Nonsinusoidal Waves in Rectangular Waveguides

It is widely believed that a waveguide behaves like a lossless dispersive medium, which implies that only sinusoidal waves can be transmitted without distortions. This is correct for the particular solutions of Maxwell's equations that have been in use since Rayleigh's original investigation in 1897. More general solutions can be found that show that a large class of nonsinusoidal periodic waves can be transmitted distortion-free by a lossless waveguide. These solutions are readily derived for rectangular waveguides by means of the Fourier series, while a generalization of the Fourier series is required for cylindrical waveguides.