Manifestation of the roughness-square-gradient scattering in surface-corrugated waveguides

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

doi:10.1103/physrevb.73.155421

Cited by 16 publications

(41 citation statements)

References 28 publications

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“…In recent papers 22 it was shown that apart from the wellknown terms in surface scattering potentials appearing in the first-order perturbation theory, one should keep some specific terms that were neglected due to their seeming smallness. It was demonstrated that these terms, although formally belonging to the second-order terms, can play a decisive role in the scattering in some region of parameters.…”

Section: Introductionmentioning

confidence: 99%

“…22 where a particular case of one rough surface was considered, below we develop a general approach by concentrating our attention on quasi-onedimensional ͑quasi-1D͒ waveguides with two corrugated surfaces that are either statistically uncorrelated or correlated. Our main interest is in the expression for the attenuation length L n ͑also known as the scattering length, or the total mean free path͒, corresponding to a specific nth propagating mode.…”

Section: Introductionmentioning

confidence: 99%

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Square-gradient mechanism of surface scattering in quasi-one-dimensional rough waveguides

2007

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We develop a perturbative approach that allows one to study surface scattering in quasi-one-dimensional waveguides with rough boundaries. Our approach is based on the construction of an effective "bulk" potential of a very complicated structure. A detailed analysis of this potential reveals that apart from well-known terms considered in previous studies, one should keep specific terms that depend on the square of the derivative of the boundaries. As was found, in spite of an apparent smallness of these square-gradient scattering ͑SGS͒ terms, there is a physically important region of parameters in which they cannot be neglected. Our approach also demonstrates that the contribution of the SGS mechanism of scattering strongly depends on the type of rough boundaries ͑uncorrelated, symmetric, or antisymmetric͒.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Square-gradient mechanism of surface scattering in quasi-one-dimensional rough waveguides

2007

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“…It should be stressed that the GISterms, due to their proportionality to a2, were neglected in previous studies of the transport properties of surfacedisordered waveguides. A similar situation occurs for the SGS-terms that have been analyzed only recently in [4]. As we show below, these terms can give the main contribution in the scattering, although formally they may be treated as negligible ones.…”

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confidence: 76%

“…It is also related to the RSGP spectrum through the third term in the expression (16) (see Table 2 Ref. [4] in details. Specifically, it was shown that the validity of presented results is restricted by two independent criteria of the weak suface scattering, An << 2Ln RC << 2Ln *…”

Section: And(kx -Kx")t(kx(kx -Kx')mentioning

confidence: 99%

“…Here, we follow the self-energy formalism developed in Ref. [4] to perform the transition from the problem for the random Green's function g(kx,kj') to the problem for the Green's function (g(kx , k)') averaged over the surface disorder. The imaginary part of the self-energy obtained from the Dyson-type equation for (g(kx, k') , within the second-order approximation in the scattering potential, yields the desired scattering length Ln.…”

Section: And(kx -Kx")t(kx(kx -Kx')mentioning

confidence: 99%

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Square-Gradient Mechanism of Surface Scattering in Waveguides with Random Rough Surfaces

Rendón

Makarov

Izrailev

2007

2007 International Kharkiv Symposium Physics and Engrg. Of Millimeter and Sub-Millimeter Waves (MSMW)

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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 ofthe surface scattering.The goal of this contribution is to study competing mechanisms of surface scattering and their manifestation in the wave attenuation length Ln (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-i D waveguides in which the total number Nd of propagating modes (or conducting channels) is large Nd >> 1 The roughness of the lower and upper boundaries of such waveguides are described, respectively, by the random functions 5, (x) and $, (x). The relationship between those functions defines the waveguide's profile or configuration. Here four profiles are of our particular interest:The waveguide with one rough boundary, ;, (x) = 0The waveguide with the uncorrelated boundaries, 5, (x) and 4 (x).The waveguide with the antisymmetric boundaries, J (x) = T (x) = 5(X)The waveguide with symmetric boundaries, -(x)= t (x) = 4X) 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 kn + kn a where kn is its unperturbed value and in = Yn + i(2L ) *.(1)The real part Y,, is responsible for a roughness-induced correction to the phase velocity of a given mode. As is known, the shift Yn does not change the transport properties of a disordered system. Our model is the open waveguide of the average width d, stretched along the x axis. The lower and upper surfaces of the waveguide are assumed to be described, respectively, by the boundaries z = ur, (x), and z = d + 4~( x). Here o-is the root-mean-square roughness height that is assumed to be identical for both boundaries. In other words, the waveguide occupies the region -oo < x so a:; (x)< z < d + or, (x) of the (x, z) -plane. The fluctuating width is defined by w(x) = d + a[CL (x) -4, (x)] with w(4x) = d We emphasize that wherever being possible, we will develop our approach in a general form in order to include the four waveguide's profiles defined above. Then, the expressions of the attenuation length will be given for each profile.

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Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wires

Usatenko¹,

Melnik²,

Kroon³

et al. 2008

Physica A: Statistical Mechanics and its Applications

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Manifestation of the roughness-square-gradient scattering in surface-corrugated waveguides

Cited by 16 publications

References 28 publications

Square-gradient mechanism of surface scattering in quasi-one-dimensional rough waveguides

Square-gradient mechanism of surface scattering in quasi-one-dimensional rough waveguides

Square-Gradient Mechanism of Surface Scattering in Waveguides with Random Rough Surfaces

Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wires

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