Multipole analysis of unidirectional light scattering from plasmonic dimers

We analyze unidirectional scattering produced by sub-wavelength plasmonic dimers formed by two silver strips separated by a thin dielectric spacer and embedded in a uniform dielectric medium. Achieving the Kerker condition, which requires matching the strengths of the electric and magnetic-type contributions of the same multipolar order, is possible with such structures for both forward and backward unidirectional scattering by matching the geometric shape-leveraged resonant magnetic dipolar response with the off-resonant electric dipolar contribution. However, unidirectionality is strongly affected by coupling between the two elements in the dimer structure, leading to the manifestation of the electric quadrupole response in the far field. We develop an approach allowing for an easy inverse scattering retrieval of various multipole contributions to the far-field pattern produced by this type of geometry. The retrieval shows unambiguously that the electric quadrupole response contributes up to 30% of the scattered far-field intensity, in addition to strong manifestation of both electric and magnetic dipolar modes. A modified condition for unidirectionality can be developed based on the principle that suppression of radiation in either the forward or backward direction can be achieved whenever the combined strength of multipolar modes of a certain parity, radiating along the propagation direction, matches that of an opposite parity, and noting that parities of electric and magnetic modes interchange with increasing multipole order. With this condition satisfied, unidirectionality of 26 dB/17 dB for forward/backward scattering, respectively, can be achieved with dimer geometries. We also perform a detailed quantitative analysis of scattering cross sections of dimer structures compared to those of Si and gold spheres, accounting for the actual material losses. We show that dimer structures allow for improving backscattering unidirectionality by 10 dB compared to what is achievable with Si spheres, owing to their reliance on off-resonant electric dipolar response; they also allow for a significant (below lambda/10) reduction of the size of a unidirectionally scattering nanoelement.