Electromagnetic scattering by nonspherical particles: Recent advances

This note gives a short introduction to the reprint of the article “Numerical methods in electromagnetic scattering theory” by Kahnert, M (JQSRT 2003;79-80:775-824). Some of the most important developments in the field since the publication of this article are briefly reviewed. A list of typos that have been identified in the original article is given in the appendix.     

Scattering in thick multifractal clouds, Part I: Overview and single scattering

Over the last twenty years, many studies have been made of radiative transfer in scaling cloud fields, the vast majority of which have been limited to numerical studies in clouds with relatively small optical thickness. An exception to this was the development of a formalism for treating single scattering in optically thick but conservative multifractal clouds without significant holes. In part I of this paper we show how these results can be extended to general “universal” multifractal clouds dominated by low density “Lévy holes”. In part II, we demonstrate how the analytic single scattering results can be generalized to multiple scattering including the case of very thick clouds as well as to realistic nonconservative clouds.     

Scattering in thick multifractal clouds, Part II: Multiple scattering

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to long range correlations, the photon paths are “subdiffusive” with the corresponding fractal dimensions tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This is explored further using discrete angle radiative transfer (DART) approach in which the radiances decouple into non-interacting families with only four (for 2-D clouds) radiance directions each. Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the accuracy is only limited by the spatial discretization.By “renormalizing” the cloud density, we relate the mean transmission statistics to those of an equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating effects act in contrary directions: the “holes” which lead to increased single scatter transmission and the tendency for multiply scattered photons to become “trapped” in optically dense regions, thus decreasing the overall transmission.     

“Step-up” versus “step-down” scattering asymmetry in the neutralization of H on free-electron vicinal metal surfaces

The charge transfer between H⁻ and a free-electron vicinal metallic surface is studied using a wave-packet propagation method. We apply a statistical Thomas-Fermi-von Weizsäcker model with a local density approximation for the exchange-correlation energy to compute the ground-state electronic structure of the substrate. The long-range image charge effects in the electron transfer are included on a phenomenological level. We obtain the ion-survival probability from a rate equation for a set of realistic scattering trajectories of projectiles that are incident with a kinetic energy of 50 eV. Our calculations reveal a pronounced substrate orientation dependence of the charge transfer dynamics expressed in a “left-right” (or “step-up-step-down”) scattering asymmetry in the final ion-survival probability, which is caused by an enhancement of electron loss on the outgoing part of those ion trajectories which approach steps from below.     

Multiple scattering with a linearized propagator

Scattering by a many-body system is studied within the framework of the “fixed scatterer” approximation and the eikonal approximation formulated in terms of a linearized propagator. If properly treated, the “fixed scatterer” approximation is able to take into account the center-of-mass motion. We specifically study the linearized propagator proposed by Abarbanel and Itzykson. Although for potential scattering the above approximation is essentially equivalent to the Glauber eikonal approximation, its physical implications are quite different when applied to scattering by a composite system. The multiple-scattering series can generally no longer be simply expressed in terms of the individual on-shell scattering amplitudes, and the additivity of phase shifts is shown to break down for overlapping potentials. The implications for phenomenological calculations are discussed. Finally, the above approximation is explicitly applied to high-energy elastic nucleon-deuteron scattering and the results are compared with several variants of the Glauber multiple-scattering formalism.     

Analytic bounds on transmission probabilities

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrödinger equation for some complicated potential whose properties we are trying to investigate in terms of some simpler potential whose properties are assumed known, plus a (possibly large) “shift” in the potential. Doing so permits us to extract considerable useful information without having to exactly solve the full scattering problem.     

A Nonperturbative, Finite Particle Number Approach to Relativistic Scattering Theory

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described.     

A transparent macroscopic sphere is cross-sectionally equivalent to a superposition of two quantum-like radial potentials

We consider two frameworks (i) the electromagnetic generalized Lorenz-Mie theory describing the interaction between an electromagnetic arbitrary shaped beam and a homogeneous, non-magnetic sphere, with an isotropic, linear, material and (ii) a quantum generalized Lorenz-Mie theory describing the interaction between a quantum eigen-arbitrary shaped beam and a quantum radial potential. For the time being, we restrict ourselves in this paper to elastic scattering cross-sections. We then demonstrate that a transparent macroscopic sphere in the first framework is equivalent to a superposition of two quantum-like radial potentials in the second framework. The restrictive meaning of “quantum-like” will be discussed when appropriate.     

Light scattering by “soft” particles of arbitrary shape and size: II—Arbitrary orientation of particles in the space

In this part of the article a new version analysis of light scattering by “soft” particles is presented that makes it possible to reduce and simplify the process of numerical calculations. The calculation results of the integral scattering cross-sections and indicatrices for spheroid, parallelepiped and cylinder for their arbitrary orientation in space are given as an illustration. The results are accompanied by transparent physical interpretations, based on the examination of the contour graphs of the three-dimensional spectra of particles.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

A planar electromagnetic “black hole” based on graphene

Graphene can be used as a platform for transformation-optics devices due to its tunability of conductivity. Besides conductivity, we show that the loss of graphene can also be controlled. Using this priority and taking the advantage of transformation optics, we realize the concept of electromagnetic “black hole” by using of a single-layer graphene. Numerical simulations demonstrate that the surface plasmon polariton waves incident to the “black hole” are bent towards the central area and absorbed by the inner core. The advantages of graphene-based “black hole” are its planar, isotropic, and nonmagnetic characteristics.     

Considerations to Rayleigh’s hypothesis

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.     

Minkowski domain walls in hyperbolic metamaterials

Minkowski domain walls are being actively considered in gravitation theory. They may form during a vacuum phase transition, or as a result of braneworld collision. Despite having interesting physical properties, Minkowski domain walls had remained in the theoretical domain only since their first introduction a few decades ago. Here we demonstrate how to make an electromagnetic analogue of a Minkowski domain wall using hyperbolic metamaterials. We analyze electromagnetic field behavior at the wall, and present a simple experimental model of “Minkowski domain wall” formation due to “collision” of two Minkowski spaces.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.     

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在"星光Ⅱ"钕玻璃激光装置上,开展了脉宽约0.8ns、能量~70J的351nm激光在不同条件下辐照Au盘靶的实验,研究了激光光束质量对受激布里渊散射(SBS)谱的影响。SBS散射光谱测量结果表明,在激光束未匀滑条件下,SBS散射谱范围为352~360nm;在采用透镜列阵将激光束匀滑聚焦的条件下,激光等离子体密度变得更加均匀,SBS散射光谱范围变为351~351.5nm。实验数据为透镜列阵对光束的匀滑效果提供了直接支持。     

Physics of strongly coupled quark-gluon plasma

This review covers our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in: (i) explaining the RHIC data by hydrodynamics; (ii) describing lattice data using electric-magnetic duality; (iii) understanding of gauge-string duality known as AdS/CFT and its application for “conformal” plasma. In view of the interdisciplinary nature of the subject, we include a brief introduction into several topics “for pedestrians”. Some fundamental questions addressed are: Why is sQGP such a good liquid? What is the nature of (de)confinement and what do we know about “magnetic” objects creating it? Do they play any important role in sQGP physics? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical “gravity dual” to heavy ion collisions?     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.