Rough surface scattering in many‐mode conducting channels: gradient versus amplitude scattering

Izrailev, F. M.; Makarov, N. M.; Rendón, M.

doi:10.1002/pssb.200460769

Cited by 11 publications

(18 citation statements)

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“…It is important to mention that this calculation is performed using both propagating and evanescent modes and hence, this method can be considered as exact. The statistical properties of any transport parameter obtained from 10 in surface disordered waveguides [11,[32][33][34][35][36]. This could be the origin of the differences between bulk and surface distributions.…”

Section: Random Walk In the Transfer-matrix Space: Statistical Conducmentioning

confidence: 99%

Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics

et al. 2007

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We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length δL are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem.Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account.For one propagating mode, N = 1, we have been able to solve the diffusion equation for a number of particular observables, and the solution is in excellent agreement with the results of microscopic calculations. In general, we have not succeeded in finding a solution of the diffusion equation.We have thus developed a numerical simulation, to be called "random walk in the transfer matrix space", in which the universal statistical properties of a "building block" are first implemented numerically, and then the various building blocks are combined to find the statistical properties of the full waveguide. The reported results thus obtained (in which use was made of a "shortwavelength approximation") are in very good agreement with those arising from truly microscopic calculations, for both bulk and surface disorder.

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Section: Random Walk In the Transfer-matrix Space: Statistical Conducmentioning

confidence: 99%

Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics

et al. 2007

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“…As was predicted in Refs. [13][14][15][16], the weak surface scattering in single-mode waveguides is determined by two different mechanisms: amplitude (A) and square-gradient (SG) surface scattering. Correspondingly, the transport is specified by two power spectra.…”

Section: The Modelmentioning

confidence: 99%

“…Thus, one can discriminate one of them through the selection of the wave number k x . In the other situation, with Gaussian correlations [13][14][15][16][17], when both terms 1/L (A) loc and 1/L (SG) loc are nonzero, one has to compare which mechanism prevails.…”

Section: Transmittance and Localization Lengthmentioning

confidence: 99%

“…We have already demonstrated that the surface scattering consists of two basic mechanisms: the well-known amplitude mechanism and the square-gradient mechanism (see Refs. [13][14][15][16]). Correspondingly, the inverse attenuation length is expressed via two terms.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in the case of Gaussian correlations in the rough surface profile, these two mechanisms compete with each other, and the result of the competition essentially depends on the value of the wave number; see Refs. [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Discrimination between two mechanisms of surface scattering in a single-mode waveguide

2011

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Transport properties of a single-mode waveguide with rough boundary are studied by discrimination between two mechanisms of surface scattering, the amplitude and square-gradient ones. Although these mechanisms are generically mixed, we show that for some profiles they can separately operate within nonoverlapping intervals of wave numbers of scattering waves. This effect may be important in realistic situations due to inevitable long-range correlations in scattering profiles.

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Transport of waves in disordered waveguides: A potential model

Mello

Yépez

Froufe‐Pérez

et al. 2007

Physica A: Statistical Mechanics and its Applications

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Rough surface scattering in many‐mode conducting channels: gradient versus amplitude scattering

Cited by 11 publications

References 11 publications

Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics

Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics

Discrimination between two mechanisms of surface scattering in a single-mode waveguide

Transport of waves in disordered waveguides: A potential model

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