We don’t like to think of conducting traces on PCBs (printed circuit boards) as waveguides because it forces us to confront the ongoing lie we’ve been living in our cosy, digital domiciles in this harsh analogue reality.
Think back to the college version of waveguides and the friendly geometry presented in homework problems. It’s a simple boundary value problem: What are the cutoff frequencies for TE (transverse electric) and TM (transverse magnetic) waves propagating along a uniform conducting cylinder?
By solving Maxwell’s equations subject to the conditions that the tangential component of the electric field and the normal component of the magnetic field are zero on the conducting surface, we get a set of TE waves that happily propagate along the cylinder. The boundary conditions limit the waves that the guide can transmit to those above a cutoff frequency. That cutoff is easy to remember because the boundary conditions are the same for an oscillating guitar string: the longest wavelength the guide can hope to transmit is twice the largest transverse dimension of the wave guide. For a cylinder, the wave has to have a wavelength smaller than twice its diameter.
Optic fibres as waveguides are similar, but the boundary conditions are messier. Light propagates down the fibre core and evanesces in the cladding. Evanescence means that tiny fractions of the wave’s energy propagate within the cladding. The diameter of the core of a single-mode fibre is small enough that only one mode can propagate within the wavelength range of the transmitting laser.
“Modal dispersion” occurs in multimode fibers when the core has a diameter larger than a full wavelength of light, allowing two or more distinct modes of oscillation. The signal disperses because each mode travels at a different velocity.
next; multimoding in pcbs