Why is the lowest TM mode TM11 and not TM10 in a waveguide?

[rabbit44]

Homework Statement

I have to find the ratio of the lowest TM cutoff frequency to the lowest TE cutoff frequency.

Homework Equations

The Attempt at a Solution

I have derived the general form of the cutoff frequency (which seems to be the same for both). I get the right answer if I take TE10 and TM11; but why is this? I know why you can't have TE00 or TM00, but why can't TM take TM10?

Thanks

 

[gabbagabbahey]

What shape waveguide is this in reference to?

Assuming you are talking about a rectangular waveguide, what happens to the component of the electric field along the axis of the waveguide for TM10 and TM01? What does that make all the other components? Are those really TM modes?