# Waveguides

## Waveguide Animations

Here are some waveguide animations I generated with Mathematica. The animations show the temporal and spatial dependencies of either the electric ($\vec{E}$) or magnetic ($\vec{H}$) fields for different TE and TM modes propagating through rectangular/right-triangular hollow waveguides. Unlike the plain plane-wave solutions typical of electromagnetic waves in free space, the boundary conditions for hollow waveguides don’t allow TEM modes. Instead, the most generic field propagation through a hollow waveguide can be decomposed into modes of two types of: Transverse Electric (TE) and Transverse Magnetic (TM). In a TE mode the E-field is entirely transverse (perpendicular to the direction of propagation), but the H-Field will have a longitudinal component, and vice-versa for a TM mode.

### Right-Triangular Waveguide Modes

Transverse Magnetic (TM) Transverse Electric (TE)

## Mathematica Notebook

The animations on this page, as well as several others, can be viewed from my github repository. The repository also contains the Mathematica notebook I wrote to generate the rectangular waveguide animations: AnimationsRectangular.nb. I’m not including any code particular to the right-triangular geometry, but feel free to download this notebook and generate your own animations for different modes, or linear combinations of modes.