Transient propagation of optical beams in active media

The coherent interaction of short optical pulses with a nonlinear active resonant medium is calculated. The rigorous and self-consistent solution of the coupled nonlinear Maxwell-Bloch equations including transverse and time-dependent phase variations predicts the onset on an on-resonance self-focusing that agrees very well with a previous perturbation treatment and with recent experiments in sodium and neon. The formation of this dynamic self-action effect is elucidated as being due to the combined effects of diffraction and the inertial response of the active media. Accuracy and computational economy are achieved simultaneously by redistributing the computational grid points according to the physical requirements of the problem. Evenly spaced computational grids are related to variable grids in physical space by a range of stretching and rezoning techniques including adaptive rezoning where the coordinate transformation is determined by the actual physical solution. Work supported in part by the Mobil Oil Corporation and the Office of Naval Research.     

Transient acoustic wave propagation in rigid porous media: a time-domain approach

Wave propagation of acoustic waves in porous media is considered. The medium is assumed to have a rigid frame, so that the propagation takes place in the air which fills the material. The Euler equation and the constitutive relation are generalized to take into account the dispersive nature of these media. It is shown that the connection between the fractional calculus and the behavior of materials with memory allows time-domain wave equations, the coefficients of which are no longer frequency dependent, to be worked out. These equations are suited for direct and inverse scattering problems, and lead to the complete determination of the porous medium parameters.     

Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.     

Polymer-based waveguides with low propagation loss and polarization-dependent loss

Polymeric optical waveguides based on a new synthesized bisphenol A–aldehyde polymer (PA-1 resin) have been fabricated using photolithography and reactive ion etching technique. The polymer is novel with relatively high refractive index, low birefringence and absorption at the optical communication wavelengths. The single-mode channel waveguides exhibit a propagation loss of 0.41±0.05 dB/cm at a wavelength of and 0.5±0.05 dB/cm at for both the TE and TM polarizations. The polarization-dependent loss of the waveguides is 0.1±0.05 dB/cm at these wavelengths.     

Beam propagation factor of partially coherent beams in gain or absorbing media

The definition of second-order intensity moments in the spatial domain and spatial frequency domain has been generalized for the case that the linear gain or absorbing media are included, where the wave number is generally complex. The formula for beam propagation M²-factor of partially coherent beams in linear gain or absorbing media has been given. The partially coherent flat-topped Schell-model beam is taken as an example. The closed-form expression for the beam propagation M²-factor of partially coherent flat-topped beam in gain or absorbing media has been derived. The changes of the M²-factor in media have been discussed with numerical examples. It can be shown that the M²-factor of flat-topped Schell-model beams in gain or absorbing media depends on the coherent parameter β, the coherent length σ₀, the beam order M, the propagation distance B, the imaginary part of the wave number K_i, as well as the real part of the wave number K_r.     

Transient chaos in quantum and classical mechanics

Bogolubov's classical example of statistical relaxation in a many-dimensional linear oscillator is discussed. The relation of the discovered relaxation mechanism to quantum dynamics as well as to some new problems in classical mechanics is considered.     

Wave propagation in distributed media

The problem of chemical reaction-diffusion wave propagation through a random, heterogeneous medium is considered using a model based on cubic autocatalysis with decay. The autocatalyst is taken to diffuse and react through a reactant loaded at constant initial concentration in a reaction domain except that there may be gaps of arbitrary width in which the reactant concentration is zero. We first study the propagation of a permanent-form wave across a single gap and determine the critical width of the gap in terms of the kinetic parameters in the system. The numerical results are compared with an analytical estimate. Next, the critical conditions for propagation across two gaps separated by a domain are determined numerically, and this is extended to a series of three gaps. From these results, a series of "rules" is established to allow us to predict whether a wave will pass through an arbitrary random array of gaps of a given size subject to some imposed total void fraction for the material. (c) 2001 American Institute of Physics.     

Neutrino propagation in magnetized media

After a short presentation of the general techniques used to determine neutrino potentials in a magnetized medium I will discuss some applications to MSW resonant oscillations. I will also consider the relevance of our results for the pulsar velocity problem.     

Coherent acoustic wave propagation in media with pair-correlated spheres

Propagation of plane compressional waves in a non-viscous fluid with a dense distribution of identical spherical scatterers is investigated. The analysis is based on the multiple scattering approach proposed by Fikioris and Waterman, and is generalized to include arbitrary choice of the pair-correlation functions used to represent the distribution of the scatterers. A closed form solution for the effective wavenumber as a function of the concentration of pair-correlated finite-size spheres is derived up to the second order. In the limit of uncorrelated point-scatterers, this solution is identical to that obtained by Lloyd and Berry. Different pair-correlation functions are exemplified and compared, and the resulting differences discussed.     

Velocity of pulse propagation in media with amplitude nonlinearity

The propagation velocity of optical wave fronts can be accelerated by the influence of gain saturation. We report systematic measurements for the specific case of Brillouin gain in optical fibers. A simplified analytic rate equation approach permits a qualitative understanding of the observations in terms of a pure amplitude nonlinearity. We point out that there is a close analogy to a mode-locked laser with gain saturation. Pursuing this analogy, we can explain why the changes in propagation velocity are hardly measurable for synchronously pumped lasers, but easily amount to several percent for amplifiers or lasers based on stimulated Brillouin scattering.     

On propagation in continuous random media

Abstract

The analysis of wave propagation in continuous random media typically proceeds from the parabolic wave equation with back scatter neglected. A closed hierarchy of moment equations can be obtained by using the Novikov–Furutsu theorem. When the same procedure is applied in the spatial Fourier domain, one obtains a closed hierarchy of coupled moment equations for the forward- and back-scattered wavefields that is not restricted to narrow scattering angles nor to small local perturbations. The general equations are difficult to solve, but a Markov-like approximation is suggested by the form of the scattering terms. Simple algebraic solutions can be obtained if a narrow-angle-scatter approximation is then invoked. Thus, three distinct approximations are explicit in this analysis, namely closure, Markov and narrow-angle scatter.

The results show that the extinction of the coherent wavefield has a distinctly different form from the corresponding result for propagation in a sparse distribution of discrete scatteres. Furthermore, when the scatter is constrained to narrow forwardand back-scattered cones, there is no back-scatter enhancement. These results are discussed within the context of the extension of the spectral-domain formalism to discrete random media. The general continuous-media moment equations are developed but not solved. The results correct and extend an earlier analysis that used a perturbation approach to compute the scattering functions rather than the Novikov–Furutsu theorem.     

Microwave propagation in dense random media

Summary Using simple, approximate arguments, we obtain a formula that relates the average spacing between peaks in the transmitted intensityvs. wave frequency distribution of a single configuration of a random distribution of scatterers to the diffusion constant, sample thickness, and effective absorption length. The value of the diffusion constant obtained this way is found to be within 20% of the value obtained via intensity-intensity autocorrelation function techniques. The author of this paper has agreed to not receive the proofs for correction.     

Light propagation in twisted dielectric media

A periodically stratified medium is investigated. Especially, we use a dielectric tensor, which describes an optically uniaxial crystal, whose axis lies obliquely in space and rotates about thez-axis as function ofz. The interpretation of the results differs considerably from that for another often treated kind of anisotropy.