Level-set based topology optimization for electromagnetic dipole antenna design

This paper presents a level-set framework for a typical electromagnetic design problem of dipole antenna. In this study, the geometrical configuration of an antenna is represented by the zero-level contour of a higher-dimensional level-set function. The governing equation for the induced current flow on a metal surface is the Electric Field Integral Equation (EFIE), which takes into account the electric component of the incident wave. The design objective is formulated in terms of the surface current and incident electric field. The normal velocity of the level-set model, which reflects the sensitivity of the objective function, is derived from the adjoint variable method and shape derivative. By optimizing the objective function, the area with the highest current density, to which the voltage feeding should be applied, can be reshaped. The advantages of adopting the level-set technique for electromagnetic design lie in its capacity for capturing sophisticated topological changes and facilitation in mathematical representation of the design configuration. The demonstrative examples of dipole antenna design show that the level-set method results in a fairly smooth optimization process, where the vacuum/metal interface gradually attains its optimal configuration. A series of design cases with self-adjoint and non-self-adjoint sensitivity analyses are studied and compared to the benchmarking problems in dipole antenna.