Experimental investigation and numerical simulation of the influence of resonator-length detuning on the output power,pulse duration and spectral width of a cw mode-locked picosecond optical parametric oscillator

We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency.     

The Hausdorff dimension of graphs of Weierstrass functions

The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.

     

The signature theorem and some related questions

Some corollaries of the Hirzebruch-Thom signature theorem are discussed. The multiplicativity of the signature and the naturalness of the Pontryagin classes for coverings in the case of ℚ-homology manifolds is proved. A geometric proof of Hirzebruch’s well-known “functional equation” for the virtual signature is outlined. Bibliography: 25 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 197–209. Translated by N. Yu. Netsvetaev.     

Formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation

The first results regarding the formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation are presented. The conditions are established, and the mechanism of the formation of such structures is discussed. Zh. Tekh. Fiz. 67, 97–99 (December 1997)     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

Effect of iodine sorption on the free volume of polycarbonate

 The effect of iodine sorption on the free volume of polycarbonate is investigated by Positron Annihilation Lifetime method. The observed results are interpreted in terms of the Charge Transfer Complex formation and precipitation of iodine at the initial and final stages of sorption, respectively. At higher levels of sorption, changes in the second lifetime and its intensity seem to suggest a conformational transformation, probably due to the net change in the amorphous-crystalline boundary regions of the polymer matrix. The free volume cavities have been predominantly occupied by I^- ₃ species and the diffusion process obeys Fick’s law. An exponential type correlation has been observed between fractional free volume and the diffusion coefficient. Received: 13 June 1996/Accepted: 20 September 1996     

A poincaré-bendixson theorem for analytic families of vector fields

We provide a characterization of the limit periodic sets for analytic families of vector fields under the hypothesis that the first jet is non-vanishing at any singular point. Also, applying the family desingularization method, we reduce the complexity of some of these sets.     

Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.