Talbot effect for dispersion in linear optical fibers and a wavelet approach

We shortly recall the mathematical and physical aspects of Talbot's self-imaging effect occurring in near-field diffraction. In the rational paraxial approximation, the Talbot images are formed at distances z=p/q, where p and q are coprimes, and are superpositions of q equally spaced images of the original binary transmission (Ronchi) grating. This interpretation offers the possibility to express the Talbot effect through Gauss sums. Here, we pay attention to the Talbot effect in the case of dispersion in optical fibers presenting our considerations based on the close relationships of the mathematical representations of diffraction and dispersion. Although dispersion deals with continuous functions, such as gaussian and supergaussian pulses, whereas in diffraction one frequently deals with discontinuous functions, the mathematical correspondence enables one to characterize the Talbot effect in the two cases with minor differences. In addition, we apply, for the first time to our knowledge, the wavelet transform to the fractal Talbot effect in both diffraction and fiber dispersion. In the first case, the self similar character of the transverse paraxial field at irrational multiples of the Talbot distance is confirmed, whereas in the second case it is shown that the field is not self similar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed outComment: 15 text pages + 7 gif figs, accepted at Int. J. Mod. Phys. B, final version of a contribution at ICSSUR-Besancon (May/05). Color figs available from the first autho

Collapse of the Gd3+Gd^{3+} ESR fine structure throughout the coherent temperature of the Gd-doped Kondo Semiconductor CeFe4P12CeFe_{4}P_{12}

Experiments on the $Gd^{3+}$ Electron Spin Resonance (ESR) in the filled skutterudite $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ ($x \approx 0.001$), at temperatures where the host resistivity manifests a smooth insulator-metal crossover, provides evidence of the underlying Kondo physics associated with this system. At low temperatures (below $T \approx K$), $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ behaves as a Kondo-insulator with a relatively large hybridization gap, and the $Gd^{3+}$ ESR spectra displays a fine structure with lorentzian line shape, typical of insulating media. The electronic gap is attributed to the large hybridization present in the coherent regime of a Kondo lattice, when Ce 4f-electrons cooperate with band properties at half-filling. Mean-field calculations suggest that the electron-phonon interaction is fundamental at explaining the strong 4f-electron hybridization in this filled skutterudite. The resulting electronic structure is strongly temperature dependent, and at about $T^{*} \approx 160 K$ the system undergoes an insulator-to-metal transition induced by the withdrawal of 4f-electrons from the Fermi volume, the system becoming metallic and non-magnetic. The $Gd^{3+}$ ESR fine structure coalesces into a single dysonian resonance, as in metals. Still, our simulations suggest that exchange-narrowing via the usual Korringa mechanism, alone, is not capable of describing the thermal behavior of the ESR spectra in the entire temperature region ($4.2$ - $300$ K). We propose that temperature activated fluctuating-valence of the Ce ions is the missing ingredient that, added to the usual exchange-narrowing mechanism, fully describes this unique temperature dependence of the $Gd^{3+}$ ESR fine structure observed in $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$.Comment: 19 pages, 6 figure

Magnetotransport in the Kondo model with ferromagnetic exchange interaction

We consider the transport properties in an applied magnetic field of the spin S=1/2 Kondo model with ferromagnetic exchange coupling to electronic reservoirs, a description relevant for the strong coupling limit of underscreened spin S=1 Kondo impurities. Because the ferromagnetic Kondo interaction is marginally irrelevant, perturbative methods should prove accurate down to low energies. For the purpose of this study, we use a combination of Majorana diagrammatic theory with Density Matrix Numerical Renormalization Group simulations. In the standard case of antiferromagnetic Kondo exchange, we first show that our technique recovers previously obtained results for the T-matrix and spin relaxation at weak coupling (above the Kondo temperature). Considering then the ferromagnetic case, we demonstrate how the low-energy Kondo anomaly splits for arbitrary small values of the Zeeman energy, in contrast to fully screened Kondo impurities near the strong coupling Fermi liquid fixed point, and in agreement with recent experimental findings for spin S=1 molecular quantum dots.Comment: 14 pages, 13 figures, minor changes in V

Trion dynamics in coupled double quantum wells. Electron density effects

We have studied the coherent dynamics of injected electrons when they are either free or bounded both in excitons and in trions (charged excitons). We have considered a remotely doped asymmetric double quantum well where an excess of free electrons and the direct created excitons generate trions. We have used the matrix density formalism to analyze the electron dynamics for different concentration of the three species. Calculations show a significant modification of the free electron inter-sublevel oscillations cWe have studied the coherent dynamics of injected electrons when they are aused by electrons bound in excitons and trions. Based on the present calculations we propose a method to detect trions through the emitted electromagnetic radiation or the current density.Comment: 14 pages, 13 figure

Appearance of room temperature ferromagnetism in Cu-doped TiO2−δ_{2-\delta} films

In recent years there has been an intense search for room temperature ferromagnetism in doped dilute semiconductors, which have many potentially applications in spintronics and optoelectronics. We report here the unexpected observation of significant room temperature ferromagnetism in a semiconductor doped with nonmagnetic impurities, Cu-doped TiO$_2$ thin films grown by Pulsed Laser Deposition. The magnetic moment, calculated from the magnetization curves, resulted surprisingly large, about 1.5 $\mu_B$ per Cu atom. A large magnetic moment was also obtained from ab initio calculations using the supercell method for TiO$_2$ with Cu impurities, but only if an oxygen vacancy in the nearest-neighbour shell of Cu was present. This result suggests that the role of oxygen vacancies is crucial for the appearance of ferromagnetism. The calculations also predict that Cu doping favours the formation of oxygen vacancies.Comment: 4 pages, 3 figures, published in Phys. Rev. B (Rapid Comm.