Numerical method for full calculation of the electromagnetic field in a rectangular waveguide within overmoded configuration, using the fast Fourier transform

This paper describes a method of calculation of the transverse distributions of electric E(x, y) and magnetic H(x, y) fields, in a rectangular waveguide within overmoded configuration – i.e., when a large number eigenmodes are present. It uses the fast Fourier transform, instead of the conventional decomposition in a series of TEMpq modes. Although not using the eigenmode decomposition, this method still exhibits the amplitude of the whole set of eigenmodes TEMpq. As an example, a single mode propagation is shown to facilitate understanding of the method. Another example is shown, using a 2D Gaussian profile as input, which contains a large number of eigenmodes (overmoded configuration). As a result, a series of 2D profiles are displayed along the longitudinal axis z of the waveguide, to show the transverse amplitude distribution of the fields E(x, y, z) and H(x, y, z) when a Gaussian profile is used at waveguide entrance. This non-standard configuration may be observed, for example, in infrared Free-Electron Lasers. This method is used here to calculate the ohmic losses which are integrated along the waveguide propagation, and which are deduced from the transverse distribution of magnetic field