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# TE Modes in a Rectangular Waveguide

**Dan McCoy**

and

Matthew Beyer

**May 8, 1997
**

### Abstract:

This project explores the behavior of electromagnetic plane waves confined to a hollow pipe (waveguide), rectangular in shape. We consider the walls of the waveguide to be perfectly conducting. This allows us to consider the parallel component of and the perpendicular component of to be equal to zero at the inner wall of the waveguide. Using these boundary conditions, it is possible to derive a relationship for transverse electric (TE) waves propagating down the waveguide. The equation for TE waves has a number of solutions, called modes, which are differentiated by a corresponding eigenvalue. These modes are graphically depicted in figures to follow. It can be seen, through an analysis of the angular frequency and wavenumber, that only waves of a certain frequency can propagate down the waveguide. Also, the energy, and hence the information, carried by the wave, travels at a specific group velocity, given in terms of angular frequency. Wave phenomenon confined to a rectangular waveguide is therefore described in terms of mode, cut off frequency, and group velocity.

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*Electromagnetism *

Thu May 8 10:47:29 EDT 1997