# Light-Matter Interactions

Within the following problems we will discuss different **models** to understand the interaction of light with matter. The acquired knowledge will help us to derive fundamental **electrodynamic effects** and deduce the electrodynamic properties of materials, for example their **dispersion relation**. The problems shall provide a connection to following courses on theoretical optics.

The Drude model explains the electrodynamic **properties of metals**. The **simple approach** is to regard the conduction band electrons as non-interacting electron gas and yields a fairly **accurate description** of metals like silver, gold or aluminium.

It is known that a **free electron gas** prone to a periodic electric field obeys **oscillations**. One might ask what happens if an **additional external magnetic** field is acting on the plasma. In this problem we will discover how the magnetic field changes the **dispersion relation**. This will later allow us to understand how the magnetic field in the universe is measured using the "**Faraday Rotation**".

In The Dispersion Relation of a Magnetized Plasma we found that a magnetic field alters the dispersion relation differently for left and right polarized light passing through a plasma. But what about a **linear polarized** wave? The emerging effect is termed the "**Faraday Rotation**" and has numerous applications. Find out what we can learn about the **cosmos** and **graphene** using this effect.

**Graphene** is a monolayer of carbon atoms and offers extremely interesting physics. Its **unique properties** may very well make it the silicon of the 21st century. For practical applications it is of great importance to **model** this material containing the main electromagnetic features. Find out in this problem how graphene can be represented as a **thin layer** with a **certain permittivity** and how this can be used for next-generation electromagnetic devices.