<p>We consider the two-phase design optimization problem for a linear scalar second-order elliptic equation with complex-valued material parameters modeling dielectric and conductive properties in time-harmonic electrostatics as they arise, e.g., in sensor design optimization. Owing to the complex-valued material parameters, application of well-established topology optimization theory is not directly possible. We discuss obstacles and limitations of the relaxation via homogenization method in this context and derive a gradient descent method based on restriction of admissible designs to simple laminates. Numerical simulations showcase the functioning of the method for optimizing the design of an electric field sensor.</p>