IR Bismuth active centers in optical fibers: Combined excitation-emission spectroscopy

3D excitation-emission luminescence spectra of Bi-doped optical fibers of various compositions were measured in a wide wavelength range 450-1700 nm. Such luminescence spectra were obtained for Bi-doped pure silica and germania fibers, and for Bi-doped Al- or P-codoped silica fibers (at room and liquid nitrogen temperatures). The energy level schemes of IR bismuth active centers in pure silica and germania core fibers were derived from spectra obtained. The energy level schemes similarity of bismuth active centers in these two types of fibers was revealed.Comment: 12pages, 7 figures, 5 table

A CLT for Plancherel representations of the infinite-dimensional unitary group

We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.Comment: 12 page

Determinantal point processes associated with Hilbert spaces of holomorphic functions

International audienceWe study determinantal point processes on C induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc D induced by the reproducing kernels of generalized Bergman spaces. In the first case, we show that all reduced Palm measures of the same order are equivalent. The Radon-Nikodym derivatives are computed explicitly using regularized multiplicative functionals. We also show that these determinantal point processes are rigid in the sense of Ghosh and Peres, hence reduced Palm measures of different orders are singular. In the second case, we show that all reduced Palm measures, of all orders, are equivalent. The Radon-Nikodym derivatives are computed using regularized multiplicative function-als associated with certain Blaschke products. The quasi-invariance of these deter-minantal point processes under the group of diffeomorphisms with compact supports follows as a corollary

The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\partial f/\partial w, \partial f/\partial z)$ on ${\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.Comment: 6 page

Logarithmically Slow Expansion of Hot Bubbles in Gases

We report logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem first solved, when the temperature has compact support. Then temperature profile decaying exponentially at large distances is considered. The periphery of the bubble is shown to remain essentially static ("glassy") in the process of cooling until it is taken over by a logarithmically slowly expanding "core". An analytical solution to the problem is obtained by matched asymptotic expansion. This problem gives an example of how logarithmic corrections enter dynamic scaling.Comment: 4 pages, 1 figur

The Design Optimization and Experimental Investigation of the 4.4 μm Raman Laser Basedon Hydrogen-filled Revolver Silica Fiber

Optical properties of hollow-core revolver fibers are numerically investigated depending on various parameters: the hollow-core diameter, the capillary wall thickness, the values of the minimum gap between the capillaries, the number of capillaries in the cladding and the type of glass (silica and chalcogenide). Preliminary, similar calculations are made for simple models of hollow-core fibers. Based on the obtained results, the optimal design of the revolver fiber for Raman laser frequency conversion (1.56 μm → 4.4 μm in 1H2) was determined. As a result, efficient ns-pulsed 4.42 μm Raman laser based on 1H2-filled revolver silica fiber is realized. Quantum efficiency as high as 36 % is achieved and output average power as high as 250 mW is demonstrated

Selfsimilarity and growth in Birkhoff sums for the golden rotation

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.Comment: 14 pages, 8 figure

Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio