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Advanced Course, 5 credits, PAP315, Autumn 2020, Period 1

The course Electromagnetic Scattering I offers an introduction and theoretical foundation for elastic electromagnetic scattering by arbitrary objects (usually called particles). As compared to the wavelength, the sizes of the objects can be small or large, or of the order of the wavelength. As to the shape of the objects, main emphasis is on spherical particles and, subsequently, on the so-called Mie scattering. The optical properties of the objects are typically described by the refractive indexComputational light scattering assesses elastic light scattering (electromagnetic scattering) by particles of arbitrary sizes, shapes, and optical properties. Particular attention is paid to advanced computational methods for both single and multiple scattering, that is, to methods for isolated particles and extended media of particles (cf. dust particles in cometary comae and particulate media on asteroids). Theoretical foundations are described for the physics of light scattering based on the Maxwell equations and for a number of computational methods. In single scattering, the methods include, for example, the volume integral equation, discrete-dipole approximation, T-matrix or transition matrix, and finite-difference time-domain methods. In multiple scattering, the methods are typically based on Monte Carlo ray tracing. These include far-field radiative transfer and coherent backscattering methods and their extensions incorporating full-wave interactions. Students are engaged in developing numerical methods for specific scattering problems. The development and computations take place in both laptop and supercomputing environments.

Course is held virtually in Zoom, on Mondays 10-12 and Wedsnesdays 12-14. Exercise sessions are also in Zoom, on Mondays 9-10 and Wednesdays 9-10.

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Recommended preliminary knowledge: basic courses in Physics, basic courses in Mathematics, Electrodynamics, Mathematical Methods for Physicists I & II, Scientific Computing I.

The scattering course starts by a review of classical electromagnetics introducing the Maxwell equations, the energy and impulse of electromagnetic fields, and Poynting's theorem. The wave equations are derived from the Maxwell equations and electromagnetic plane waves are discussed. The fundamentals of electromagnetism are followed by the necessary framework for classical scattering theory, defining the incident, internal, and scattered fields and the scattering plane as well as the scattering angle. The Stokes parameters and Mueller matrices are introduced. Thereafter, the 2 x 2 amplitude scattering matrix and the 4 x 4 scattering matrix are described.

The Fresnel reflection and refraction of electromagnetic plane waves on a plane interface are discussed as the first electromagnetic scattering problem, utilizing 4 x 4 Mueller matrices for reflection and refraction. A treatment on scattering at long wavelengths follows, introducing the electric and magnetic multipoles and Rayleigh scattering, in particular. Particle shape is next taken into account in what is called the Rayleigh-Gans approximation. The scattering problem is presented in the volume-integral-equation formalism.

The rigorous treatment on electromagnetic scattering by spherical particles (Mie scattering) follows thereafter using multipole expansions. This involves the development of mathematical methods utilizing vector spherical harmonics. After Mie scattering, scattering at short wavelengths follows, relying partly on the reflection and refraction treatments in the early parts of the course. Main emphasis is however in diffraction of waves by obstacles, shedding light on Fraunhofer and Fresnel diffraction as well as on Kirchhoff integral relations between fields near the obstacles and the far fields. Towards the end of the course, the student will learn basics of computational methods for scattering by nonspherical particles, such as the discrete-dipole approximation and the T-matrix method.

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