Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

Epitaxial growth and magnetic properties of half-metallic Fe3O4 on GaAs(100)

The growth and magnetic properties of epitaxial magnetite Fe3O4 on GaAs(100) have been studied by reflection high-energy electron diffraction, x-ray photoelectron spectroscopy, magneto-optical Kerr effect, and x-ray magnetic circular dichroism. The epitaxial Fe3O4 films were synthesized by in situ post growth annealing of ultrathin epitaxial Fe films at 500K in an oxygen partial pressure of 5×10−5mbar. The XMCD measurements show characteristic contributions from different sites of the ferrimagnetic magnetite unit cell, namely, Fetd3+, Feoh2+, and Feoh3+. The epitaxial relationship was found to be Fe3O4(100)⟨011⟩∕∕GaAs(100)⟨010⟩ with the unit cell of Fe3O4 rotated by 45° to match that of GaAs(100) substrate. The films show a uniaxial magnetic anisotropy in a thickness range of about 2.0–6.0nm with the easy axes along the [011] direction of the GaAs(100) substrate.

Lars Vegard:key communicator and pioneer crystallographer

The Norwegian physicist Lars Vegard studied with William H. Bragg in Leeds and then with Wilhelm Wien in Würzburg. There, in 1912, he heard a lecture by Max Laue describing the first X-ray diffraction experiments and took accurate notes which he promptly sent to Bragg. Although now remembered mainly for his work on the physics of the aurora borealis, Vegard also did important pioneering work in three areas of crystallography. He derived chemical insight from a series of related crystal structures that he determined, Vegard's Law relates the unit-cell dimensions of mixed crystals to those of the pure components, and he determined some of the first crystal structures of gases solidified at cryogenic temperatures. © 2013 Taylor and Francis.

Piezoelectric and dielectric properties of Ce substituted La2Ti2O7 ceramics

The ferroelectric and dielectric properties of cerium (Ce) substituted La2Ti2O7 (LTO) have been investigated. Single phase, dense La2-xCexTi2O7 (x=0.15, 0.25, 0.35) ceramics were prepared by spark plasma sintering. The solubility limit of Ce in La2-xCexTi2O7 was found to be between 0.35 and 0.5. The a-, b- and c-axes of the unit cell decrease with increasing Ce substitution. The Curie point (Tc) of La2-xCexTi2O7 (x=0, 0.15, 0.25, 0.35) decreases and dielectric constant and loss increase with increasing Ce substitution. Cerium can increase the d33 of La2Ti2O7. The highest d33 was 3.9±0.1pC/N for La1.85Ce0.15Ti2O7 textured ceramic. © 2012 Elsevier Ltd.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Ferroelectric and dielectric properties of Nd2−xCexTi2O7 ceramics

The solid solution system Nd2−xCexTi2O7 has been investigated. The solubility limit of Ce in Nd2−xCexTi2O7 was found to be 0·5–0·75 according to X-ray diffraction and X-ray photoelectron spectroscopy results. Ce substitution increases the b and c axes and the volume of the unit cell due to its larger ionic radius. Nd2−xCexTi2O7 (x  = 0·05, 0·25, 0·5, 0·75) textured ceramics were fabricated using spark plasma sintering. The ferroelectric and dielectric properties of the ceramics were studied. Ce substitution decreases the Curie point Tc of Nd2−xCexTi2O7 compounds. The results suggest that the Tc of Ce2Ti2O7 is <1445°C.

Nanostructured copper oxides and phosphates from a new solid-state route

Nanostructured copper containing materials of CuO, Cu3(PO4)3 and Cu2P2O7 have been prepared by solid-state pyrolysis of molecular CuCl2·NC5H4OH (I), CuCl2·CNCH2C6H4OH (II), oligomeric [Cu(PPh3)Cl]4 (III), N3P3[OC6H4CH2CN·CuCl]6[PF6] (IV), N3P3[OC6H5]5[OC5H4N·Cu][PF6] (V), polymeric chitosan·(CuCl2)n (VI) and polystyrene-co-4-vinylpyridine PS-b-4-PVP·(CuCl2) (VII) precursors. The products strongly depend on the precursor used. The pyrolytic products from phosphorus-containing precursors (III), (IV) and (V) are Cu phosphates or pyrophosphates, while non-phosphorous-containing precursors (VI) and (VII), result in mainly CuO. The use of chitosan as a solid-state template/stabilizer induces the formation of CuO and Cu2O nanoparticles. Copper pyrophosphate (Cu2P2O7) deposited on Si using (IV) as the precursor exhibits single-crystal dots of average diameter 100 nm and heights equivalent to twice the unit cell b-axis (1.5–1.7 nm) and an areal density of 5.1–7.7 Gigadots/in.2. Cu2P2O7 deposited from precursor (VI) exhibits unique labyrinthine high surface area deposits. The morphology of CuO deposited on Si from pyrolysis of (VI) depends on the polymer/Cu meta ratio. Magnetic measurements performed using SQUID on CuO nanoparticle networks suggest superparamagnetic behavior. The results give insights into compositional, shape and morphological control of the as-formed nanostructures through the structure of the precursors.

A Mineralogical Study of a Dravitic Tourmaline from the Grenville Province

Tourmaline from a gem-quality deposit in the Grenville province has been studied with X-ray diffraction, visible-near infrared spectroscopy, Fourier transform infrared spectroscopy, scanning electron microscopy, electron microprobe and optical measurements. The tourmaline is found within tremolite-rich calc-silicate pods hosted in marble of the Central Metasedimentary Belt. The crystals are greenish-greyish-brown and have yielded facetable material up to 2.09 carats in size. Using the classification of Henry et al. 2011 the tourmaline is classified as a dravite, with a representative formula shown to be (Na0.73Ca0.2380.032)(Mg2+2.913Fe2+0.057Ti4+0.030) (Al3+5.787Fe3+0.017Mg2+0.14)(Si6.013O18)(BO3)3(OH)3((OH,O)0.907F0.093). Rietveld analysis of powder diffraction data gives a = 15.9436(8) Å, c = 7.2126(7) Å and a unit cell volume of 1587.8 Å3. A polished thin section was cut perpendicular to the c-axis of one tourmaline crystal, which showed zoning from a dark brown core into a lighter rim into a thin darker rim and back into lighter zonation. Through the geochemical data, three key stages of crystal growth can be seen within this thin section. The first is the core stage which occurs from the dark core to the first colourless zone; the second is from this colourless zone increasing in brown colour to the outer limit before a sudden absence of colour is noted; the third is a sharp change from the end of the second and is entirely colourless. These events are the result of metamorphism and hydrothermal fluids resulting from nearby felsic intrusive plutons. Scanning electron microscope, and electron microprobe traverses across this cross-section revealed that the green colour is the result of iron present throughout the system while the brown colour is correlated with titanium content. Crystal inclusions in the tourmaline of chlorapatite, and zircon were identified by petrographic analysis and confirmed using scanning electron microscope data and occur within the third stage of formation.

Efficient Blue Electroluminescence Using Quantum-Confined Two-Dimensional Perovskites

Solution-processed hybrid organic–inorganic lead halide perovskites are emerging as one of the most promising candidates for low-cost light-emitting diodes (LEDs). However, due to a small exciton binding energy, it is not yet possible to achieve an efficient electroluminescence within the blue wavelength region at room temperature, as is necessary for full-spectrum light sources. Here, we demonstrate efficient blue LEDs based on the colloidal, quantum-confined 2D perovskites, with precisely controlled stacking down to one-unit-cell thickness (n = 1). A variety of low-k organic host compounds are used to disperse the 2D perovskites, effectively creating a matrix of the dielectric quantum wells, which significantly boosts the exciton binding energy by the dielectric confinement effect. Through the Förster resonance energy transfer, the excitons down-convert and recombine radiatively in the 2D perovskites. We report room-temperature pure green (n = 7–10), sky blue (n = 5), pure blue (n = 3), and deep blue (n = 1) electroluminescence, with record-high external quantum efficiencies in the green-to-blue wavelength region.

Manifestation of Colossal Thermoelectric Power by Charge Ordered Small and Intermediate Bandwidth Manganites

Thermoelectric materials are revisited for various applications including power generation. The direct conversion of temperature differences into electric voltage and vice versa is known as thermoelectric effect. Possible applications of thermoelectric materials are in eco-friendly refrigeration, electric power generation from waste heat, infrared sensors, temperature controlled-seats and portable picnic coolers. Thermoelectric materials are also extensively researched upon as an alternative to compression based refrigeration. This utilizes the principle of Peltier cooling. The performance characteristic of a thermoelectric material, termed as figure of merit (ZT) is a function of several transport coefficients such as electrical conductivity (σ), thermal conductivity (κ) and Seebeck coefficient of the material (S). ZT is expressed asκσTZTS2=, where T is the temperature in degree absolute. A large value of Seebeck coefficient, high electrical conductivity and low thermal conductivity are necessary to realize a high performance thermoelectric material. The best known thermoelectric materials are phonon-glass electron – crystal (PGEC) system where the phonons are scattered within the unit cell by the rattling structure and electrons are scattered less as in crystals to obtain a high electrical conductivity. A survey of literature reveals that correlated semiconductors and Kondo insulators containing rare earth or transition metal ions are found to be potential thermoelectric materials. The structural magnetic and charge transport properties in manganese oxides having the general formula of RE1−xAExMnO3 (RE = rare earth, AE= Ca, Sr, Ba) are solely determined by the mixed valence (3+/4+) state of Mn ions. In strongly correlated electron systems, magnetism and charge transport properties are strongly correlated. Within the area of strongly correlated electron systems the study of manganese oxides, widely known as manganites exhibit unique magneto electric transport properties, is an active area of research.Strongly correlated systems like perovskite manganites, characterized by their narrow localized band and hoping conduction, were found to be good candidates for thermoelectric applications. Manganites represent a highly correlated electron system and exhibit a variety of phenomena such as charge, orbital and magnetic ordering, colossal magneto resistance and Jahn-Teller effect. The strong inter-dependence between the magnetic order parameters and the transport coefficients in manganites has generated much research interest in the thermoelectric properties of manganites. Here, large thermal motion or rattling of rare earth atoms with localized magnetic moments is believed to be responsible for low thermal conductivity of these compounds. The 4f levels in these compounds, lying near the Fermi energy, create large density of states at the Fermi level and hence they are likely to exhibit a fairly large value of Seebeck coefficient.

Optimization of Li-ion solid electrolytes

The synthesis and optimization of two Li-ion solid electrolytes were studied in this work. Different combinations of precursors were used to prepare La0.5Li0.5TiO3 via mechanosynthesis. Despite the ability to form a perovskite phase by the mechanochemical reaction it was not possible to obtain a pure La0.5Li0.5TiO3 phase by this process. Of all the seven combinations of precursors and conditions tested, the one where La2O3, Li2CO3 and TiO2 were milled for 480min (LaOLiCO-480) showed the best results, with trace impurity phases still being observed. The main impurity phase was that of La2O3 after mechanosynthesis (22.84%) and Li2TiO3 after calcination (4.20%). Two different sol-gel methods were used to substitute boron on the Zr-site of Li1+xZr2-xBx(PO4)3 or the P-site of Li1+6xZr2(P1-xBxO4)3, with the doping being achieved on the Zr-site using a method adapted from Alamo et al (1989). The results show that the Zr-site is the preferential mechanism for B doping of LiZr2(PO4)3 and not the P-site. Rietveld refinement of the unit-cell parameters was performed and it was verified by consideration of Vegard’s law that it is possible to obtain phase purity up to x = 0.05. This corresponds with the phases present in the XRD data, that showed the additional presence of the low temperature (monoclinic) phase for the powder sintered at 1200ºC for 12h of compositions with x ≥ 0.075. The compositions inside the solid solution undergo the phase transition from triclinic (PDF#01-074-2562) to rhombohedral (PDF#01-070-6734) when heating from 25 to 100ºC, as reported in the literature for the base composition. Despite several efforts, it was not possible to obtain dense pellets and with physical integrity after sintering, requiring further work in order to obtain dense pellets for the electrochemical characterisation of Li Zr2(PO4)3 and Li1.05Zr1.95B0.05(PO4)3.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.