Analytical formulae for the optimization of the process of low-power phase modulation in a quadratic nonlinear medium

We show that using the approximation of fixed intensity analytical formulae, describing the process of induced phase modulation for the beams involved in second-order nonlinear optical processes can be derived. Expressions that allow the optimization of the phase shifts experienced by the fundamental and generated waves are presented for nonlinear quadratic processes, second-harmonic generation and sum-frequency mixing. In the case of seeding at the generated wavelength, the phase shift of the fundamental wave is due to two interactions: (i) a cubic one, based on coupled second-order processes (cascade cubic nonlinearity) and (ii) single quadratic interaction with participation of the seeding wave. By comparison with the exact numerical solution, we defined the input parameters of the beams for which this analytical approach is valid. It is shown that phase shifts exceeding /2 can be correctly predicted using the expressions obtained.     

Temperature measurements in CO2-laser-induced pyrolysis flames for SiC and ternary SiC/C/B powder synthesis by means of CARS

The hot luminescent reaction zones of CO₂-laser-induced pyrolysis flames using SiH₄/C₂H₂ gas mixtures with different silane to acetylene ratios and with and without diborane additives were investigated by means of H₂ Q-branch CARS spectroscopy, leading to spatial temperature profiles in gas flow direction. In the case of B₂H₆ additive to the stoichiometric SiH₄/C₂H₂ mixture a high temperature plateau ( 800–1000 K) of the reactant gas volume develops already several millimetres before reaching the CO₂-laser focus line. This precursor preheating zone could be explained by the catalytic effect of boron atoms or boron-containing intermediate species in the flame. A similar behaviour for acetylene-rich flames operating at half laser power was not observed.     

Laser nitriding of iron: Influence of the laser parameters on the nitriding efficiency

Laser nitriding of Armco iron in nitrogen was studied for KrF-excimer-laser irradiation. The influence of the energy density and number of pulses on the nitrogen take-up and the nitride phases formed was investigated using Resonant Nuclear Reaction Analysis (RNRA) and Mössbauer spectroscopy. Besides the original a-iron, austenite-Fe(N), martensite-Fe(N),-Fe₂₊N, and-Fe₁₆N₂ were identified. The fraction of the e-phase was found to increase with the number of pulses and the energy density. A threshold energy density of 1.8(2) J/cm² for the laser nitriding process was found.     

The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the correspondingn-point distributions, called microlocal spectrum condition (SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.     

Crossover from Mott to Efros-Shklovskii variable range-hopping in Si:P

The low-temperature conductivity of uncompensated insulating Si:P with P concentration just below the metal-insulator (MI) transition shows with decreasingN a crossover from Mott variable range hopping (VRH) to Efros-Shklovskii VRH. From the concentration dependence of the Mott temperatureT _M a correlation-length exponent ν=1.1 is obtained which is compatible with the conductivity exponent μ=1.3 for metallic samples.