We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanied by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

RIPL – Reference Input Parameter Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations

A new method is proposed for the computation of the radar cross section and other associated field quantities arising when a smooth, perfectly conducting obstacle is illuminated by an incident electromagnetic wave. The scattered wave is first represented by a distribution of electric dipoles over the surface in question, with the response from any dipole proportional to the induced surface current density at that point. The surface current is then determined by the "boundary condition" that the scattered wave, through interference, precisely cancels the incident wave inside the obstacle. One obtains in this mariner a pair of coupled (infinite) matrix equations for the surface current. Green's identity permits decoupling of the equations, reducing the problem to roughly the equivalent of two independent scalar problems. The equations have been specialized to axially symmetric obstacles and then solved numerically on the IBM 7094 for several examples of interest. Reciprocity and energy conservation are also examined and the resonant mode (interior) problem set up explicitly in matrix form.

Matrix formulation of electromagnetic scattering

Light transport algorithms generate realistic images by simulating the emission and scattering of light in an artificial environment. Applications include lighting design, architecture, and computer animation, while related engineering disciplines include neutron transport and radiative heat transfer. The main challenge with these algorithms is the high complexity of the geometric, scattering, and illumination models that are typically used. In this dissertation, we develop new Monte Carlo techniques that greatly extend the range of input models for which light transport simulations are practical. Our contributions include new theoretical models, statistical methods, and rendering algorithms. We start by developing a rigorous theoretical basis for bidirectional light transport algorithms (those that combine direct and adjoint techniques). First, we propose a linear operator formulation that does not depend on any assumptions about the physical validity of the input scene. We show how to obtain mathematically correct results using a variety of bidirectional techniques. Next we derive a different formulation, such that for any physically valid input scene, the transport operators are symmetric. This symmetry is important for both theory and implementations, and is based on a new reciprocity condition that we derive for transmissive materials. Finally, we show how light transport can be formulated as an integral over a space of paths. This framework allows new sampling and integration techniques to be applied, such as the Metropolis sampling algorithm. We also use this model to investigate the limitations of unbiased Monte Carlo methods, and to show that certain kinds of paths cannot be sampled. Our statistical contributions include a new technique called multiple importance sampling, which can greatly increase the robustness of Monte Carlo integration. It uses more than one sampling technique to evaluate an integral, and then combines these samples in a

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Robust Monte Carlo methods for light transport simulation

1. Introduction: mesoscopic physics 2. Wave equations in random media 3. Perturbation theory 4. Probability of quantum diffusion 5. Properties of the diffusion equation 6. Dephasing 7. Electronic transport 8. Coherent backscattering of light 9. Diffusing wave spectroscopy 10. Spectral properties of disordered metals 11. Universal conductance fluctuations 12. Correlations of speckle patterns 13. Interactions and diffusion 14. Orbital magnetism and persistent currents 15. Formulary Index.

/pdf/mesoscopic-physics-of-electrons-and-photons-3ycvopdvcp.pdf

Mesoscopic Physics of Electrons and Photons

Diffuse Surface Optical Model for Nucleon-Nuclei Scattering

Approximate expressions are obtained for the coherent radiation loss by electrons in a synchrotron in the presence of finite parallel plate metallic shields, such as the pole faces of the magnet. The results would seem to provide a useful interpolation between the two simple limiting cases of shielding by infinite plates and no shielding at all.

Suppression of Coherent Radiation by Electrons in a Synchrotron

Tensor Scattering Matrix for the Electromagnetic Field

Modifications of the Hulth\'en-Kohn variational principle are introduced with the hope of increasing the usefulness of variational methods. Although no simple formulation of general utility is found, it is shown that there exists a great variety of stationary expressions which make possible a greater freedom in the choice of variational principles than has hitherto been demonstrated. Some criteria for the selection of special forms are discussed.

Variational Methods in Scattering Problems

AMERICAN ASSOCIATION FOR Libe] THE ADVANCEMENT OF SCIENCE Science serves its readers as a forum for the presentaOur I tion and discussion of important issues related to the even a 1 advancement of science, including the presentation of minority or conflicting points of view, rather than by unable publishing only material on which a consensus has been science reached. Accordingly, all articles published in Science-including editorials, news and comment, and the futu book reviews-are signed and reflect the individual idea as views of the authors and not official points of view adopted by the AAAS or the institutions with which the acquair authors are affiliated. and th(

David S. Saxon

Papers

Diffuse Surface Optical Model for Nucleon-Nuclei Scattering

Suppression of Coherent Radiation by Electrons in a Synchrotron

Tensor Scattering Matrix for the Electromagnetic Field

Variational Methods in Scattering Problems

Liberal education in a technological age.