Amplitude and gradient scattering in waveguides with corrugated surfaces

Abstract

We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering walls. We demonstrate numerically and explain theoretically that the gradient scattering can be quite strong even if the amplitude of scattering profiles is very small in comparison with the width of waveguides. 05.45.Mt, 41.20.Jb, 42.25.Dd, 71.23.An During last decade much attention has been paid to the theory of quasi-1D disordered solids with the so-called bulk scattering. By this term one describes the situation where the whole volume of a scattering region contains scatters whose density determines the mean free path λ for a propagation of electrons. According to the theory, apart from λ, transport properties of finite samples are described by two other characteristic lengths: size L of a sample and localization length l ∞ . The latter is deterimied by the degree of the decrease of the amplitude of eigenstates along infinite samples with the same scattering characteristics. The core of the modern theory of the transport for such quasi-1D systems is the so-called single-parameter scaling. It was shown that when the mean free path is much less than both L and l ∞ , all statistical characteristics of the transport are fully described by the only scaling parameter which is the ratio of the localization length to the size of a sample (see, e.g. [1] and references therein).Another kind of quasi-1D systems that has attracted much attention in past few years, is the many-mode waveguide with rough surfaces. In this case the scattering is entirely related to statistical characteristics of scattering walls, therefore, one can speak about surface scattering. For some time it was believed that the surface scattering can be analytically described by modified methods thoroughly developed for bulk scattering. However, recent numerical studies of such systems [2,3] have revealed a principal difference between surface and bulk scattering (see discussion and references in [4]). Specifically, it was found that the transport through quasi-1D waveguides with rough surfaces essentially depends on many characteristic lengths, not on one length as in the case of the bulk scattering. This fact is due to a non-isotropic character of scattering in the channel space. In particular, the transmission coefficient smoothly decreases with an increase of the angle of incoming waves, since characterictic lengths for backscattering are different for different channels [3,5].The latter subject of the surface scattering has a direct link to the problem of quantum chaos. The point is that the waveguides with rough walls can be treated from the viewpoint of classical and quantum mechanics that describe a particle moving inside billiards and having multiple reflections from the walls. One of the problems of quantum chaos is the quantum-classical correspondence for the situation when, in the classical limit, glob...

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

“…Here we have used the standard definition of the mean free path (mfp) ℓ ab associated with the incoherent sum of reflections from channel b to a from a sequence of ν = 1/d scatterers per unit length, i.e., 1 34) together with the fact that the average reflection coefficient for a delta slice is r-independent and approximately given, in the weak-scattering regime, Eq. (3.17), by [see Eqs.…”

“…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.…”

“…In particular, the dependence of ℓ ab on a 2 b 2 [see Eq. (4.17)] reflects the strong channel anisotropy of transport in surface disordered waveguides [11,[32][33][34][35][36]. This could be the origin of the differences between bulk and surface distributions.…”

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

“…In the subsequent papers devoted to the subject (see Ref. [31]), the slope mechanism was more reasonably named the "gradient" one, so this particular term will further be used in the present paper.…”

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

“…In particular, the transmission coefficient smoothly decreases with an increase of the angle of incoming waves, see details in [2,4]. Below we present an analytical treatment of the electron/wave scattering in waveguides with rough surfaces, paying main attention to the interplay between "amplitude" and "gradient" scattering mechanisms [5,6].…”