Shape optimization for the strong directional scattering of dielectric nanorods

In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing light. studied setting, light interacts with penetrable dimension comparable to wavelength an incoming planar wave. The design objective is maximize scattering efficiency inside target angle window. For this, Helmholtz problem piecewise constant refractive index medium models wave propagation, and accurate Dirichlet-to-Neumann map exterior domain. strategy consists using high-order finite element (FE) discretization combined gradient-based numerical optimization. latter quasi-Newton (BFGS) backtracking line search. A discrete adjoint method used compute sensitivities respect variables. Particularly, for FE representation curved shape, use bilinear transfinite interpolation formula, which admits explicit differentiation We exploit fact show in detail how are obtained setting. test our variety angles, different frequencies, indexes. all cases, efficiently reach designs featuring high efficiencies that satisfy required criteria.