Why do small waveguides support less modes than larger ones?

[Jin Huang]

I've taken several courses on Electromagnetics and Waveguide. It has become common sense to me that small waveguides support less modes than larger ones. I've also learned the graphical method to calculate the number of modes in a 3-layer slab waveguide.

What I don't get is why small waveguides support less modes than larger ones. Is there a reasonable analogy to help get insight on this fact?

Thanks very much!

 

[marcusl]

In an ideal waveguide the modes are the same, but their frequencies scale with dimension.

 

[sophiecentaur]

In an ideal waveguide the modes are the same, but their frequencies scale with dimension.

Yes. The modes are all the same - just scaled according to wavelength / waveguide dimensions.
It's possible that the very highest modes for the smaller waveguides may be attenuated faster due to the practical properties of the interior surface of the waveguide - the geometry has to yield to surface impedance.