Shape optimization of the total scattering cross section for cylindrical scatterers

We propose and test a gradient-based shape optimization algorithm for the total scattering cross section of infinitely long cylinders, by means of changing the shape of the cylinder's cross section. On the basis of the optical theorem, we derive sensitivity expressions for both dielectric and metal cylinders given an incident plane wave, where the wave vector is perpendicular to the cylinder axis. Both the transverse electric (TE) case and the transverse magnetic case are considered. The sensitivity expressions are based on the continuum form of Maxwell's equations, and they provide the sensitivity with respect to an arbitrary number of shape parameters in terms of the field solution of the original scattering problem and an adjoint scattering problem. These results are used to construct a gradient-based optimization algorithm that we exploit for the reduction of the total scattering cross section in the TE case for metal cylinders, e.g., struts used in reflector antennas. We present optimized cross sections that are oblong in the direction of the incident wave vector, and some of these designs feature corrugations that are parallel to the cylinder axis. We show designs with asymmetric cross sections that yield a low monostatic scattering cross section for certain directions in combination with a low total scattering cross section, which can be used to reduce the noise temperature contributions from the upper strut in an inverted Y tripod reflector antenna