In the last 20 years a considerable research effort has been dedicated to light transport phenomena in complex dielectric structures like photonic crystals and disordered dielectrics. In disordered systems light follows a diffusive type of propagation, like electrons in a resistor. In that context, several optical analogies of electron transport phenomena have been identified, like localization of light, the optical Hall effect, and optical Bloch oscillations. If optical gain is added to a random material, a unique light source is obtained, often referred to as a random laser. On the other extreme, periodic dielectric structures behave as a crystal for light waves. The study of how light waves behave in complex photonic structures is interesting from a fundamental point of view but also has enormous potential applications in the field of photonics, telecommunications, and medical diagnostics.
In this seminar I will give an overview of recent results in this field of research. I will start from disordered structures, then give examples of intermediate systems like liquid crystals and quasi-crystals, and end with ordered photonic crystals.