• Electrodynamics
  • Math Basics
  • Science Blog
  • Tools
  • Contribute
  • About
  • Publications

Photonics101

Electrostatics

  • Charges → Electric Fields
  • Forces and Movement
  • Multipole Moments
  • Capacitors & Co - Dielectrics
  • Boundary Value Problems

Magnetostatics

  • Currents → Magnetic Fields
  • Magnetic Fields in Matter

Circuit Theory

  • Transmission Lines
  • Basic A.C. Circuits

Full Electrodynamics

  • Light-Matter Interactions
    • The "Permittivity" of Graphene
    • The Dispersion Relation of a Magnetized Plasma
    • The Faraday Rotation
    • Drude Model: Metal Conductivity
  • Radiation and Antennas
  • Relativistic Electrodynamics

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.

Drude model: Deriving the Conductivity and Permittivity of Metals

  • plasma frequency
  • Ohms law

The conductivity of metals is derived using the Drude model, schematic.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.

Read more ...

The Dispersion Relation of a Magnetized Plasma

A circular polarized plane wave acts on an electron.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".

Read more ...

The Faraday Rotation - How an Electron Gas and a Magnetic Field Rotate a Plane Wave

  • plasma frequency
  • dispersion relation

A plane polarized wave gets rotated by a magnetized plasma.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.

Read more ...

The "Permittivity" of Graphene

Calculation of a three dimensional permittivy of graphene.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.

Read more ...