Interference between the Modes of an All-Dielectric Meta-atom
The modes of silicon meta-atoms are investigated, motivated by their use as building blocks of Huygens' metasurfaces. A model based on these modes is presented, giving a clear physical explanation of all features in the extinction spectrum. Counter-intuitively, this can show negative contributions to extinction, which are shown to arise from the interference between non-orthogonal modes. The direct and interference contributions to extinction are determined, showing that conservation of energy is preserved. The Huygens' condition of matched electric and magnetic dipole moments leads to strong forward scattering and suppressed back scattering. It is shown that higher order modes with appropriate symmetry generalise this condition, leading to multiple bands of directional scattering. The presented results are obtained using a robust approach to find the modes of nano-photonic scatterers, commonly referred to as quasi-normal modes. By utilising an integral formulation of Maxwell's equations, this work avoids the problem of normalising diverging far-fields, which other approaches require. The model and presented results are implemented in open-source code.