Inner cladding influence on large mode area photonic crystal fiber properties under severe heat load

International audienceThe influence of the size and the air-filling fraction of the inner microstructure on the first HOM confinement in Yb-doped LMA PCFs under different heat load values has been investigated with a full-vector modal solver based on the finite element method, used also to solve the steady-state heat equation. In particular, the air-cladding inner dimension and the air-hole diameter in Symmetry-Free PCFs and Large Pitch Fibers have been modified in order to study which conditions facilitate the coupling between HOM and cladding modes, thus improving the delocalization of the former and making the fiber single-mode behavior more robust

Large mode area aperiodic fiber designs for robust singlemode emission under high thermal load

International audienceIn this paper, we investigate the potential of various large mode area bers under thermal load, that is the state-of-the-art air-silica large pitch bers, as well as the recently devised symmetry-reduced photonic crystal ber and aperiodic all-solid by carefully considering the degrees of freedom oered all along the ber fabrication. This work aims to discuss the mode ltering ability of these structures in regard to the power scaling and to conrm their potential for robust singlemode operation at high power level. Structural principles contributing to improve their performances such as the impact of air holes / solid inclusions size will be presented. We also intend to establish that the range of average absorbed/output power for which a robust singlemode operation is available can be shifted to full user requests in term of power range

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field H_A of F. We prove an Iwasawa Main Conjecture for the (Z_p)^∞-extension mathcal{F}/F generated by the mathfrak{p}-power torsion of Φ (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or mathfrak{p}-adic characters, interpolates the Goss Zeta-function or some mathfrak{p}-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the \mathfrak{p}-power torsion of \Phi (\mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.Comment: to appear in Publicacions Matem\`atique

Analysis of the modal content into large-mode-area photonic crystal fibers under heat load

International audienceThanks to their capability to provide very large mode area together with effective suppression of high-order modes, while allowing strong pump absorption and efficient conversion, Yb-doped double-cladding photonic crystal fibers are one of the key enabling factors for the development of high power fiber lasers. Thermal effects are currently appointed as the main bottleneck for future power scaling since, beyond a certain average power, they allow guidance of high order modes and energy transfer to them, causing a sudden degradation of the beam quality. In this paper the effects of heat load on the modes of double cladding fibers are thoroughly analyzed with a full-vector modal solver based on the finite-element method with integrated steady-state heat equation solver. Fibers with different inner cladding designs are compared to provide a deeper understanding of the mechanisms beyond the mode reconfinement and coupling. The influence of the fiber design on the robustness of the single-mode regime with respect to fiber heating has been demonstrated, providing a clear picture of the complex interaction between modes. On the basis of simulation results it has been possible to group fiber modes into three families characterized by peculiar reaction to heating. Index Terms—Photonic crystal fibers, thermo-optic effect, fiber lasers and amplifiers

STICKELBERGER SERIES AND IWASAWA MAIN CONJECTURE FOR FUNCTION FIELDS

Let F be a global function \ufb01eld in characteristic p>0. There exists many di\ufb00erent types of L-functions that can be associated to F, such as the Artin L-functions, the Goss Zeta function or the p-adic L-functions. In this work i have investigated the correlations between these analytic objects and the Stickelberger series, which is a formal power series whose coe\ufb03cients lie in a suitable Galois algebra. In the second part of this work i have studied the Iwasawa extension generated by the p-torsion of a Hayes module and i have used the Stickelberger series to prove a "main conjecture" for the p-part of the class group

Hybrid Ytterbium-doped large-mode-area photonic crystal fiber amplifier for long wavelengths.

A large-mode-area Ytterbium-doped photonic crystal fiber amplifier with build-in gain shaping is presented. The fiber cladding consists of a hexagonal lattice of air holes, where three rows are replaced with circular high-index inclusions. Seven missing air holes define the large-mode-area core. Light confinement is achieved by combined index and bandgap guiding, which allows for single-mode operation and gain shaping through distributed spectral filtering of amplified spontaneous emission. The fiber properties are ideal for amplification in the long wavelength regime of the Ytterbium gain spectrum above 1100 nm, and red shifting of the maximum gain to 1130 nm is demonstrated