Three-dimensional quasi-conformal transformation optics through numerical optimization

In this paper we demonstrate the possibility to achieve 3-dimensional quasi-conformal transformation optics through parametrization and numerical optimization without using sliding boundary conditions. The proposed technique, which uses a quasi-Newton method, is validated in two cylindrical waveguide bends as design examples. Our results indicate an arbitrarily small average anisotropy can be achieved in 3D transformation optics as the number of degrees of freedom provided by the parametrization was increased. The waveguide simulations confirm modal preservation when the residual anisotropy is neglected.