Experimental investigation and numerical simulation of the influence of resonator-length detuning on the output power,pulse duration and spectral width of a cw mode-locked picosecond optical parametric oscillator

We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency.     

Chiral stationary phases for LC and SFC obtained by “Polymer coating”

Summary Chirally substituted Si–H-containing polysiloxanes were synthesized, which can be immobilized on small particle silica gel as well as on the smooth surfaces of fused silica capillaries. Immobilization is achieved either by crosslinking or by chemical bonding to the surfaces via silanol groups; both reactions can only be performed by addition of H₂PtCl₆, which acts as catalyst for hydrosilylation and as stoichiometric reagent for crosslinking. Chiral substituents of systematically varied chemical structure were introduced into the polysiloxanes by hydrosilylation. The mechanism of immobilization was investigated by spectroscopic methods, notably²⁹Si-NMR. Homogenous stationary-phase coatings of variable film thickness and corresponding retentivity can easily be achieved. The enantioselectivity of the phase systems was characterized in dependency on the chemical structure of the chiral selectors attached to the polysiloxane chain of the chiral stationary phases and also in terms of the functional groups introduced into the solutes by derivatisation.     

Quantification of Volatile Aldehydes Deriving from In Vitro Lipid Peroxidation in the Breath of Ventilated Patients

Exhaled aliphatic aldehydes were proposed as non-invasive biomarkers to detect increased lipid peroxidation in various diseases. As a prelude to clinical application of the multicapillary column–ion mobility spectrometry for the evaluation of aldehyde exhalation, we, therefore: (1) identified the most abundant volatile aliphatic aldehydes originating from in vitro oxidation of various polyunsaturated fatty acids; (2) evaluated emittance of aldehydes from plastic parts of the breathing circuit; (3) conducted a pilot study for in vivo quantification of exhaled aldehydes in mechanically ventilated patients. Pentanal, hexanal, heptanal, and nonanal were quantifiable in the headspace of oxidizing polyunsaturated fatty acids, with pentanal and hexanal predominating. Plastic parts of the breathing circuit emitted hexanal, octanal, nonanal, and decanal, whereby nonanal and decanal were ubiquitous and pentanal or heptanal not being detected. Only pentanal was quantifiable in breath of mechanically ventilated surgical patients with a mean exhaled concentration of 13 ± 5 ppb. An explorative analysis suggested that pentanal exhalation is associated with mechanical power—a measure for the invasiveness of mechanical ventilation. In conclusion, exhaled pentanal is a promising non-invasive biomarker for lipid peroxidation inducing pathologies, and should be evaluated in future clinical studies, particularly for detection of lung injury.     

On the Integrability of q-Oscillators Based on Invariants of Discrete Fourier Transforms

A discretization of the quantum mechanical phase space is presented in the context of q-noncommutative structures. We give two generalizations of the Heisenberg algebra in the arising lattice phase space. In contrast to ordinary quantum mechanics, there is, a priori, no systematic approach to an integrable oscillator Hamiltonian in lattice quantum mechanics. This is the central obstacle to deal with in this Letter. To do so, we show how in general the integrability of the harmonic oscillator is related to the Fourier transform between momentum and space variables. This will be done in both cases, the continuous and the discrete one. As an application, we finally obtain an integrable lattice Hamiltonian for the harmonic oscillator with generalized Hermite eigenfunctions.     

On Schrödinger-Hermite Operators in Lattice Quantum Mechanics

Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q-discrete Hermite polynomials occur via their recurrence relations. Within this framework we obtain the special case of an interesting result, proved by Christian Berg in a much larger ge-nerality: The orthogonality measure for q-discrete Hermite polynomials of type II is not uniquely determined on q-exponential lattices.     

High-power picosecond LiB3O5 optical parametric oscillators tunable in the blue spectral range

The paper reports on an experimental investigation and numerical analysis of noncritically and critically phasematched LiB₃O₅ (LBO) optical parametric oscillators (OPOs) synchronously pumped by the third harmonic of a cw diode-pumped mode-locked Nd:YVO₄ oscillator–amplifier system. The laser system generates 9.0 W of 355-nm mode-locked radiation with a pulse duration of 7.5 ps and a repetition rate of 84 MHz. The LBO OPO, synchronously pumped by the 355-nm pulses, generates a signal wave tunable in the blue spectral range 457–479 nm. With a power of up to 5.0 W at 462 nm and 1.7 W at 1535 nm the conversion efficiency is 74%. The OPO is characterized experimentally by measuring the output power (and its dependence on the pump power, the transmission of the output coupler and the resonator length) and the pulse properties (such as pulse duration and spectral width). Also the beam quality of the resonant and nonresonant waves is investigated. The measured results are compared with the predictions of a numerical analysis for Gaussian laser and OPO beams. In addition to the blue-signal output visible-red 629-nm radiation is generated by sum-frequency mixing of the 1.535-μm infrared idler wave with the residual 1.064-μm laser radiation. A power of 1.25 W of 1.535-μm idler radiation and 5.7 W of 1.064-μm laser light generated a red 629-nm output power of 2.25 W. Received: 2 February 2000 / Revised version: 28 July 2000 / Published online: 22 November 2000     

All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator

4 (KTA) optical parametric oscillator (OPO) synchronously pumped by a cw diode-pumped mode-locked Nd:YVO₄ oscillator–amplifier system. The laser system (pumped by 84 W of cw 808-nm diode radiation) generates 7-ps-long pulses at 1.064 μm with a repetition rate of 83.4 MHz and an average power of 29 W. The OPO, synchronously pumped by the 1.064-μm laser pulses, consists of a 15-mm-long KTA crystal (cut for type II noncritical phase-matching) in a folded signal resonant linear resonator. The average powers of the 1.54-μm signal radiation and the 3.47-μm idler radiation are 14.6 W and 6.4 W, respectively. The total OPO output of 21 W corresponds to an internal efficiency of 75%. The experimental investigations include measurements of the OPO output power (and its dependence on the pump power, the transmission of the output coupler, and the resonator length) and of the pulse properties (such as pulse duration and spectral width). The measured results are in good agreement with the predictions of a numerical analysis based on a split-step Fourier method. Received: 4 May 1998     

String branchings on complex tori and algebraic representations of generalized Krichever-Novikov algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two-and three-point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b–c systems. The defining cocycle for this central extension deforms to the well-known Virasoro cocycle for certain kinds of degenerations of the torus.     

Method of separation of the variables for basic analogs of equations of mathematical physics

We apply method of separation of the variables to q-analogs of several equations of mathematical physics. Dedicated to Dick Askey on his 70th birthday. 2000 Mathematics Subject Classification Primary—33D45, 42C10; Secondary—33D15.