III Localization of Waves in Media With One-Dimensional Disorder

Publisher Summary This chapter discusses the localization of waves in media with 1D disorder. 1D problems represent exactly solvable problems that enable the researcher to test sometimes uncontrollable approximations. In addition, the study of 1D models is important for understanding the physics of multiple scattering, as in the case of wave propagation in such media the interference effects are most pronounced. The strong localization in 1D systems and its natural applications to the problem of wave propagation in randomly layered media are considered. The chapter reviews the statistical properties of the various physical quantities in random media. The characteristics of the media—that is, the dielectric constant and the random potential, are spatially homogeneous random functions with decreasing correlations. The chapter focuses on 1D localization and also describes the waves in layered media.

[1]  T. Verheggen.  Transmission coefficient and heat conduction of a harmonic chain with random masses: Asymptotic estimates on products of random matrices , 1979 .

[2]  Haim Sompolinsky,et al.  Localization in a disordered elastic medium near two dimensions , 1983 .

[3]  K. Andres,et al.  Sharp Metal-Insulator Transition in a Random Solid , 1980 .

[4]  E. Abrahams,et al.  Resistance fluctuations in disordered one-dimensional conductors , 1980 .

[5]  A. J. O'Connor,et al.  Heat conduction and sound transmission in isotopically disordered harmonic crystals , 1974 .

[6]  T. V. Ramakrishnan,et al.  Disordered electronic systems , 1985 .

[7]  Kirkpatrick,et al.  Localization and resonant transmission of third-sound waves on a random substrate. , 1986, Physical review. B, Condensed matter.

[8]  L. Pastur,et al.  Quantum dynamics of quasiparticles in a stochastic field and nonlinear dissipation of wave packets , 1988 .

[9]  Yanovskaya,et al.  Dark-pulse solitons in nonlinear-optical fibers. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[10]  Etemad,et al.  Weak localization of photons: Universal fluctuations and ensemble averaging. , 1986, Physical review letters.

[11]  Spectral properties of open disordered systems and propagation of waves in random media , 1991 .

[12]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[13]  A theory of sound propagation in disordered one-dimensional metals , 1988 .

[14]  Nevill Mott,et al.  The theory of impurity conduction , 1961 .

[15]  M. Azbel'.  Eigenstates and properties of random systems in one dimension at zero temperature , 1983 .

[16]  F. Dunlop,et al.  Localization of gravity waves on a channel with a random bottom , 1988, Journal of Fluid Mechanics.

[17]  Kirkpatrick,et al.  Resonant scattering and Anderson localization of acoustic waves. , 1987, Physical review. B, Condensed matter.

[18]  Cohen,et al.  Localization of third sound by a disordered substrate. , 1985, Physical review letters.

[19]  R. Landauer.  Electrical resistance of disordered one-dimensional lattices , 1970 .

[20]  Nonlinear resonant interaction between acoustic impulse and electrons in superconductors , 1985 .

[21]  E. Abrahams,et al.  Numerical studies of inverse localisation length in one dimension , 1980 .

[22]  Willemsen,et al.  Transmission of acoustic waves in a random layered medium. , 1985, Physical review. A, General physics.

[23]  T. R. Kirkpatrick,et al.  Localization of acoustic waves. , 1985, Physical review. B, Condensed matter.

[24]  D. Escande,et al.  Localization of waves in a fluctuating plasma , 1984 .

[25]  S. Gredeskul,et al.  Propagation and scattering of nonlinear waves in disordered systems , 1992 .

[26]  A. Sa’ar,et al.  Light Wave Localization in Dielectric Wave Guides , 1988 .

[27]  J. Woodhouse,et al.  Confinement of vibration by structural irregularity , 1981 .

[28]  S. A. Gredeskul,et al.  Randomly layered media: fluctuation waveguide , 1990 .

[29]  Ė. Kaner,et al.  The spatial dispersion of conductivity in one-dimensional disordered metals , 1987 .

[30]  T. Schneider,et al.  Electromagnetic wave propagation in quasiperiodically stratified media , 1988 .

[31]  M. Azbel'.  Resonance tunneling and localization spectroscopy , 1983 .

[32]  É. Guazzelli,et al.  Localization of Surface Waves on a Rough Bottom: Theories and Experiments , 1987 .

[33]  Pierre Devillard,et al.  Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium , 1986 .

[34]  Arthur R. McGurn,et al.  Localization effects in the elastic scattering of light from a randomly rough surface , 1987 .

[35]  J. Kowalski,et al.  Tunneling in one‐dimensional ideal barriers , 1987 .

[36]  É. Guazzelli,et al.  On the localization of shallow water waves by a random bottom , 1983 .

[37]  V. D. Freylikher,et al.  Localization of the field of a point source in a randomly layered medium , 1991 .

[38]  White,et al.  Minimum wave-localization length in a one-dimensional random medium. , 1986, Physical review. B, Condensed matter.

[39]  Transmission properties of random point scatterers for waves with two-band dispersion law , 1990 .

[40]  A. Abrikosov,et al.  Conductivity of quasi-one-dimensional metal systems , 1978 .

[41]  Eugenio R. Mendez,et al.  Experimental study of scattering from characterized random surfaces , 1987 .

[42]  L. Pastur,et al.  A pure point spectrum of the stochastic one-dimensional schrödinger operator , 1977 .

[43]  Philip W. Anderson,et al.  New method for a scaling theory of localization , 1980 .

[44]  C. Enz.  Landauer-type localization of light in randomly “broken” optical fibres , 1987 .

[45]  K. Ishii,et al.  Localization of Eigenstates and Transport Phenomena in the One-Dimensional Disordered System , 1973 .

[46]  George Papanicolaou,et al.  Power statistics for wave propagation in one-dimension and comparison with radiative transport theory. II , 1973 .

[47]  Maradudin,et al.  Localization effects in the scattering of light from a randomly rough grating. , 1985, Physical review. B, Condensed matter.

[48]  A. J. Sant,et al.  Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers. , 1989, Optics letters.