Enhanced backscattering and blazing effect from gratings,quasi-gratings and randomly rough surfaces

Abstract

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces

A review is made of theoretical and experimental work on retroreflection enhancements in the diffuse component of light elastically reflected from randomly rough surfaces. These effects are seen as a narrow peak in the angular distribution of the intensity of diffusely reflected light which is centered about the direction for reflected light motion antiparallel to the original incident beam. This peak is observed in the scattering of light from many different types of rough surfaces and has been studied in fields as diverse as solid state physics, astronomy, geophysics, meterology and radar. Work covering all of these fields will be presented in this review.

Retroreflection enhancements arise both from shadow casting properties of surface irregularities and from the phase coherence of retroreflected light. These mechanisms can act to create retroreflection enhancements from rough surfaces of dielectric and/or metallic compositions and of surface disorders characterizable on length scales which are large, comparable to or small compared to the wavelength of the scattered light.

Specific discussions will be presented of three types of enhanced retroreflectance: (1) A treatment of the optical glory and Heiligenschein phenomena which are concerned with the meterological and geophysical study of light reflected from clouds and terraine will be given. (2) The theory of the opposition effect, encountered in astronomy as an enhanced retroreflection in the light scattered from atmosphereless planets and space debris, will be used to provide a theoretical basis to understand shadowing effects. (3) A recently discovered phenomenon of enhanced retroreflection from weakly rough metallic mirrors, associated with the Anderson localization of surface waves, is also presented. This last phenomenon and its relationship to the study of the Anderson localization of surface waves will be emphasized throughout our discussions.

Similar enhancement effects in the scattering of acoustic waves from rough surfaces and a brief outline of some recent work on optical backscattering enhancements due to the Anderson localization of bulk polariton modes, is also presented.     

Time-local gaussian processes,path integrals and nonequilibrium nonlinear diffusion

In this paper we discuss the concept of time-local gaussian processes. These are processes for which the state variable at time t + τ is gaussian distributed around its most probable value at that time, for a specified realization a small time interval τ earlier. On one hand it will be shown that these processes are related to a very simple path sum. On the other hand the associated stochastic differential equation is derived by means of the Kramers-Moyal method, and will be seen to be the most general nonlinear Fokker-Planck equation. The significance of the present formulation for nonequilibrium processes and the comprehension of critical phenomena will be evaluated.     

Effects of magnetic atoms on the properties of ternary superconductors

Conclusion It is noteworthy that while only two classes of systems (the Chevrel phases and the rare-earth rhodium borides) have so far received extensive study, nonetheless a great many new phenomena have been encountered. This, however, should only be considered the beginning of a new and potentially very rich field, especially if one considers the vast number of possibilities of ternary compounds that can be produced. To take only one other example, recent work has shown that the compound Sc₂Fe₃Si₅ is superconducting with a superconducting transition of 4.5 K (29). This at first may appear surprising since ever in the Chevrel phase materials, the addition of Fe atoms is detrimental to superconductivity. However, recent Mossbauer effect experiments (29) have shown that the Fe in this material is not magnetic, having a magnetic moment of less than 0.03 µ_B. These silicides have also been made with rare-earth ions in place of the Sc(²⁸). The compounds show magnetic transitions and are currently under investigation. Several other interesting systems have been synthesized, and it appears that many more will be coming in the near future. The results reported above have shown the utility of hyperfine data in clarifying many of the new phenomena that occur, and it should be expected that as this new field grouws, these kinds of measurements will continue to play an active role (30).     

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.     

Detection of nano-interfacial space charge field at metal–organic film interface by SHG and surface potential

At the metal–organic film nano-interface, surface polarization phenomena are observed, due to the displacement of excess charges from metal to the films as well as alignment of polar dipoles. Surface potential method has been employed to examine these surface polarization phenomena, and the distribution of space charges and distribution of electronic density of states have been determined. However, for further understanding of the nanometric interface phenomena, it is very helpful to develop an experimental method that can detect electrical and optical phenomena induced by the space charge formation. In this paper, it is shown that optical second harmonic generation measurement is effective through our experiment on phthalocyanine films deposited on Al and Au electrodes.     

Hybridization effect in coupled metamaterials

Although the invention of the metamaterials has stimulated the interest of many researchers and possesses many important applications, the basic design idea is very simple: composing effective media from many small structured elements and controlling its artificial EM properties. According to the effective-media model, the coupling interactions between the elements in metamaterials are somewhat ignored; therefore, the effective properties of metamaterials can be viewed as the “averaged effect” of the resonance property of the individual elements. However, the coupling interaction between elements should always exist when they are arranged into metamaterials. Sometimes, especially when the elements are very close, this coupling effect is not negligible and will have a substantial effect on the metamaterials’ properties. In recent years, it has been shown that the interaction between resonance elements in metamaterials could lead to some novel phenomena and interesting applications that do not exist in conventional uncoupled metamaterials. In this paper, we will give a review of these recent developments in coupled metamaterials. For the “metamolecule” composed of several identical resonators, the coupling between these units produces multiple discrete resonance modes due to hybridization. In the case of a “metacrystal” comprising an infinite number of resonators, these multiple discrete resonances can be extended to form a continuous frequency band by strong coupling. This kind of broadband and tunable coupled metamaterial may have interesting applications. Many novel metamaterials and nanophotonic devices could be developed from coupled resonator systems in the future.     

Scattering of a narrow wave beam by a randomly rough locally diffuse surface subject to pulse illumination

We consider the scattering of a narrow pulse wave beam by a randomly rough surface with a complex local scattering indicatrix. Analytical expressions are found for the mean received power for a normal distribution of heights and slopes of the surface in two cases: where the direction to the receiver is close to the direction of mirror reflection and where the direction to the receiver is very different from the direction of mirror reflection. It is shown that in these two cases the echo pulse is very different in shape and is controlled by the parameters of the source and receiver, the sounding scheme, and the variance of heights of a rough surface. The received power is strongly dependent on the width of the local scattering indicatrix, and the form of this dependence is determined by the angles of illumination and reception. The analytical expressions for the mean received power are in good agreement with the results of numerical calculations. Institute for Radioelectronics and Laser Engineering of the N. é. Bauman State Technical University of Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No.4, pp. 333–339, April 1999.     

Some mathematical aspects of the scaling limit of critical two-dimensional systems

It has been observed long ago that many systems from statistical physics behave randomly on macroscopic level at their critical temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanks to conformal field theory, that led to the derivation of the exact value of various critical exponents that describe their behavior near the critical temperature. In the last couple of years, combining ideas of complex analysis and probability theory, mathematicians have constructed and studied a family of random fractals (called ‘Schramm-Loewner evolutions’ or SLE) that describe the only possible conformally invariant limits of the interfaces for these models. This gives a concrete construction of these random systems, puts various predictions on a rigorous footing, and leads to further understanding of their behavior. The goal of this paper is to survey some of these recent mathematical developments, and to describe a couple of basic underlying ideas. We will also briefly describe some very recent and ongoing developments relating SLE, Brownian loop soups and conformal field theory.     

高能碰撞多粒子末态间歇现象与关联积分的研究

用理论分析和Monte Carlo模拟表明:研究间歇现象时用关联积分代替阶乘矩的统计会改变快度bin减小时的反常标度行为. 指出,关联函数积分与阶乘矩可能分别反映不同的物理内容.提出了一种随机移动分bin起点的统计阶乘矩方法以消除分bin造成的人为因素.证明了,“钉子”事件对间歇指数有重要贡献.     

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

A unified theory for the conductance of an infinitely long multimode quantum wire whose finite segment has randomly rough lateral boundaries is developed. It enables one to rigorously take account of all feasible mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the perfect leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier, which is proportional to the average slope squared, specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small, up to zero, values if the asperities are sufficiently sharp. The consecutive channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder per se but rather is of entropic or (equivalently) geometric origin. The fluctuating part of the effective barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops in the corrugated waveguide, which have the form of asymptotically decoupled extended modes subject to individual solely intramode random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode waveguides, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus shown to coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson (disorder-driven) localization. If the particular mode propagates across the rough segment ballistically, the Fabry–Pérot-type oscillations should be observed in the conductance, which are suppressed for the mode transferred in the Anderson-localized regime.     

Experimental investigation of the effect of pump incoherence on nonlinear pump spectral broadening and continuous-wave supercontinuum generation

The development of high-power cw fiber lasers has triggered a great interest in the phenomena of nonlinear pump spectral broadening and cw supercontinuum generation. These effects have very convenient applications in Raman amplification, optical fiber metrology, and fiber sensing. In particular, it was recently shown that pump incoherence has a strong impact in these processes. We study experimentally the effect of pump incoherence in nonlinear pump spectral broadening and cw supercontinuum generation in optical fibers. We show that under certain experimental conditions an optimum degree of pump incoherence yields the best performance in the broadening process. We qualitatively explain these results, and we point out that these results may have important implications in cw supercontinuum optimization.     

Surface scattering in media with time and spatial dispersion

Scattering of scalar and vector waves from a randomly rough interface between media, in which several types of waves (modes) exist due to the time and spatial dispersion, has been studied in the Kirchhoff approximation. As a wave of a certain type is reflected from the interface, it transforms into other modes not only in the diffusive fields but in the coherent components as well. We have calculated the mean (coherent) field and the angular diagram of the diffusively scattered intensity. It is shown that the coherent components of the waves generated on reflection (cross-modes) propagate in directions that are different from the specular one. The dispersion gives rise to the frequency dependence of the scattering diagram even in the geometric-optics approximation.     

Surface scattering in media with time and spatial dispersion

Scattering of scalar and vector waves from a randomly rough interface between media, in which several types of waves (modes) exist due to the time and spatial dispersion, has been studied in the Kirchhoff approximation. As a wave of a certain type is reflected from the interface, it transforms into other modes not only in the diffusive fields but in the coherent components as well. We have calculated the mean (coherent) field and the angular diagram of the diffusively scattered intensity. It is shown that the coherent components of the waves generated on reflection (cross-modes) propagate in directions that are different from the specular one. The dispersion gives rise to the frequency dependence of the scattering diagram even in the geometric-optics approximation.     

涌浪条件下的浅海表面声道脉冲声传播*

在冬季,海水表面受到海面强风的影响,普遍存在表面声道。当声源位于表面声道中并且声源频率高于表面声道的截止频率时,声能量几乎被完全限制其中,不与海底作用,十分有利于声传播。但当表面声道上边界为较大涌浪所形成的粗糙界面时,这种优良性能会被破坏。在南海北部陆坡海区的一次冬季实验中,发现表面声道以下水听器接收到的首个脉冲的幅度明显增加,通过研究表明,其原因是：存在较大涌浪时,部分表面声道内传播的声能量,经粗糙海面反射作用后进入下层水体中,使得位于表面声道以下的水听器的第一个到达的脉冲幅度增强。     

Photoproduction ofK + Λ andK +*∑0 from hydrogen between 1.3 and 1.45 GeV

It will be shown that the perturbation theory approach with respect to the amplitude of the roughness for the scattering of light by rough surfaces is equivalent to a model consisting of a smooth surface and surface current sources. This model has an obvious physical meaning and allows a simple calculation of the scattered fields, which are given. The model and the previous one given by Stern are identical up to the position of the surface currents, which have to be placed into the vacuum. Consequently the former explanation has to be corrected, which says that the peak of the scattered radiation at the plasma frequency is generated by surface roughness. We will show that it is possible to generate this maximum by statistical inhomogenities within the metal.