These notes accompany the lecture 'Crystal Optics in Intense Light Fields' taught by Prof. Fiebig in 2025. I chose to cover this course because it provides a solid fundamental basis for my PhD work. The material is primarily based on the unofficial notes from 2015 (as Prof. Fiebig refers to them), combined with his current lecture slides, though the order has been slightly adjusted. All content is written in my own words.

Table of Contents

These lecture notes explore how light interacts with matter in modern materials and systems, with a special focus on the role of symmetry. We will look at both linear and nonlinear effects, building from fundamental concepts to phenomena at the forefront of current research.

We begin with a macroscopic view of crystal optics, introducing symmetry operations and their use in tensor equations. This naturally leads to the basics of group theory, which provides a powerful framework for understanding optical effects in crystals. After a brief review of light polarisation and common notations, we examine how light behaves in crystals without external influences.

From there, we move into the study of linear optical effects, including how light is influenced by electric and magnetic fields. One chapter is dedicated to magneto-optics, where we also take a first step toward a microscopic understanding of these interactions.

The second half of the course shifts toward nonlinear optics—phenomena that arise when materials respond in a non-proportional way to light. We introduce the general theory and then apply it to key examples. Finally, we look at the experimental techniques used to probe these nonlinear effects.

Throughout, the goal is to build an understanding of how symmetry and light together shape the behaviour of materials, from basic effects to advanced applications.

Table of Contents

1 Macroscopic Description of Crystal Optical Effects
2 Light Polarisation and Dispersion
3 Magneto-Optics
4 Light-Matter Interaction
5 Nonlinear Optics
6 Experimental Methods of Nonlinear Optics