Linear Amplifier Breakdown and Concentration Properties of a Gaussian Field Given that its L2\bm{L^2}-Norm is Large

In the context of linear amplification for systems driven by the square of a Gaussian noise, we investigate the realizations of a Gaussian field in the limit where its $L^2$-norm is large. Concentration onto the eigenspace associated with the largest eigenvalue of the covariance of the field is proved. When the covariance is trace class, the concentration is in probability for the $L^2$-norm. A stronger concentration, in mean for the sup-norm, is proved for a smaller class of Gaussian fields, and an example of a field belonging to that class is given. A possible connection with Bose-Einstein condensation is briefly discussed.Comment: REVTeX file, 11 pages, 1 added paragraph in the introduction, 2 added references, minor modifications in the text and abstract, submitted to J. Stat. Phy

Approach to equilibrium for the stochastic NLS

We study the approach to equilibrium, described by a Gibbs measure, for a system on a $d$-dimensional torus evolving according to a stochastic nonlinear Schr\"odinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is {\it uniform} in the frequency truncation $N$. The limit $N\to\infty$ is discussed.Comment: 15 p

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation $\partial_t{\cal E} - {\cal D}\Delta {\cal E} = \lambda S^2{\cal E}$, where $S(x,t)$ is a Gaussian stochastic field with covariance $C(x-x',t,t')$, and $x\in {\mathbb R}^d$. It is shown that the coupling $\lambda_{cN}(t)$ at which the $N$-th moment diverges at time $t$, is always less or equal for ${\cal D}>0$ than for ${\cal D}=0$. Equality holds under some reasonable assumptions on $C$ and, in this case, $\lambda_{cN}(t)=N\lambda_c(t)$ where $\lambda_c(t)$ is the value of $\lambda$ at which diverges. The ${\cal D}=0$ case is solved for a class of $S$. The dependence of $\lambda_{cN}(t)$ on $d$ is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, ${\cal D}\to i{\cal D}$, the case of interest for backscattering instabilities in laser-plasma interaction.Comment: 19 pages, in LaTeX, e-mail addresses: [email protected], [email protected], [email protected], [email protected]

Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling

We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement

Effect of the speckle self-focusing on the stationary SBS reflectivity from a randomized laser beam in an inhomogeneous plasma

The effect of laser light self-focusing (SF) in speckles on stimulated Brillouin scattering (SBS) in an inhomogeneous plasma is studied. It is found that below but near critical power SF dramatically enhances the SBS reflectivity from an individual speckle, while above the critical power the pump power depletion due to SBS prevents strong SF and limits the maximum laser intensity in a speckle. The parameters that control the SBS/SF interplay are the ratio of plasma inhomogeneity scale length to the speckle length and the product of the plasma density and the speckle cross-section. The consequences of the SF effect on the averaged SBS reflectivity of the randomized laser beam are revealed and their manifestations in recent SBS experiments with preformed plasmas are discussed. Physics of Plasmas 4(12) (1997) PACS numbers: 52.40.Nk, 52.35.Mw, 52.35.Nx, 42.65.Jx Typeset using REVT E X I. INTRODUCTION A lot of experimental and theoretical work has been devoted to the study of parametric..

SBS reflectivity from spatially smoothed laser beams: random phase plates versus polarization smoothing

The reflectivity due to stimulated Brillouin backscattering (SBS) from an ensemble of independent laser speckles is investigated for different speckle statistics. Calculations are based on numerical simulations with a multidimensional code and a compact model describing the main features of speckle self-focusing. In particular, the simulations and the model are applied to speckle ensembles due to the random phase plate (RPP) and polarization smoothing (PS) techniques. A stronger SBS inhibition for PS with respect to the RPP technique is demonstrated. PACS numbers: 52.40Nk, 52.35.Mw, 52.35.Nx I. INTRODUCTION The development of laser beam smoothing techniques is currently an important element of laser fusion research. Most smoothing techniques translate the spatial intensity distribution of generic laser beams into an intensity distribution consisting of a stochastic ensemble of small-scale "speckles" or "hot spots". 1--4 Although such techniques remove large-scale intensity fluctuat..

Extra ion feature of Thomson scattered light in the interaction of a 600 ps laser with helium gas jet

International audienceThe interaction of a 600 ps laser pulse at 0.53 μm wavelength with helium gas jet with an electron density of 8×10^19 cm^−3 has been studied. In this experiment the plasma parameters for density and temperature were well-defined via time-resolved Thomson scattering. Ion Thomson scattering measurements at 45° show two extra satellites which correspond to the rescattering of the Brillouin backscattered light off the thermal ion acoustic waves. Analysis of the relative amplitudes of these satellites gives a very high value of 65% of the instantaneous reflectivity at its maximum. Theoretical spectra are in good agreement with the experimental ones