In spite of the extensive research devoted to the subject of wave scattering in surface-random-corrugated guiding systems (see, e.g., [1, 2]), there is a number of open questions to be resolved. Experimental and numerical works have revealed transport properties of such waveguides which challenge the possibility of an analytical treatment [3]. Thus, it is important to analyze what are specific mechanisms of the surface scattering. The goal of this contribution is to study competing mechanisms of surface scattering and their manifestation in the wave attenuation length L{sub}n (also known as the scattering length or the total mean-free-path corresponding to specific nth propagating mode) of multimode waveguides or electron conducting wires. We focus our attention on quasi-1D waveguides in which the total number N{sub}d of propagating modes (or conducting channels) is large N{sub}d 1. The roughness of the lower and upper boundaries of such waveguides are described, respectively, by the random functions ξ{sub}↓(x) and ξ{sub}↑(x). The relationship between those functions defines the waveguide's profile or configuration. Here four profiles are of our particular interest: (1) The waveguide with one rough boundary, ξ{sub}↓(x) = 0. (2) The waveguide with the uncorrelated boundaries, ξ{sub}↓(x) and ξ{sub}↑(x). (3) The waveguide with the antisymmetric boundaries, ξ{sub}↓(x) = ξ{sub}↑(x) = ξ(x). (4) The waveguide with symmetric boundaries, - ξ^s{sub}↓(x) = ξ{sub}↑(x) = ξ(x). We assume that due to the multiple scattering of a traveling wave from the rough boundaries, the longitudinal wave number of an nth propagating mode can be written as k{sub}n + δk{sub}n, where k{sub}n is its unperturbed value and δk{sub}n = γ{sub}n + i(2L{sub}n){sup}(-1). (1) The real part γ{sub}n is responsible for a roughness-induced correction to the phase velocity of a given mode. As is known, the shift γ{sub}n does not change the transport properties of a disordered system.
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机译：尽管对表面随机波纹引导系统中的波浪散射的波浪散射进行了广泛的研究（参见，例如，[1,2]），有许多要解决的开放问题。实验和数值作品揭示了这种波导的运输性质，其挑战分析治疗的可能性[3]。因此，重要的是分析表面散射的特定机制。该贡献的目标是研究表面散射的竞争机制及其在波衰减长度L {sub} n中的表现形式（也称为与多模对应于特定的第n个传播模式的散射长度或总惯用路径）波导或电子导线。我们将注意力集中在拟1D波导上，其中传播模式（或导电通道）的总数n {sub} d是大的n {sub} d 1.这种波导的较低和上边界的粗糙度是分别由随机函数描述ξ{sub}↓（x）和ξ{sub}↑（x）。这些功能之间的关系定义了波导的配置文件或配置。这里有四个配置文件是我们的特殊兴趣：（1）具有一个粗略边界的波导，ξ{sub}↓（x）= 0.（2）波导具有不相关的边界，ξ{sub}↓（x）和ξ {sub}↑（x）。 （3）具有反对称界限的波导，ξ{sub}↓（x）=ξ{sub}↑（x）=ξ（x）。 （4）具有对称边界的波导， - ξ^ s {sub}↓（x）=ξ{sub}↑（x）=ξ（x）。我们假设由于来自粗略边界的行波的多个散射，第n传播模式的纵波数可以被写为k {sub} n +Δk{sub} n，其中k {sub} n是它的不受干扰的值和ΔK{sub} n =γ{sub} n + i（2l {sub} n）{sup}（ - 1）。 （1）实部γ{Sub} N负责粗糙度校正对给定模式的相位速度的校正。众所周知，移位γ{sub} n不改变无序系统的传输属性。
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