Topology optimization of optical nanoantennas with desired multipoles

Engineering the field scattered by an object is an important problem across the entire electromagnetic spectrum. For example, directional scattering achieved by means of nanoantennas is sought for applications in integrated optics, nanophotonics, sensing, single photon sources, and quantum information processing. Since a scattered field can be decomposed into a superposition of multipolar fields, the multipole decomposition technique provides an ideal platform for scattering engineering. In this paper, we present a topology optimization method for the inverse design of nanostructures to achieve specific multipoles with amplitude and phase control at a given wavelength. Our technique is formulated based on the discrete dipole approximation (DDA), and the optimization objective is specified as the current density associated with each multipole. Our approach operates on near-field quantities and is computationally lighter than similar methods targeting the far-field. Moreover, we can enforce a desired size/shape of the design volume, e.g., to meet fabrication or diffractionless constraints. We demonstrate our method by optimizing dielectric and metallic nanoantennas to achieve directional scattering based on the Kerker effect, using different excitation sources, including a plane wave and a dipole emitter. However, the generality of our approach makes it suitable for engineering nanoantennas with arbitrary scattering properties under various illumination conditions.