Anderson localization and propagation of electromagnetic waves through disordered media

We have used the dynamic method to calculate the frequency dependence of the localization length in a disordered medium, using the amplitude change and the redshift of the spectral density of the propagating incident pulse. The frequency dependence of the localization length in an effectively one-dimensional disordered medium is computed in terms of the strength of the disorder. The results obtained with the dynamic method are confirmed by computing the same results using the transfer-matrix method.     

New phenomena in the propagation of optical waves through random media

A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the 'polarization memory effect'), correlations and statistical fluctuations ('microstatistics'). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.     

New phenomena in the propagation of optical waves through random media

Abstract

A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the ‘polarization memory effect’), correlations and statistical fluctuations (‘microstatistics’). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.     

Wave propagation in nonlinear disordered media

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We discuss resonance probabilities, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.     

Instabilities of waves in nonlinear disordered media

We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the nonlinearity exceeds a threshold value. The instability is due to a feedback provided by the multiple scattering and manifests itself in spontaneous fluctuations of the scattered intensity. The development of instability is independent of the sign of nonlinearity.     

Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.     

Localization of matter waves in two-dimensional disordered optical potentials

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.     

The parity function in optical waves propagation

We propose a generalization of the concept of parity as a continuous function and show that it is conserved in optical waves free propagation. Some properties are commented and an experimental implementation to optically generate a representation is suggested.     

Energy propagation for dispersive waves in dissipative media

University of Bologna, Italy. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 7, pp. 650–664, July, 1993.     

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.     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

Spatio-temporal pulse propagation in nonlinear dispersive optical media

We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions. We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.     

光纤放大器中非自治光畸波的传播控制研究

本文采用一个通用的理论,即用相似变换的方法,研究构建了(1+1)维变系数非线性薛定谔方程的精确畸形波解,首先讨论了一阶光畸波在光纤放大器中的传播问题.发现光学畸波的特性,如宽度、振幅和位置,可通过非线性光学介质特性和光脉冲的初始参量进行控制;然后在选择可控参数条件下,讨论了可控光畸波在非线性介质的传播行为,包括延迟激发、抑制、以及保持.这在理论和实际应用上具有启迪价值.     

Coherent pulse propagation through resonant media

Hyperfine Interactions - Resonant pulse propagation (RPP) is reviewed with special emphasis on the propagation of synchrotron radiation (SR) pulses through nuclear single-resonance media. The most...