2
$\begingroup$

I understand (from Feynman lectures) that in a rectangular waveguide multiple reflections from the boundary of the conducting walls gives rise to an interference-like pattern and hence they propagate with a dispersive phase constant. And only TE (transverse electric) and TM (tranverse magnetic) waves can be possible within the waveguide due to the boundary conditions.

But my doubt is:

  • what happens if the other end of the waveguide is left open and the waves can travel into free space? will the waves continue to travel as TE, TM waves or they change into TEM (tranverse electro magnetic waves)?

  • Do different frequencies have different phase constant?

It would be really helpful if I get this clarified.

Improve this question
$\endgroup$

2 Answers 2

Reset to default
2
$\begingroup$

A waveguide terminating to free space is an aperture antenna. As with any antenna, the radiated waves in the far field (many wavelengths and aperture dimensions away from the aperture) propagate as TEM waves.

As Feynman also makes explicit, the phase constant is frequency dependent: $$ \beta = k\sqrt{1-\omega_c^2/\omega^2}=\frac 1 c\sqrt{\omega^2-\omega_c^2} $$ $c$ is the propagation velocity and $\omega_c$ is the cutoff frequency, which depends on the mode and waveguide dimensions.

Improve this answer
$\endgroup$
0
$\begingroup$

In free space you can have waves that are TE and TM, but the TE and TM components decay rapidly with distance to the source (as a power of $R/\lambda$). The TEM components of free space waves decay much less rapidly.

Your second question about phase contrast seems unrelated, I would need further clarification to answer this.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.