Optimization of facet coating for highly strained InGaAs quantum well lasers operating at 1200 nm

The optical output power of a laser diode can be enhanced by anti-reflection (AR) and high-reflection (HR) facet coatings, respectively, at the front and back facet. AR and HR coatings also serve the purpose of protection and passivation of laser diode facets. In this work, we have designed and optimized a single layer λ/4 thick Al₂O₃ film for the AR coating and a stack of λ/4 thick Al₂O₃/λ/4 thick Si bi-layers for the HR coating for highly strained InGaAs quantum-well edge emitting broad area (BA) laser diodes. Effect of the front and back facet reflectivities on output power of the laser diodes has been studied. The light output versus injected current (L–I characteristics) measurements were carried out on selected devices before and after the facet coatings. We have also carried out the numerical simulation and analysis of L–I characteristics for this particular diode structure. The experimental results have been compared and verified with the numerical simulation.     

Optical absorption and photoluminescence studies of Eu-doped phosphate and fluorophosphate glasses

Phosphate (P₂O₅+K₂O+BaO+Al₂O₃+Eu₂O₃) and fluorophosphate (P₂O₅+K₂O+BaO+BaF₂+Al₂O₃+Eu₂O₃) glasses with different Eu³⁺ ion concentrations have been prepared and characterized through optical absorption, photoluminescence and decay times. An intense red luminescence is observed from the ⁵D₀ emitting level of Eu³⁺ ions in these glasses. The relative luminescence intensity ratio of ⁵D₀→⁷F₂→⁵D₀→⁷F₁ transitions has been evaluated to estimate the local site symmetry around the Eu³⁺ ions. The emission spectra of these glasses show a complete removal of degeneracy for the ⁵D₀→⁷F₁ and ⁵D₀→⁷F₂ transitions. Second and fourth rank crystal-field (CF) parameters have been calculated together with the CF strength parameter by assuming the C_2v symmetry for the Eu³⁺ ions in both the phosphate and fluorophosphate glasses. Judd-Ofelt parameters have been evaluated from the luminescence intensity ratios of ⁵D₀→⁷F_J (J=2, 4 and 6) to ⁵D₀→⁷F₁ transitions. These parameters have been used to derive radiative properties such as transition probabilities, branching ratios, radiative lifetimes and peak stimulated emission cross-sections for the ⁵D₀→⁷F_J transitions. Decay curves of the ⁵D₀ level of Eu³⁺ ions in these two Eu³⁺:glass systems have been measured by monitoring the ⁵D₀→⁷F₂ transition (611 nm) at room temperature. The experimental lifetime of the ⁵D₀ level in the title glasses is found to be higher than Eu³⁺-doped niobium phosphate glasses. The analysis indicates that the lifetime of the ⁵D₀ level is found to be less sensitive to the Eu³⁺ ion concentration and addition of BaF₂ has no significant effect on the optical properties of Eu³⁺-doped phosphate glasses.     

Sibling Curves of Polynomials

Abstract

Sibling curves were demonstrated in papers [2, 3] as a novel way to visualize the zeros of complex valued functions. In this paper, we continue the work done in those papers by focusing solely on polynomials. We proceed to prove that the number of sibling curves of a polynomial is the degree of the polynomial.     

Calculus in positive characteristic p

We revisit hyperderivatives to build on the integral theory of calculus in positive characteristic p. In particular, we give necessary and sufficient conditions for the exactness of a hyperdifferential form associated with hyperderivatives and then propose a closed formula for finding the hyperantiderivative of an exact form.     

Synthesis and characterization of functional fluorinated telomers

The synthesis and characterizations of fluorinated telomers based on vinylidene fluoride (VDF) by iodine transfer polymerization (ITP) are presented. These telomers were prepared in the presence of ω‐iodoperfluorinated functional chain transfer agents, C₆F₁₃I or C₄F₉I. ITPs were initiated by thermal decomposition of bis(4‐tert‐butylcyclohexyl) peroxydicarbonate (BBCHPDC), in solution (in the presence of acetonitrile). The obtained telomers were characterized by different analyses such as elemental analyses, nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy, size exclusion chromatography, X‐ray diffraction (XRD), and finally by thermal analyses such as differential scanning calorimetry (DSC) and thermogravimetric analyses. These technical analyses enabled one to assess their chemical structures, various thermal properties, and their crystalline forms. The assignments of the characteristic signals obtained by ¹⁹F NMR spectroscopy enabled one to calculate the average degrees of polymerization (DPn) and percentages of ? CH₂CF₂I end group functionalities that depend on the initiator and the fractionation process after reaction. A good control of polymerization was shown by the absence of reversed ? CH₂CF₂? CF₂CH₂? (VDF–VDF dyads) and narrow polydispersity indices (<1.2). The XRD and DSC evidenced the influence of the chain length of the telomers on the crystallinity rate (>70%) and indicated two crystalline forms, α and β, that depended on DPn values. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A local limit theorem for a transient chaotic walk in a frozen environment

This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle’s initial location is random and uniformly distributed, this dynamical system can be reduced to a random walk in a one-dimensional inhomogeneous environment with a forbidden direction. Our main result is a local limit theorem which explains in detail why, in the long run, the random walk’s probability mass function does not converge to a Gaussian density, although the corresponding limiting distribution over a coarser diffusive space scale is Gaussian.     

Effectivity of Brauer–Manin obstructions on surfaces

We study Brauer–Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.     

Orthogonal and symplectic parabolic bundles

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.