Complex structured singular value analysis using fixed-structure dynamic D-scales

Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σ_max (D(jω)G(jω)D^-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H₂/H_∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration.     

Properties of silver halide core-clad fibers and the use of fiber bundle for thermal imaging

Abstract

Optical infrared (IR) fibers with core-clad structure are of great importance because they have better qualities than unclad fibers for most IR fiber applications, especially in CO₂ laser power delivery and radiometry. We have fabricated core-clad polycrystalline silver halide optical fibers with different compositions and core diameters, and although their loss is still higher than that of unclad fibers, they already have many advantages and new capabilities. The behavior of the scattering loss along these fibers and other optical properties was measured and compared with that of unclad silver halide fibers. We show that the higher loss of clad fibers results mainly from excessive scattering. The improvement in the process of fabricating clad fibers enabled the production of new elements such as single-mode fibers (SMFs) and fiber bundles for thermal imaging.     

60-fs pulses from a diode-pumped Nd:glass laser

We demonstrate 60-fs pulses with an average output power of 84 mW from a diode-pumped Nd:glass laser mode locked by a low-finesse antiresonant Fabry-Perot saturable absorber (A-FPSA). The mode-locked spectrum spreads over most of the available Nd:glass fluorescence bandwidth. At increased pulse energy fluence or decreased negative group-velocity dispersion, multiple pulsing was observed. We experimentally characterize this behavior, which can be explained by the saturation behavior of the A-FPSA and the limited available gain bandwidth. These considerations are significant for the design of saturable absorbers to achieve stable passive mode locking.     

Femtosecond diode-pumped Nd:glass laser with more than 1 W of average output power

We have demonstrated 175-fs pulses with 1 W and 300-fs pulses with 1.2 W of average output power at a pulse repetition rate of 117 MHz from a Nd:phosphate (Schott LG 760) glass laser pumped by a 1-cm-wide, 20-W diode laser bar. Stable soliton mode locking was achieved by use of an intracavity semiconductor saturable absorber mirror. We obtained more than 2 W of average power without mode locking. Using cylindrical cavity mirrors, we adapted the laser mode inside the Nd:glass to the highly elliptical pump beam in both dimensions (tangential and sagittal axes) while maintaining a nearly ideal circular TEM(00) output beam with M(2) approximately 1.2 . Overpumping the laser mode in the tangential plane and efficient unidirectional heat removal in the sagittal plane using a 0.8-mm thin Nd:glass also contributed to the good output-beam quality.     

High performance deep red AlAs/AlGaAs top-emitting VCSELs grown by MOVPE at high growth rates

Top-emitting Alas/AlGaAs vertical cavity surface emitting lasers emitting at 765 nm with minimum threshold currents of 0.6 mA and threshold voltages of 1.9 V have been grown by MOVPE. In order to keep the growth time low, we investigated the possibility to grow these structures at growth rates of 5 μm/h. Special attention was paid to the homogeneity that can be achieved over a 2″ wafer under these growth conditions. Spatially resolved reflectivity measurements on GaAs/AlAs distributed Bragg reflectors showed, that the growth rate varies less than 0.3% in the center of the wafer and decreases by 1% at the wafer edge.     

Methyl 4-((E)-2-{3-[(3-{ (E)-2-[4-(methoxycarbonyl)phenyl]- 1-diazenyl}-5,5-dimethylhexahydro-1-pyrimidinyl)methyl]-5,5-dimethylhexahydro-1-pyrimidinyl-1-diazenyl) benzoate. X-ray crystal structure

Methyl 4-((E)-2-{3-[(3-{(E)-2-[4-(methoxycarbonyl)phenyl]-1-diazenyl}-5, 5-dimethyl hexahydro-1-pyrimidinyl)methyl]-5, 5- dimethylhexahydro-1- pyrimidinyl}-1- diazenyl) benzoate (1) has been synthesized by reaction of a mixture of formaldehyde and 2,2-dimethyl-1,3-propanediamine with p-methoxycarbonylbenzenediazonium chloride. The crystal structure of 1 has been determined by single crystal X-ray diffraction analysis. The crystals of 1 displayed problems of disorder; the asymmetric unit is built up by two independent molecules, which display disorder within a methoxycarbonyl group. The two independent molecules in the asymmetric unit are very similar, differing only slightly about the mutual orientation of the aryltriazenyl groups. With respect to the N–C–N bridge between the hexahydropyrimidinyl rings, the two equivalent fragments containing the triazene moieties are in a cis orientation. The N–N single bonds, in the range 1.319(4)–1.348(4) Å, and the N=N double bonds, in the range 1.255(5)–1.275(4) Å, indicate significant conjugations within the triazene moieties. All the hexahydropyrimidine six-membered rings adopt a chair conformation as shown by their puckering parameters. The crystal packing is determined only by simple van der Waals interactions. The crystal structure of 1 is compared with the previously reported structure of the unbranched hexahydropyrimidine analogue 2. Crystal data: 1 C29H40N8O4, triclinic, space group P-1, a = 13.9652(2), b = 14.2908(3), c = 16.6129(4) Å, = 97.279(1), = 90.872(1), = 107.385(1), V = 3133.6(1) ų, for Z = 4.     

Homogeneous line width in a zinc borate glass activated by Eu

In this work we report on the temperature depedence of the homogeneous line width (Γ_h) in 4ZnO · 3B₂O₃:Eu³⁺ glass in the region between 30 K and room temperature. The time resolved resonant fluorescence line narrowing technique was applied to the ⁷F₀ ↔ ⁵D₀ transition of Eu³⁺. We obtain that Γ_h follows the commonly found behaviour T² in the whole range of temperature (30–300 K). The Γ_h is comparable to that measured in borate glasses with a small amount of network modifier. This result, together with a linear increase of Γ_h with the excitation energy within the inhomogeneous profile, is indicative of a specific local environment around the Eu³⁺ ion in the zinc borate glass.