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.