What they are

• A waveguide is a constrained path into which waves are sent. It essentially consists of a tube open at the ends, whose walls reflect the waves and trap them inside the tube itself.
• There are waveguides of different types, depending on the nature of the waves that are to be "guided".

Some examples:

electromagnetic waves: microwave guides are metal tubes into which microwaves are radiated. They usually have a rectangular cross-section. Optical fibres are waveguides for light. They consist of a tube of transparent material (such as glass, or certain polymers), surrounded by a cladding of a material with a lower refractive index. Internal reflection occurs in this case because of the phenomenon of the critical angle.

Optical fibre carrying a red laser beam

sound waves: the speaking tube once used for internal communication on ships, aircraft, submarines and other vehicles[1] the ear canal (the cavity leading from the outer ear to the eardrum). See anatomy of the auditory system.

Speaking tube in the military museum of Fort McArthur, San Pedro, California

What they are for

The very name of these devices indicates that they force a wave to follow a certain path, instead of propagating freely in the surrounding space. The example of optical fibres is perhaps the easiest to see: light, instead of propagating in all directions, follows the fibre. In the case of electromagnetic waves, waveguides are used both to guide the power of the wave and, in telecommunications, the signals it carries.

In the acoustic case too, waveguides act as directional amplifiers, because they concentrate the energy of the sound wave in a particular direction in space (see the section on wind instruments).

How they work

• The waves enter at one end and propagate in the guide.
• Propagation along the guide is free (travelling wave), while in the transverse direction standing waves are formed
• This mode of propagation, which "mixes" travelling waves and standing waves, produces some interesting properties, the most important of which are the following:

1. The guide is in general a dispersive medium, even if the medium it contains (the one in which the wave actually propagates) is not dispersive. That is to say, waves of different frequencies in general propagate in the guide with different velocities.
2. In general there is a cut-off frequency, that is, below a certain frequency the waves cannot propagate along the guide at all. They enter it at one end, but no signal comes out at the other. The cut-off frequency typically depends on the width of the guide. The narrower the guide, the higher the cut-off frequency. (In acoustic guides and in optical fibres, however, the fundamental mode propagates at any frequency: the cut-off concerns the higher modes.)
3. The phase velocity of the wave in the guide can be greater than the propagation speed in the medium (see the page dispersion). For electromagnetic waves this means that the phase velocity in the guide can be greater than the speed of light in the medium.

Links

• To explore the properties of waveguides interactively, follow the 2D Waves app paths
• For further details see more on waveguides