Example of self-averaging in three dimensions: Anderson localization of electromagnetic waves in random distributions of pointlike scatterers

1997 ◽  
Vol 56 (5) ◽  
pp. 6090-6094 ◽  
Author(s):  
Marian Rusek ◽  
Arkadiusz Orłowski
Keyword(s):  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Three Dimensions ◽  
Random Distributions

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

Scattering of a Plane Elastic Wave From Objects Near an Interface

1972 ◽  
Vol 39 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Stephen B. Bennett
Keyword(s):  
Elastic Wave ◽  
Electromagnetic Waves ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Scattering Problems ◽  
Reflection And Refraction ◽  
Time Harmonic ◽  
Incident Plane ◽  
Boundary Curves ◽  
Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

ANDERSON LOCALIZATION IN THE SEVENTIES AND BEYOND

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1507-1525 ◽  
Author(s):  
David Thouless
Keyword(s):  
Quantum Hall Effect ◽  
Anderson Localization ◽  
Quantum Hall ◽  
Experimental Tests ◽  
Three Dimensions ◽  
Electronic Systems ◽  
Atomic Systems ◽  
One Dimensional ◽  
Extended States ◽  
Energy States

Little attention was paid to Anderson's challenging paper on localization for the first ten years, but from 1968 onwards it generated a lot of interest. Around that time a number of important questions were raised by the community, on matters such as the existence of a sharp distinction between localized and extended states, or between conductors and insulators. For some of these questions the answers are unambiguous. There certainly are energy ranges in which states are exponentially localized, in the presence of a static disordered potential. In a weakly disordered one-dimensional potential, all states are localized. There is clear evidence, in three dimensions, for energy ranges in which states are extended, and ranges in which they are diffusive. Magnetic and spin-dependent interactions play an important part in reducing localization effects. For massive particles like electrons and atoms the lowest energy states are localized, but for massless particles like photons and acoustic phonons the lowest energy states are extended. Uncertainties remain. Scaling theory suggests that in two-dimensional systems all states are weakly localized, and that there is no minimum metallic conductivity. The interplay between disorder and mutual interactions is still an area of uncertainty, which is very important for electronic systems. Optical and dilute atomic systems provide experimental tests which allow interaction to be much less important. The quantum Hall effect provided a system where states on the Fermi surface are localized, but non-dissipative currents flow in response to an electric field.

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