Surface scattering and band gaps in rough waveguides and nanowires

Dietz, Otto; Stöckmann, H.‐J.; Kuhl, Ulrich; Izrailev, F. M.; Makarov, N. M.; Doppler, J.; Libisch, Florian; Rotter, Stefan

doi:10.1103/physrevb.86.201106

Cited by 14 publications

(27 citation statements)

References 41 publications

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“…In particular, by imposing specific long-range correlations one can practically create the devices with given transmission/reflection characteristics. This effect of enhancement or suppression of the Anderson localization was recently observed experimentally in waveguides with both the bulk [10] or surface [11] correlated disorder. It should be stressed that specific long-range correlations can emerge naturally in physical systems, not only in systems with intentionally included correlations; one such example will be discussed in this paper.New perspectives in creating devices with unusual transport characteristics are related to specific optic properties of metamaterials embedded in periodic structures [12][13][14][15][16][17][18][19][20][21][22].…”

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confidence: 59%

Non-conventional Anderson localization in a matched quarter stack with metamaterials

2013

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We study the problem of non-conventional Anderson localization emerging in bilayer periodic-on-average structures with alternating layers of materials, with positive and negative refraction indices n a and n b . Attention is paid to the model of the so-called quarter stack with perfectly matched layers (the same unperturbed by disorder impedances, Z a = Z b , and optical path lengths, n a d a = |n b |d b , with d a and d b being the thicknesses of basic layers). As was recently numerically discovered, in such structures with weak fluctuations of refractive indices (compositional disorder), the localization length L loc is enormously large in comparison to the conventional localization occurring in the structures with positive refraction indices only. In this paper we develop a new approach, which allows us to derive the expression for L loc for weak disorder and any wave frequency ω. In the limit ω → 0 one gets a quite specific dependence, L −1 loc ∝ σ 4 ω 8 , which is obtained within the fourth order of perturbation theory. We also analyze the interplay between two types of disorder, when in addition to the fluctuations of n a and n b , the thicknesses d a and d b slightly fluctuate as well (positional disorder). We show how conventional localization recovers with the addition of positional disorder. vicinity of band edges or resonances, a fact that leads to the dramatic complication of a rigorous analysis (see review [9]).Another effect which needs specific analytical tools in its analysis is the influence of various correlations in a disorder. As is already understood, underlying correlations either of the short or long-range type can significantly suppress or enhance the localization length, therefore, strongly influence the global characteristics of the transmission [9]. In particular, by imposing specific long-range correlations one can practically create the devices with given transmission/reflection characteristics. This effect of enhancement or suppression of the Anderson localization was recently observed experimentally in waveguides with both the bulk [10] or surface [11] correlated disorder. It should be stressed that specific long-range correlations can emerge naturally in physical systems, not only in systems with intentionally included correlations; one such example will be discussed in this paper.New perspectives in creating devices with unusual transport characteristics are related to specific optic properties of metamaterials embedded in periodic structures [12][13][14][15][16][17][18][19][20][21][22]. A particular system of increasing interest is an array of two alternating a -and b -layers with equal optical path lengths, n a d a = |n b |d b . Here the a -layers are made of the right-handed (RH) material with positive refractive index n a > 0 and thickness d a . In contrast, the b -layers refer to the lefthanded (LH) material with negative index n b < 0 and thickness d b . In such a model the phase shift of the wave gained in the a -layer is fully compensated by the subsequent shift in the nex...

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confidence: 59%

Non-conventional Anderson localization in a matched quarter stack with metamaterials

2013

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“… used in different contexts (see, e.g., [33][34][35]) is restricted to Gaussian random processes and cannot be applied for the present step-like surface profiles. Indeed, as we will see below, this simplification would lead to a severe underestimation of the SGS mechanism in the present context.…”

Section: Methodsmentioning

confidence: 99%

“…Also note that we have used ensemble averaging for the derivation of the above equations (10) and (11) (to ensure convergence of equation (A.3) in the appendix) [40]. Recent work demonstrates, however, that an application of the predictions following from the two different correlators above also yields good quantitative agreement for individual disorder realizations as in single disordered waveguides [33].…”

Section: Methodsmentioning

confidence: 99%

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

et al. 2014

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We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at welldefined resonance values. Based on detailed numerical and analytical calculations, we can unambiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.The problem of scattering off a rough surface is a central topic in physics which occurs for many different types of waves and on considerably different length scales [1][2][3][4]. Phenomena induced by surface corrugations play a major role in the study of acoustic, electromagnetic, and matter waves alike and appear in macroscopic domains such as acoustic oceanography and atmospheric sciences [5,6], but also emerge on much smaller length scales, e.g., for photonic crystals [7], optical fibers and waveguides [8,9], surface plasmon polaritons [10], metamaterials [11], thin metallic films [12-14], layered structures [15], graphene nanoribbons [16,17], nanowires [18][19][20], and confined quantum systems [21,22]. While having a detrimental effect on the performance of many of the above systems, surface roughness can also be put to use, e.g., for the fabrication of high-performance thermoelectric devices [23,24] and for light trapping in silicon solar cells [25]; rough surfaces cause anomalously large persistent currents in metallic rings [26] and provide the necessary scattering potential to manipulate ultra-cold neutrons which are bound by the earthʼs gravity potential [27].In view of this sizeable research effort, it might come as a surprise that even quite fundamental effects emerging in surface-disordered systems are still not fully understood. Consider here, in particular, the problem of wave transmission through a surface-corrugated guiding system which we will study in the following. As demonstrated in detail below, even a very elementary and well-studied model system, consisting of a two-dimensional (2D) waveguide with a step-like surface disorder on either boundary (see figure 1), can only be inadequately described with conventional techniques. The reason why the knowledge on surface-disordered waveguides is still far behind the state of the art for bulk-disordered systems is mainly because of the difficulties arising from the non-homogeneous character of transport via different propagating modes (channels). As was numerically shown in [28], the transmission through multi-mode waveguides depends on many characteristic length scales which are specific for each mode. As a result, one can observe a coexistence of b...

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“…A simple measurement of the scattering matrix (or a subpart of it) at neighboring frequencies [27] yields the time-delay matrix from which particle-like state inputs can be extracted. Such a measurement can be routinely performed through 3D scattering media whether it be in optics [6,12], in the microwave regime [13,35] or in acoustics [33,34]. As to the generation of particle-like wave packets, multi-element technology is a powerful tool for the coherent control of acoustic waves and electromagnetic waves [60].…”

Section: Discussionmentioning

confidence: 99%

“…This highly dimension S-matrix relates any arbitrary wave-field at the input to the output of the scattering medium, and in principle, allows the reconstruction or prediction of either. It fully describes wave propagation across a scattering medium and can meanwhile be routinely measured not only in acoustics [33,34], but also in microwave technology [13,35] and optics [6,12]. The sub-blocks of the scattering matrix contain the complex-valued transmission (t, t ) and reflection (r, r ) matrices with a certain number N of input and output channels, S = r t t r .…”

Section: Introductionmentioning

confidence: 99%

Particle-like wave packets in complex scattering systems

Gérardin

Laurent

Ambichl

et al. 2016

2016 URSI International Symposium on Electromagnetic Theory (EMTS)

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A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes. Controlling wave propagation through complex systems is thus of fundamental interest in many areas, ranging from optics or acoustics to medical imaging or telecommunications. Here, we study the propagation of elastic waves in a cavity and a disordered waveguide by means of laser interferometry. From the direct experimental access to the time-delay matrix of these systems, we demonstrate the existence of particle-like wave packets that remain focused in time and space throughout their complex trajectory. Due to their limited dispersion, their selective excitation will be crucially relevant for all applications involving selective wave focusing and efficient information transfer through complex media.

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Surface scattering and band gaps in rough waveguides and nanowires

Cited by 14 publications

References 41 publications

Non-conventional Anderson localization in a matched quarter stack with metamaterials

Non-conventional Anderson localization in a matched quarter stack with metamaterials

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

Particle-like wave packets in complex scattering systems

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