindrical rods under single shot and repetition rate conditions. The design of a particular circuit is given as well as experimental results.     

Dynamic fluctuations in optical bistability

We present results on the time correlation function of a system undergoing absorptive optical bistability. We first use the Zwanzig-Mori formalism to calculate time correlation functions both near marginal stability points and in the coexistence region. Near marginal stability the theory predicts large deviations from a single exponential form of the correlation function. The truncated continued fraction expansion is shown to become inapplicable close to the coexistence point. The difficulties are due to the presence of long time scales, viz. the very large mean first passage times between the two metastable steady states. When these scales are important we show that the memory kernel relaxation is no longer faster than that of a field fluctuation. An increase in the size of the system increases the disparity of the time scales and thus exacerbates the problems of the projection operator formalism as used here following reference [14].We next present an ansatz for the correlation function incorporating the four major time scales important near coexistence, the two single branch relaxation times and the two mean first passage times for transitions between the stable states. This form of the correlation function avoids the difficulties cited in connection with the use of the projection operator method.