Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier

We report generation of the second, third, fourth, and fifth harmonics of the output of a Yb-doped fiber amplifier seeded by a passively Q-switched Nd:YAG microchip laser. We obtained high conversion efficiencies using a simple optical arrangement and critically phase-matched nonlinear crystals. Starting with 320 mW of average power at 1064 nm (86 μJ per pulse at a 3.7 kHz repetition rate), we generated 160 mW at 532 nm, 38 mW at 355 nm, 69 mW at 266 nm, and 18 mW at 213 nm. The experimental results are in excellent agreement with calculations.     

The Thermodynamic Limit in Mean Field Spin Glass Models

 We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N ₁ and N ₂ sites, respectively, with N ₁ +N ₂ =N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site. Received: 19 April 2002 / Accepted: 22 April 2002 Published online: 6 August 2002     

Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier

We report a multimode, double-clad, Yb-doped fiber amplifier that produces diffraction-limited, 0.8-ns pulses with energies of 255 muJ and peak powers in excess of 300 kW at a repetition rate of ~8 kHz . Single-transverse-mode operation was obtained by bend-loss-induced mode filtering of the gain fiber.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.     

Braiding structures on formal Poisson groups and classical solutions of the QYBE

If is a quasitriangular Lie bialgebra, the formal Poisson group can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G=SL₂) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.     

Trace Functionals for a Class of Pseudo-Differential Operators in R n

In this paper we define trace functionals on the algebra of pseudo-differential operators with cone-shaped exits to infinity. Furthermore, we improve the Weyl formula on the asymptotic distribution of eigenvalues and make use of it in order to establish inclusion relations between the interpolation normed ideals of compact operators in L ²(R ⁿ ) and the above operator classes.     

On the one loop equivalence of dual σ models

It is shown that in the one loop order of perturbation theory the coupling constant and parameter(s) of an (Abelian T) dual sigma model get renormalized in the same way as in the ‘original’ model.     

Precision and sensitivity optimization of quantitative measurements in solid state NMR

This work presents a methodology for optimizing the precision, accuracy and sensitivity of quantitative solid state NMR measurements based on the external reference method. It is shown that the sample must be exclusively located within and completely span the coil region where the NMR response is directly proportional to the sample amount. We describe two methods to determine this "quantitative" coil volume, based on whether the probe is equipped or not with a gradient coil. In addition, to improve the sensitivity and the accuracy, an optimum rotor packing design is described, which allows the sample volume of the rotor to be matched to the quantitative coil volume. Experiments conducted on adamantane and NaCl, which are representative of a soft and hard material, respectively, show that one order of magnitude increase in experimental precision can be achieved with this methodology. Interestingly, the precision can be further improved by using the ERETIC method in order to compensate for most instrumental instabilities.     

Poisson Geometrical Symmetries Associated to Non-Commutative Formal Diffeomorphisms

Let be the group of all formal power series starting with x with coefficients in a field of zero characteristic (with the composition product), and let F [ ] be its function algebra. In [BF] a non-commutative, non-cocommutative graded Hopf algebra was introduced via a direct process of disabelianisation of F [ ], taking the like presentation of the latter as an algebra but dropping the commutativity constraint. In this paper we apply a general method to provide four one-parameter deformations of , which are quantum groups whose semiclassical limits are Poisson geometrical symmetries such as Poisson groups or Lie bialgebras, namely two quantum function algebras and two quantum universal enveloping algebras. In particular the two Poisson groups are extensions of , isomorphic as proalgebraic Poisson varieties but not as proalgebraic groups.Acknowledgements. The author thanks Alessandra Frabetti and Loic Foissy for many helpful discussions.     

Solid-state NMR as an analytical tool: quantitative aspects

Analytical methods based on solid-state NMR are becoming increasingly popular. However, these flourishing activities bring up the issue of how accurately NMR can assess an analyte proportion in a solid sample. The use of a chemical intensity reference for this purpose is a natural but often unsuitable choice, due to sample stability or preciousness. We propose here a protocol to perform quantitative measurements in solid-state NMR, by calibration of the circuit response through a low-power pulse injected during the acquisition (the so-called ERETIC method). Although this method has been in use for some time in liquid-phase and in vivo NMR, we point out here some peculiarities and useful applications typical of solids. Namely, the temperature dependence of the signal intensity imposes care in the application to MAS experiments.