So, you have to start by being clear what waveguide you are talking about - there are many types (some authors, such as Orfanidis, even consider transmission lines a subset of waveguides). For example, optical fiber is also a waveguide.
I'm going to assume that you are reffering to a metal, rectangular or circular waveguide.
First we need to understand what a
propagation mode is. A very poor description is that a mode is a kind of ''stable'' configuration of the fields in a propagating wave. Think of it as if the wave were resonating between the top and bottom walls of the waveguide while it moves forwards. For example, the electric field of a TE
10 mode (where the names come from is not really important right now) looks like this, where you can see how it is ''resonating'' between the sides and resulting in a peak at the center:
What I think people are referring to when they describe a metal waveguide as a high-pass filter is the fact that for a certain size of waveguide, you need a minimum frequency before this "resonance" can occur - in other words, they only allow propagation above a certain frequency - below this they don't work
1.
But then why are waveguides given with a band of operation instead of just a minimum frequency? Because there can be multiple modes (if the wavelength is so small that it fits more than once within the tube, it can form a more complex resonance patter). The second TE mode, the TE
20 mode, for example, is shown below:
Because the resonance requires the wavelength to be at least half as short as the previous mode, this mode can only start propagating at a higher frequency.
Okay, but why is this an issue? As long as the wave is propagating we are good, no?
Not really! The problem is that different modes will travel at different speeds. This can give what we call
modal dispersion. This is problematic because it will change our waveform - imagine that at a certain frequency, at our detector the two modes are exactly 180 degrees out of phase - as a result, they will cancel out (don't get me started on pulse smearing and ISI). Hence we don't want to use our waveguide at this frequency because it will not perform very well (there is also the fact that we get higher losses but that is secondary to multi-mode issues).
The band that a waveguide is specified for is also called the "single-mode region" or single-mode band. The propagation constants for different modes vs frequency are often plotted in a dispersion diagram, which looks like this where we can see that the single-mode region extends from just under 7 GHz to just over 13 GHz for this waveguide:
If the difference in propagation speed is small enough for our applications, we can tolerate them and use a wider band. This is what happens in a multi-mode optical fiber: it is much bigger (= many more resonance modes possible) than the single mode fiber. But, for short ranges (few hundred meters) the modal dispersion due to the different possible modes is acceptable.
The bigger size of the multi-mode optical fiber results in it being much easier to couple light into, and hence the connectors and lasers need to be less precisely aligned, which makes things cheaper.
Notes:
1In strict theory you can say that they do work but the propagation constant will be complex even for ideal, lossless conductors and dielectrics, which means that the fields will decay very quickly