HUOM! OPINTOJAKSOJEN TIETOJEN TÄYTTÄMISTÄ KOORDINOIVAT KOULUTUSSUUNNITTELIJAT HANNA-MARI PEURALA JA TIINA HASARI

### 1. Course title

Sähkömagneettinen sironta I

Elektromagnetisk spridning I

Electromagnetic Scattering I

2. Course code

PAP315

Aikaisemmat leikkaavat opintojaksot 53919 Sähkömagneettinen sironta I, 5 op

3. Course status: optional

*-Which degree programme is responsible for the course?*Master’s Programme in Particle Physics and Astrophysical Sciences

*-Which module does the course belong to?*

PAP300 Advanced Studies in Particle Physics and Astrophysical Sciences (optional for Study Track in Astrophysical Sciences)

*-Is the course available to students from other degree programmes?*Yes

4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)

Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle

degree/EQF level 7

Doctoral level = third-cycle (doctoral) degree/EQF level 8

*-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree**on University Degrees)?*Advanced studies

5. Recommended time/stage of studies for completion

After the theoretical astrophysics package in the B.Sc. programme for physical sciences.

### 6. Term/teaching period when the course will be offered

The course is offered in the autumn in period I every other year.

### 7. Scope of the course in credits

5 cr

### 8. Teacher coordinating the course

Karri Muinonen and Antti Penttilä

### 9. Course learning outcomes

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 index.

### 10. Course completion methods

The course can also be taken individually with flexible timing after a discussion and planning session with the lecturers.

### 11. Prerequisites

Theoretical astrophysics package in the B.Sc. programme for physical sciences. Theoretical physics package including electrodynamics in the B.Sc. programme for physical sciences.

### 12. Recommended optional studies

Electromagnetic Scattering II

### 13. Course content

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.

During the course, students prepare and present short oral contributions on topics of relevance for light scattering. Additionally, each student acts as an opponent for another student.

14. Recommended and required literature

Set reading:

K. Muinonen, Electromagnetic Scattering I, Lecture Notes, 2012 (latest draft)

C. F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley & Sons, 2010

J. D. Jackson, Classical Electrodynamics, Wiley & Sons, 1998

Supplementary reading:

H. C. van de Hulst, Light Scattering by Small Particles, Wiley & Sons, 1957 (Dover, 1981)

M. I. Mishchenko, J. W. Hovenier, \& L. D. Travis, Light Scattering by Nonspherical Particles, Academic Press, 2000

M. I. Mishchenko, L. D. Travis & A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, 2002

A. Doicu, Y. Eremin & T. Wriedt, Acoustic & Electromagnetic

Scattering Analysis Using Discrete Sources, Academic Press, 2000

### 15. Activities and teaching methods in support of learning

The course is composed of exercises, a project, and a final exam.

### 16. Assessment practices and criteria, grading scale

The grading scale for accepted outcomes is 1-5 based on the final exam and the bonus points obtained from the exercises and the project work.

### 17. Teaching language

English