Multipolar theory of bianisotropic response of meta-atoms

The bianisotropy of meta-atoms is usually associated with their nonlocal response and mutual coupling between electric and magnetic dipole moments induced by an incident field. In this Letter, we generalize the theory of bianisotropy beyond the dipole response to cases of arbitrary high-order multipole resonances. We demonstrate that bianisotropy is fully connected to the geometrical structure of meta-atoms and caused exclusively by the absence of their inversion symmetry, while the strength of the bianisotropy response grows normally with the size of a meta-atom. Applying a group theory analysis, we reveal the explicit criteria when the dipole approximation is enough for the correct description of bianisotropy and when accounting for higher-order multipoles is required. We consider a triangular prism as an illustrative example of a bianisotropic particle and show how accounting for higher-order multipoles prevents the violation of Onsager-Casimir conditions for kinetic coefficients appearing in the dipole approximation. The developed theory is an essential step toward a deeper insight into the scattering properties of nanoantennas and meta-atoms.