Generalized Miller Formulae

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.Comment: 12 pages, 1 figure (4 panels

Spectral dependence of purely-Kerr driven filamentation in air and argon

Based on numerical simulations, we show that higher-order nonlinear indices (up to $n_8$ and $n_{10}$, respectively) of air and argon have a dominant contribution to both focusing and defocusing in the self-guiding of ultrashort laser pulses over most of the spectrum. Plasma generation and filamentation are therefore decoupled. As a consequence, ultraviolet wavelength may not be the optimal wavelengths for applications requiring to maximize ionization.Comment: 14 pages, 4 figures (14 panels

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

A parametric study

Based on both static (extended Köhler) and dynamic modelling, we investigate the influence of temperature,humidity, HNO3 initial concentration, as well as of the particle concentration, on the efficiency of HNO3-mediated laser- induced condensation. This mechanism is most efficient for low temperatures, high HNO3 concentration, and relative humidities. It is, however, still active up to 30 °C, down to 70% relative humidity, and below the ppm level of HNO3. Furthermore, lower particle concentration minimizing the depletion of both HNO3 and water vapor is more favourable to particle growth

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

Higher-order Kerr terms allow ionization-free filamentation in gases

We show that higher-order nonlinear indices ($n_4$, $n_6$, $n_8$, $n_{10}$) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and Argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows to reproduce experimentally observed intensities and plasma densities in self-guided filaments.Comment: 11 pages, 6 figures (11 panels

a step towards modulating precipitation?

We review the recent results about laser-induced condensation based on self- guided filaments generated by ultrashort laser pulses. After recalling the physico-chemistry of cloud particle formation in the atmosphere and the physics of laser filamentation, we discuss experimental results on laser- induced condensation and its relevance for modulating precipitation

Curved plasma channels: Kerr lens and Airy prism

We analytically calculate the transverse energy fluxes induced in high-power Airy beams by the Kerr self-focusing and the Airy profile itself, respectively. In experimental condition representative of laser filamentation experiments of high-power, ultrashort laser pulses in air and condensed media, the Kerr lens induces transverse energy fluxes much larger than the Airy "prism" at the main peak. As a consequence, the curved plasma channels in Airy beams are not only a plasma spark on a curved focus, but indeed self-guided filaments, and their curved trajectory appears as a perturbation due to the linear Airy propagation regime

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