ticks). c) and d) show the internal field intensity distributions at $\lambda=550\,$nm for TE and TM polarization, respectively (left subplot: electric, right: magnetic field). $D=100\,$nm, plane wave incident from the top. []{data-label="fig:fig1"}](fig1)

Recent publications have confirmed the possibility to obtain optimum FW scattering also from elongated structures such as nanopillars, [@person_demonstration_2013] spheroids [@lukyanchuk_optimum_2015] or even from cuboidal dielectric particles [@ee_shape-dependent_2015]. Other dielectric particles on which directional scattering was investigated include nanodiscs for FW/BW directional metasurfaces, [@staude_tailoring_2013; @decker_resonant_2016] patch antennas, [@yang_controlling_2015] V-shaped structures for multi-directional color routing, [@li_all-dielectric_2016] or asymmetric hollow nanodiscs for bi-anisotropic scattering [@alaee_all-dielectric_2015], all of them based on the interplay between electric and magnetic modes. Control over the directional scattering can also be obtained using arrangements of nanoparticles like dimers [@albella_switchable_2015; @campione_tailoring_2015; @yan_directional_2015] or via hybrid metal/dielectric nano-structures [@guo_multipolar_2016]. Even directional shaping of nonlinear emission has been demonstrated: The radiation pattern of the third harmonic generation from silicon dimers can be controlled via the geometry of the structure. [@wang_shaping_2017] In a plasmonic-dielectric hybrid structure, the interplay of electric and magnetic resonances in dielectric TiO$_2$ spheres was used to impose an uni-directional radiation pattern on the second harmonic generation from a plasmonic driver element.[@xiong_compact_2016] Compared to zero-dimensional (0D) particles 