Active mode locking of continuous-wave doubly and singly resonant optical parametric oscillators

We report on what we believe to be the first active mode locking of near-degenerate, doubly and singly resonant cw-pumped optical parametric oscillators (OPOs). We show experimentally that a steady-state regime of short pulses is reached in a few tens of microseconds under cw pumping. The oscillation buildup dynamics of both OPOs is also explored, evidencing an unusual transient behavior in the mode-locking process.     

Numerical analysis of space charge effects in electron bunches at laser-driven plasma accelerators

Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.     

Characterization of the surface of positive electrodes for Li-ion batteries using 7Li MAS NMR

The growth and evolution of the interphase, due to contact with the ambient atmosphere or electrolyte, are followed using ⁷Li magic-angle spinning nuclear magnetic resonance (MAS NMR) in the case of two materials amongst the most promising candidates for positive electrodes for lithium batteries: LiFePO₄ and LiMn_0.5Ni_0.5O₂. The use of appropriate experimental conditions to acquire the NMR signal allows observing only the «diamagnetic» lithium species at the surface of the grains of active material. The reaction of LiMn_0.5Ni_0.5O₂ with the ambient atmosphere or LiPF₆ (1 M in Ethylene Carbonated/DiMéthyl Carbonate (EC/DMC)) electrolyte is extremely fast and leads to an important amount of lithium-containing diamagnetic species compared to what can be observed in the case of LiFePO₄. The two studied materials display a completely different surface chemistry in terms of reactivity and/or kinetics of the surface towards electrolyte. Moreover, these results show that MAS NMR is a very promising tool to monitor phenomena taking place at the interface between electrode and electrolyte.     

Complete and orthonormal eigenfunctions of excitations to a one-dimensional dark soliton

We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose-Einstein condensates.     

À propos de l’indice de composition des nombres

 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d'un hyperplan

We present here an example of a plane time-dependent bounded divergence-free vector field and a bounded non-zero solution of the homogeneous Cauchy problem for the associated transport equation. To cite this article: N. Depauw, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Z-scan measurement of the nonlinear refractive index of graphene

Under strong laser illumination, few-layer graphene exhibits both a transmittance increase due to saturable absorption and a nonlinear phase shift. Here, we unambiguously distinguish these two nonlinear optical effects and identify both real and imaginary parts of the complex nonlinear refractive index of graphene. We show that graphene possesses a giant nonlinear refractive index n(2)?10(-7) cm(2) W(-1), almost 9 orders of magnitude larger than bulk dielectrics. We find that the nonlinear refractive index decreases with increasing excitation flux but slower than the absorption. This suggests that graphene may be a very promising nonlinear medium, paving the way for graphene-based nonlinear photonics.     

Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation

The main advantage of two-photon fluorescence confocal microscopy is the low absorption obtained with live tissues at the wavelengths of operation. However, the resolution of two-photon fluorescence confocal microscopes is lower than in the case of one-photon excitation. The 4Pi microscope type C working in two-photon regime, in which the excitation beams are coherently superimposed and, simultaneously, the emitted beams are also coherently added, has shown to be a good solution for increasing the resolution along the optical axis and for reducing the amplitude of the side lobes of the point spread function. However, the resolution in the transverse plane is poorer than in the case of one-photon excitation due to the larger wavelength involved in the two-photon fluorescence process. In this paper we show that a particular arrangement of the 4Pi microscope, referenced as 4Pi′ microscope, is a solution for obtaining a lateral resolution in the two-photon regime similar or even better to that obtained with 4Pi microscopes working in the one-photon excitation regime.