• Froufe Perez Luis Salvador

• Froufe Perez Luis Salvador

Abstract
This course introduces both ordered and disordered optical materials, the theory underlying its fundamental optical properties and the numerical tools commonly used in its research. The main goal being to familiarize students with the state of the art in this field.

Subjects
    • Elements of light scattering: Introduction to the basics of light scattering. Scattering by small particles. Scattering by spherical objects, an introduction to the Mie theory. Resonances, field distributions, near-field effects and its nanophotonics implications. Numerical codes for the Mie theory.
    • Photonic crystals (PCs): Photonic band structure (allowed and forbidden bands), light emission and transport in PCs, Density of states (DOS) and local density of states (LDOS) in PC's.
    • Numerical band structure determination: Planewave expansion method. Introduction to MPB (http://ab-initio.mit.edu/wiki/index.php/Main_Page) and hands-on examples.
    • Maxwell’s equation in the time domain: Finite difference Time Domain method. Numerical stability. Boundary conditions, common approaches. Introduction to MEEP (http://ab-initio.mit.edu/wiki/index.php?title=Meep) and hands-on examples.
    • Maxwell’s equations in the frequency domain: Extending the Mie theory; T-Matrix and multiple multipole expansions. The discrete dipole and coupled dipoles approximations. Discussion of other methods. Introduction to available software (DDSCAT, MSTM, etc).
    • Disorder in photonics: A gentle introduction to the radiative transfer equation. The diffusion approximation and relevant transport parameters. 
    • Optical Forces: Introduction to optical tweezers and interactions induced by random optical fields. Theory and numerics.

The objective of the course is to develop an insight on classical and advanced subjects in light transport. Students shall be familiar with the standard theoretical approaches to treat classical light-matter interaction in complex systems such as Mie scattering and its generalizations as well as the physics of photonic crystals (band theory) and the physics of disordered systems (light diffusion). On the other hand, some of the most widely adopted numerical approaches to solve electromagnetic radiation-matter interactions shall be presented as well as some freely avaiable software packages.
In a nutshell, students will be able to practically solve many common problems found in modern photonics and understand the underlying physics.

Scientific programming skills are welcomed but not strictly necessary. 
Having a reasonable understanding of basic electromagnetism is highly recommended.
The evaluation is  pass/fail and it is based on the completion of a small project of light scattering to choose among several problems. Projects will be presented early in the course so that they can have a clear idea of the expected work load.

Class notes and slides will be used together with some selected chapters of different books and relevant articles. In particular some parts of the following books might be useful.
    • “Light Scattering by Small Particles”, H.C. van de Hulst.
    • “Absorption and Scattering of Light by Small Particles”,  C.F Bohren, and D.R Huffman.
    • “Photonic Crystals: Molding the Flow of Light”, J.D. Joannopoulos, S.G. Johnson, J.N. Winn, and R.D Meade.
    • “Understanding the FDTD Method”, J. B. Schneider. Free on-line www.eecs.wsu.edu/~schneidj/ufdtd, 2010.
    • “Scattering of electromagnetic waves: numerical simulations”, L. Tsang, J. A. Kong, K-H Ding, and C.O. Ao.
    • “Principles of diffuse light propagation”, J. Ripoll.
    • “Optical Tweezers: Principles and Appilactions”. P. H. Jones, O. M. Maragó, and G. Volpe.

Presentation of a project at the end of the course.