Bodies of revolution form an interesting class of scattering objects because they represent actual finite three-dimensional objects for which highly accurate reference solutions can be produced to test general-purpose simulation software. Further, in certain applications a body of revolution is the core design assumption of e.g. an antenna that should be polarization independent. Examples are classic parabolic dishes and corrugated horn antennas.
From a computational point of view, the scatting by a perfectly electrically conducting body of revolution can be addressed by a sequence of one-dimensional integral equations (one per Fourier mode around the axis of rotation), for which the so-called modal Green function must be computed, which depends on the index of the Fourier mode. Although the integral representation is simple to express in terms of the three-dimensional free-space Green function, the actual numerical calculation of this integral has shown to be tedious and many methods have been proposed in the literature. Most of these work well for relatively small Fourier indices, but become increasingly inaccurate for Fourier indices associated with highly oscillating modes. In our research, we have developed and demonstrated two methods based on recurrence relations that are provably stable and highly accurate up to very large Fourier index. These have been demonstrated for both the electric field integral equation and the magnetic field integral equation, see [1-4].
We show here examples of a perfectly electrically conducting cone and sphere with scattering cross-sections compared to results in the literature. Further, we show the field pattern in the focal plane of a parabolic dish with a cross-sectional radius of 400 wavelengths, for an obliquely incident plane wave incident under zenith distance 胃. The results were computed using up to Fourier mode indices from -1910 to 1910 for the largest angle of incidence of 45 degrees. These results were obtained using Matlab 2019b on a laptop with 16 GB of RAM and an Intel core i7-8850H processor. More details on these results can be found in [4].
[1] Vaessen, J. A. H. M., Beurden, van, M. C., & Tijhuis, A. G. (2012)
[2] Sepehripour, F., & van Beurden, M. C. (2022)
[3] Sepehripour, F., van Beurden, M. C., & de Hon, B. P. (2022) ;
[4] Sepehripour, F., de Hon, B. P., & van Beurden, M. C. (2023)