Modulational instability in a layered Kerr medium: theory and experiment

We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of alternating glass-air layers, is the piecewise-constant nature of the material properties, which allows a theoretical linear stability analysis leading to a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between theoretical, numerical, and experimental diagnostics of the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, there are multiple instability regions rather than just one as in a uniform medium.     

Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization

We demonstrate low-threshold lasing in random amplifying layered medium via photon localization. Lasing is facilitated by resonant excitation of localized modes at the pump laser wavelength, which are peaked deep within the sample with greatly enhanced intensity. Emission occurs into long-lived localized modes overlapping the localized gain region. This mechanism overcomes a fundamental barrier to reducing lasing thresholds in diffusive random lasers, in which multiple scattering restricts the excitation region to the proximity of the sample surface.     

Approximation of the parabolic equation and the wavefield of a point source in a layered random medium

This paper studies the wavefield of a source in a multidimensional randomly layered medium. They obtained asymptotical expressions of the wave statistical characteristics for different boundary conditions both in the framework of the parabolic equation approximation and the exact formulation of the boundary problem for the Helmholtz equation. It is shown that the presence of a small but finite absorption γ is most important for the statistics. The diffraction effects turn out to be like those of absorption, but γ cannot tend to zero in this problem. In an appendix they give the factorization formulae of the wave equation solution in a layered medium.     

Approximation of the parabolic equation and the wavefield of a point source in a layered random medium

Abstract

This paper studies the wavefield of a source in a multidimensional randomly layered medium. They obtained asymptotical expressions of the wave statistical characteristics for different boundary conditions both in the framework of the parabolic equation approximation and the exact formulation of the boundary problem for the Helmholtz equation. It is shown that the presence of a small but finite absorption γ is most important for the statistics. The diffraction effects turn out to be like those of absorption, but γ cannot tend to zero in this problem. In an appendix they give the factorization formulae of the wave equation solution in a layered medium.     

Ray theory and random mode coupling in an optical fibre waveguide. I

Ray theory is used here to analyse the effect of random distortion of an optical fibre waveguide on the propagation of electromagnetic waves. In this first part, the case of step index guide is looked at in depth and agreement is found between this method and Marcuse and Gloge's theories of mode coupling. A fairly rigorous approach will be developed in this first paper in order to assess the possibility of the method. Part II will be devoted, in a more speculative fashion, to the study of random coupling in general graded fibres.     

Ray theory and random mode coupling in an optical fibre waveguide. II

Ray theory has been proved to work in Part I and is now applied to general graded fibres. A new approach to the time problem is described and a hidden effect of random distortion is analysed. It is concluded that the bandwidth of very well graded fibres may not be improved by random mode coupling.     

Method for calculating the monochromatic field in a layered medium

An approximate method is proposed for calculating the monochromatic field described by the wave equation in a layered medium. The method is based on the use of the equivalent propagation constant and makes it possible to reduce the computation time as compared to other methods based on the strictly dynamic approach. The range of correct application of the method is estimated for the problems for which the exact solution is known.     

High-Q oscillations in a layered elastic medium

Conditions of the existence of long-lived acoustic resonances that occur in a layered medium because of its oscillation with low damping factors are considered. A priori theoretical estimates relating the distribution of resonance frequencies in the complex plane to the parameters of inhomogeneity of the layered system are obtained. A scheme of resonance calculations in numerical modeling is described. Examples of geophysical media with long-lived resonances are presented.     

Ray theory of microbending

A ray theory is given for randomly bent (two-dimensional) optical fibers that have arbitrary index profiles and arbitrary curvature spectra. Simple closed form results are given for power-law profiles and spectra. No approximation is made besides the small bending approximation and the paraxial ray optics approximation. In particular, the coupling between all modes is effectively taken into account.     

Hydrodynamics in a symmetric random medium

We investigate the hydrodynamic behaviour of a one-dimensional Ginzburg-Landau model with conservation law in the presence of random conductivities. It is found that there is no interference between nonlinearity and randomness; the conductivities average out in the same way as they do in the case of the underlying random walk in the given medium. This means that we have an effective conductivity specified as the harmonic mean of microscopic conductivities. Some extensions including multidimensional systems in a small electric field are also discussed.Dedicated to Roland DobrushinSupported in part by: Hungarian National Foundation for Scientific Research Grant No. 1815, National Science Foundation Grant DMR 8612369     

Heat conduction in a random medium

The method of time-ordered cumulants is used to investigate the behavior of heat pulses in a one-dimensional medium in which the thermal conductivity is random. A partial differential equation is obtained for the average temperature profile; it is the heat equation modified by the addition of a fourth-order spatial derivative. A solution is obtained by asymptotic series. The first two spatial moments of the average temperature profile are evaluated and are shown to tend to those of a Gaussian whent is large. Finally, an equation is obtained for the covariance function.Alfred P. Sloan Fellow.