  We develop and apply an optimization method to design invisibility cloaks.
Our method is based on minimizing the forward scattering amplitude of the
cloaked object, which by the optical theorem, is equivalent to the total cross
section. The use of the optical theorem circumvents the need to evaluate and
integrate the scattering amplitude over angle at each iteration, and thus
provides a simpler, more computationally efficient objective function for
optimizing structures. We implement the approach using gradient descent
optimization and present several gradient-permittivity cloaks that reduce
scatter by metallic targets of different size and shape.

Optics