Fundamental groups of toroidal compactifications

We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D/\Gamma$, without assuming either that $\Gamma$is neat or that it is arithmetic. We also give bounds for the first Betti number.Comment: Final version. Fixes error pointed out by M. Roessler, leading to slightly but significantly changed statements: improved notatio

On negative higher-order Kerr effect and filamentation

As a contribution to the ongoing controversy about the role of higher-order Kerr effect (HOKE) in laser filamentation, we first provide thorough details about the protocol that has been employed to infer the HOKE indices from the experiment. Next, we discuss potential sources of artifact in the experimental measurements of these terms and show that neither the value of the observed birefringence, nor its inversion, nor the intensity at which it is observed, appear to be flawed. Furthermore, we argue that, independently on our values, the principle of including HOKE is straightforward. Due to the different temporal and spectral dynamics, the respective efficiency of defocusing by the plasma and by the HOKE is expected to depend substantially on both incident wavelength and pulse duration. The discussion should therefore focus on defining the conditions where each filamentation regime dominates.Comment: 22 pages, 11 figures. Submitted to Laser physics as proceedings of the Laser Physics 2010 conferenc

Reconciling different formulations of viscous water waves and their mass conservation

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge choice for the velocity vector is made that cancels the rotational contribution in the kinematic boundary condition, at the cost of rotational velocity in the bulk and a rotational pressure. The third set circumvents the problem by introducing two domains: the irrotational bulk and the vortical boundary layer. This comparison puts forward the link between rotational pressure on the surface and vorticity in the boundary layer, addresses the existence of nonlinear vorticity terms, and shows where approximations have been used in the models. Furthermore, we examine the conservation of mass for the three systems, and how this can be compared to the irrotational case.Comment: 32 pages, 5 figure

Stabilization of uni-directional water wave trains over an uneven bottom

We study the evolution of nonlinear surface gravity water wave packets developing from modulational instability over an uneven bottom. A nonlinear Schrödinger equation (NLSE) with coefficients varying in space along propagation is used as a reference model. Based on a low-dimensional approximation obtained by considering only three complex harmonic modes, we discuss how to stabilize a one-dimensional pattern in the form of train of large peaks sitting on a background and propagating over a significant distance. Our approach is based on a gradual depth variation, while its conceptual framework is the theory of autoresonance in nonlinear systems and leads to a quasi-frozen state. Three main stages are identified: amplification from small sideband amplitudes, separatrix crossing and adiabatic conversion to orbits oscillating around an elliptic fixed point. Analytical estimates on the three stages are obtained from the low-dimensional approximation and validated by NLSE simulations. Our result will contribute to understand the dynamical stabilization of nonlinear wave packets and the persistence of large undulatory events in hydrodynamics and other nonlinear dispersive media

Light Filaments Without Self Guiding

An examination of the propagation of intense 200 fs pulses in water reveals light filaments not sustained by the balance between Kerr-induced self-focusing and plasma-induced defocusing. Their appearance is interpreted as the consequence of a spontaneous reshaping of the wave packet form a gaussian into a conical wave, driven by the requirement of maximum localization, minimum losses and stationarity in the presence of non-linear absorption.Comment: Submitted to Phys. Rev. Lett. on July 7th, 200

Spectral up- and downshifting of Akhmediev breathers under wind forcing

We experimentally and numerically investigate the effect of wind forcing on the spectral dynamics of Akhmediev breathers, a wave-type known to model the modulation instability. We develop the wind model to the same order in steepness as the higher order modifcation of the nonlinear Schroedinger equation, also referred to as the Dysthe equation. This results in an asymmetric wind term in the higher order, in addition to the leading order wind forcing term. The derived model is in good agreement with laboratory experiments within the range of the facility's length. We show that the leading order forcing term amplifies all frequencies equally and therefore induces only a broadening of the spectrum while the asymmetric higher order term in the model enhances higher frequencies more than lower ones. Thus, the latter term induces a permanent upshift of the spectral mean. On the other hand, in contrast to the direct effect of wind forcing, wind can indirectly lead to frequency downshifts, due to dissipative effects such as wave breaking, or through amplification of the intrinsic spectral asymmetry of the Dysthe equation. Furthermore, the definitions of the up- and downshift in terms of peak- and mean frequencies, that are critical to relate our work to previous results, are highlighted and discussed.Comment: 30 pages, 11 figure

High-brightness switchable multi-wavelength remote laser in air

Remote laser in air based on amplified spontaneous emission (ASE) has produced rather well-collimated coherent beams in both backward and forward propagation directions, opening up possibilities for new remote sensing approaches. The remote ASE-based lasers were shown to enable operation either at ~391 and 337 nm using molecular nitrogen or at ~845 nm using molecular oxygen as gain medium, depending on the employed pump lasers. To date, a multi-wavelength laser in air that allows for dynamically switching the operating wavelength has not yet been achieved, although this type of laser is certainly of high importance for detecting multiple hazard gases. In this Letter, we demonstrate, for the first time to our knowledge, a harmonic-seeded switchable multi-wavelength laser in air driven by intense mid-infrared femtosecond laser pulses. Furthermore, population inversion in the multi-wavelength remote laser occurs at an ultrafast time-scale (i.e., less than ~200 fs) owing to direct formation of excited molecular nitrogen ions by strong-field ionization of inner-valence electrons, which is fundamentally different from the previously reported pumping mechanisms based either on electron recombination of ionized molecular nitrogen or on resonant two-photon excitation of atomic oxygen fragments resulting from resonant two-photon dissociation of molecular oxygen. The bright multi-wavelength laser in air opens the perspective for remote detection of multiple pollutants based on nonlinear spectroscopy.Comment: 18 pages, 5 figure

Mobile source of high-energy single-cycle terahertz pulses

The Teramobile laser facility was used to realize the first mobile source of high-power THz pulses. The source is based on a tilted-pulse-front pumping THz generation scheme optimized for application of terawatt laser pulses. Generation of 50-μJ single-cycle electromagnetic pulses centered at 0.19 THz with a repetition rate of 10Hz was obtained for incoming 700-fs 120-mJ near-infrared laser pulses. The corresponding laser-to-THz photon conversion efficiency is approximately 100