On typically real functions which are generated by a fixed typically real function

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ.     

Effect of pressure on fluorescence of Nd3+ in LaCl3

Abstract

Fluorescence from Nd³⁺ in LaCl₃ is measured at 100 K under pressures up to about 10 GPa. The observed variations of the energy levels are used for the evaluation of crystal field parameters. The pressure-dependence of these parameters is compared with the previous results on Pr³⁺ in LaCl₃.     

Local near field assisted ablation of fused silica

In this contribution we present recent experimental and theoretical results on local near-field assisted laser ablation. Along these lines, we have generated sub-diffraction sized nanostructures on fused silica substrates, exploiting the local near fields of highly ordered triangular gold nanoparticle arrays generated by nanosphere lithography. After preparation, the nanoparticle arrays were irradiated with a single 35 fs long laser pulse with a central wavelength of λ=790 nm. The pulse energy was set to E=3.9 μJ, resulting in a fluence well below the ablation threshold of the fused silica substrates. In addition, 3D electromagnetic simulations using a finite integration technique in time domain have been performed. The simulations demonstrate that indeed the local field in the vicinity of the tips of the triangular nanoparticles overcome the ablation threshold and easily explain the generated nanostructures. Most importantly, the simulations show, that higher order modes contribute to the ablation process. These modes cause ablation along the side edges of the nanoparticles. Finally, we demonstrate, that the optical properties of the triangular nanoparticles, which can be tuned by their morphology, are crucial parameters for the generation of the ablation structures.     

Metal particles on surfaces-desorption,optical spectra,and laser-induced size manipulation

Desorption induced by electronic excitation with laser light is discussed. Emphasis is placed on nonthermal desorption where surface plasma excitation in small particles precedes the rupture of the surface chemical bond. A scenario for the mechanism underlying such a process is proposed. In this context, calculations of the electronic spectra of small sodium particles are presented and the influence of different multipole orders of the collective electron oscillation, of different shapes of the clusters and of the substrate are outlined. Furthermore, manipulation of the size distribution of metal particles on supports is described as an application of the effect. This allows the preparation of very special surfaces with novel physical and chemical properties. Methods to characterize such adsorbate-substrate combinations, especially by use of the optical spectra of the particles, are also discussed. Finally, prospects for future experiments in this field are outlined.     

EPR study of Fe3+ and Mn2+ in CeO2 and ThO2

Attempts were made to grow CeO₂ and ThO₂ single crystals doped with transition metal ions. Only Fe³⁺ and Mn²⁺ could be detected by the EPR technique. The EPR spectrum of Fe³⁺ in CeO₂ exhibits the well-known fine structure in cubic fields. The parameters areg=2.0044(1) anda=15.6(1)·10^?4 cm^?1. The hyperfine constantA for⁵⁷Fe in hexahedral coordination was found to be 8.9(1)·10^?4 cm^?1. The EPR spectrum of Mn²⁺ in CeO₂ reveals two cubic Mn²⁺ centers. The parameters for center 1 areg=1.9999(1) andA=86.9(1)·10^?4 cm^?1 and for center 2g=1.9984(1) andA=87.0(1)·10^?4 cm^?1. Heating the Mn doped CeO₂ samples in hydrogen, the Mn²⁺ centers transform from cubic into trigonal centers with approximate values ofg=1.9988(2),A=84.5(6)·10^?4 cm^?1 andD=203(1)·10^?4 cm^?1. The two observed Mn²⁺ centers in ThO₂ exhibita priori axial symmetry with approximate values ofg=2.0006(2),A=88.9(4)·10^?4 cm^?1 andD=33(3)·10^?4 cm^?1.