Search results for " Integra"
showing 10 items of 2527 documents
PARAMETER ESTIMATION FOR FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES: NON-ERGODIC CASE
2011
We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.
Integrable Systems and Factorization Problems
2002
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is…
From finite-gap solutions of KdV in terms of theta functions to solitons and positons
2010
We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.
Near-field spectroscopy of low-loss waveguide integrated microcavities
2006
International audience; A scanning near-field spectroscopy method is used to observe loss reduction and Q-factor enhancement due to transverse-mode profile matching within photonic-crystal microcavities. Near-field measurements performed directly on cavity modes are compared with three-dimensional calculations and quantitative agreement is observed. (c) 2006 American Institute of Physics.
Titanium dioxide waveguides for supercontinuum generation and optical transmissions in the near-and mid-infrared
2019
International audience; We report the development of titanium dioxide-based waveguides for applications in the near-and mid-infrared. Thanks to embedded metal grating couplers, we demonstrate error free 10 Gbit/s optical transmissions at 1.55 and 2 µm. With additional management of the dispersion profile, we also demonstrate octave spanning supercontinuum in cm-long TiO2 waveguides.
Interface engineering for improved light transmittance through photonic crystal flat lenses
2010
In this paper, we present photonic crystal flat lenses with interfaces engineered to improve the light transmittance thanks to a broad angles impedance matching. The interface engineering consists in the realization of antireflection gratings on the edges of the lenses which are designed to reduce the propagative waves reflectivity over a wide range of incident angles. The fabricated structures were measured in optical near-field and a four times enhancement of the light transmission efficiency is reported.
Dielectric-loaded plasmonic waveguide-ring resonators
2009
International audience; Using near-field microscopy, the performance of dielectric-loaded plasmonic waveguide-ring resonators (WRRs) operating at telecom wavelengths is investigated for various waveguide-ring separations. It is demonstrated that compact ( footprint similar to 150 mu m(2)) and efficient ( extinction ratio similar to 13 dB) WRR-based filters can be realized using UV-lithography. The WRR wavelength responses measured and calculated using the effective-index method are found in good agreement. (c) 2009 Optical Society of America
Bloch mode coupling investigation in silicon-on-insulator W1 photonic crystal waveguide
2004
We report in this paper the study of a W1 photonic crystal waveguide which supports two Bloch modes having different parity. A monomode ridge waveguide etched in a Silicon-On-Insulator substrate and connecting to the photonic crystal waveguide allows us to excite the even Bloch mode. Transmission measurements, performed on a broad spectral range, evidence the even mode propagation along the defect line and experimental spectrum is discussed in light of band diagram and FDTD calculations. Then spectrally resolved near-field patterns obtained by using a scanning near field optical microscope in collection mode for wavelengths inside and outside the multimode region of the photonic crystal wav…
Exploring titanium dioxide as a new photonic platform
2019
International audience; We report the development of titanium dioxide-based waveguides for applications in the near-and mid-infrared. Thanks to embedded metal grating couplers, we demonstrate error free 10 Gbit/s optical transmissions at 1.55 and 2 µm. We also demonstrate octave-spanning supercontinuum in cm-long waveguides. We explore the way to improve such waveguides through optimized fabrication process.
Emergence of rogue waves from optical turbulence
2011
International audience; We provide some general physical insights into the emergence of rogue wave events from optical turbulence by analyzing the long term evolution of the field. Depending on the amount of incoherence in the system (i.e., Hamiltonian), we identify three turbulent regimes that lead to the emergence of specific rogue wave events: (i) persistent and coherent rogue quasi-solitons, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light or intense flashes.