Shape optimization of conformal array antennas

We present a shape optimization method for the minimization of the active reflection coefficient for conformal array antennas. Our formulation is based on the continuum form of Maxwell's equations, where the gradient of the goal function is expressed in terms of the solution to the original field problem and the solution to an adjoint field problem. The computational work for the goal function and its gradient amounts to the computation of the scattering matrix, which makes our method independent of the number of degrees of freedom used to parameterize the geometry. In addition, the field solver is decoupled from the optimization process, which offers great freedom in the choice of field solver. The method is tested in two dimensions for an array antenna that conforms to a circular cylinder. An optimum is found in approximately 10 iterations when four degrees of freedoms are used to describe the antenna geometry and in approximately 30 iterations when 40 degrees of freedoms are used.