A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Rayleigh's hypothesis and the geometrical optics limit

The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.     

Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering

In this work, a multiwavelength fiber Raman laser based on a highly birefringent photonic crystal fiber loop mirror is presented. A laser resonator is formed when the Raman amplification with cooperative Rayleigh scattering in a dispersion-compensating fiber is used as a distributed mirror and combined with a photonic crystal fiber loop mirror filtering structure. Stable multiwavelength lasing at room temperature is achieved due to the low temperature sensitivity of the highly birefringent photonic crystal fiber.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Estimation of Rayleigh scattering loss in a double-clad photonic crystal fiber

In this paper the effect of photonic crystal fiber’s structure parameters on Rayleigh scattering was investigated. Rayleigh scattering loss (RSL) has been numerically estimated by average Rayleigh scattering coefficient based on the empirical relations for \(V\) and \(W\) parameters of double-clad photonic crystal fibers (DC PCFs). The dependence of RSL on the two structural parameters—the air hole diameter and the hole pitch was demonstrated. We have shown that RSL depends on the index profiles because of the different optical power confinement factors in every layer of DC PCF. Using these results, the RSL can be optimized by adjusting the fiber parameters—air-hole diameter as well as the air-hole pitch.     

Research on synthetic aperture radar imaging technology of one-dimensional layered rough surfaces

A quick and exact imaging method for one-dimensional layered rough surfaces is proposed in this paper to study the scattering characteristics of a layered medium that exists widely in nature.The boundary integral equations of layered rough surfaces are solved by using the propagation-inside-layer expansion combined with the forward and backward spectral acceleration method(PILE+FB-SA),and the back scattering data are obtained.Then,a conventional synthetic aperture radar(SAR) imaging procedure called back projection method is used to generate a two-dimensional(2D) image of the layered rough surfaces.Combined with the relative dielectric permittivity of realistic soil,the random rough surfaces with Gauss spectrum are used to simulate the layered medium with rough interfaces.Since the back scattering data are computed by using the fast numerical method,this method can be used to study layered rough surfaces with any parameter,which has a great application value in the detection and remote sensing areas.     

Liquid filling of photonic crystal fibres for grating writing

Liquid filling of photonic crystal fibres reduces the scattering from air–glass interfaces during Bragg grating writing in many layered photonic crystal fibres. Within experimental uncertainty, the grating index modulation of a grating written in germanium-doped photonic crystal fibre with 10 rings of holes was more than doubled for a fixed fluence.     

Rigorous and approximate methods for modeling wave scattering from a locally perturbed perfectly conducting surface

Rigorous and approximate methods are considered for solving the problem of harmonic plane wave scattering from a plane surface arbitrarily perturbed along one dimension on a finite interval. This problem is treated using the Fredholm integral equations of the second kind and the Kirchhoff and Rayleigh approximations. The estimates of the computational efficiency of the integral equation method and the Rayleigh approximation are compared by calculating fields scattered from random rough surfaces in the resonance region (i.e., when the roughness height is comparable to or smaller than the incident wavelength) for an arbitrary incidence of a plane wave. Scattering patterns calculated using the integral equations and the Kirchhoff approximation are discussed in the case of large-scale random rough surface scattering. Particular attention is paid to scattering at near-grazing incidence.     

Energy‐lose induced unidirectional light propagation in porous alumina photonic crystal

Unidirectional light propagation phenomena are observed in the photonic crystal heterostructures based on anodic alumina membrane when the incident light illuminated from forward and backward directions. Transmittance / reflectance spectra measurements and theoretical calculations show that the origin of this kind of unbalanced reflection is ascribed to the energy loss induced by Rayleigh scattering. Importantly, unidirectional light propagation can be modulated over the whole visible light region by adjusting the combination of different photonic bandgap as well as the view angle. The as‐prepared heterostructures may provide potential applications in direction‐dependent photonic devices.     

Distributed high-temperature pressure sensing using air-hole microstructural fibers

We present spatially resolved Rayleigh scattering measurements in different polarization-maintaining (PM) fibers for high-temperature pressure sensing. The pressure-induced birefringence in the fiber cores is interrogated using polarization-resolved frequency-swept interferometry. The pressure responses of a PM photonic crystal fiber and a twin-air-hole PM fiber are investigated for a pressure range of 0 to 13.8 MPa (0-2000 psi) at room temperature and at temperatures as high as 800 °C. The proposed sensing system provides, for the first time to our knowledge, a truly distributed pressure-sensing solution for high-temperature applications.     

磁性多层薄膜系统中的巨磁电阻效应

考虑到量子尺寸效应以及来自杂质、粗糙表面、粗糙界面三方面的散射,运用量子统计格林函数方法和久保理论,计算了磁性多层薄膜系统中的巨磁电阻,讨论了巨磁电阻随非磁层厚度作周期性振荡,以及在(Fe/Cr)_N/Fe系统中巨磁电阻随多层基元数目N增加而增大等现象.理论计算与实验结果符合.此外,还讨论了有关各种散射引起的散射率能否相加的问题. 关键词：     

Sound scattering at fluid-fluid rough surface

Extinction theorem was used to deduce the first order scattering cross-section including the double scattering effects for the fluid-fluid rough surface. If the double scattering effects are neglected in the present method, the scattering cross-section agrees with the result obtained by the perturbation method based on Rayleigh hypothesis. Calculations of scattering strength were carried out, and comparisons with the first-order perturbation method based on Rayleigh hypothesis were also done. The results show that double scattering effects are obvious with the increase of the root mean square of surface height and the grazing angle when the valid condition k ₁ h < 1 is satisfied. Supported by the National Basic Research Program of China (Grant No. 2005CB422307)     

Effective impedance model for analysis of reflection at the interfaces of photonic crystals

We present an alternative definition of impedance to describe the reflection at the interfaces of photonic crystals. We show that this effective impedance can be defined only by the properties of the photonic crystal modes and is independent of the properties of the incident region. This approximate model successfully explains the main features in the reflection spectrum and of various interface terminations of photonic crystals. In particular, we show an impedance matching condition at which reflectionless transmission of power to a low-group-velocity photonic crystal mode is possible, a property that is attractive for various dispersion-based applications of photonic crystals.     

Quantum analytical theory for giant magnetoresistance in magnetic multilayered film systems

Taking into account the quantum size effects and considering three types of scattering from bulk impurities, rough surfaces, and rough interfaces, we use the quantum-statistical Green's function approach and Kubo theory to calculate the giant magnetoresistance (GMR) in magnetic multilayered structures. Our calculation can reproduce the main features of GMR experiments, including the oscillations of GMR with nonmagnetic thickness, and the GMR increases with increasing number of bilayers N of the (Fe/Cr)_N/Fe system and others. As well, the question whether or not the scattering rates due to the impurities, surfaces, and interfaces add up is also addressed to.     

Implementation of a beam deflection system for studies of liquid interfaces on beamline I07 at Diamond

X‐ray optics, based on a double‐crystal deflection scheme, that enable reflectivity measurements from liquid surfaces/interfaces have been designed, built and commissioned on beamline I07 at Diamond Light Source. This system is able to deflect the beam onto a fixed sample position located at the centre of a five‐circle diffractometer. Thus the incident angle can be easily varied without moving the sample, and the reflected beam is tracked either by a moving Pilatus 100K detector mounted on the diffractometer arm or by a stationary Pilatus 2M detector positioned appropriately for small‐angle scattering. Thus the system can easily combine measurements of the reflectivity from liquid interfaces (Q_z > 1 Å^?1) with off‐specular data collection, both in the form of grazing‐incidence small‐angle X‐ray scattering (GISAXS) or wider‐angle grazing‐incidence X‐ray diffraction (GIXD). The device allows operation over the energy range 10–28 keV.     

Influence of Interface Scattering and Quantum Size Effect on the Giant Magnetoresistance in a Magnetic Sandwich Structure

An analytical Green's function approach to the study of the electronic transport in a magnetic sandwich structure is presented. Taking into account the quantum size effect and considering three types of scattering from bulk impurities, rough surface, and two rough interfaces, we calculate the one-particle Green's function and the in-plane conductivity, yield a new formula for conductivity. It is found that (i). the magnetoresistance in the ultrathin spin-value sandwiches shows oscillation as a function of thickness with a period of half Fermi wavelength; (ii) in the thin-film limit and the lowest-order approximation of the surface and interface scatterings, the total conductivity is given by a sum of conductivities of all the subbands and the two spin channels, for each subband and each spin channel the scattering rates due to the impurities, surfaces and interfaces are additive.