Generalized Kerker’s conditions under normal and oblique incidence using the polarizability tensors of nanoparticles

The polarizability tensors of a particle are its characteristic parameters, which once obtained, can be applied as equivalent representations of the particle in any problems involving plane wave illuminations. In this paper, the generalized Kerker's conditions for unidirectional scattering are derived, in the case of normal and oblique incidence, in terms of the polarizability tensors of any arbitrary nanostructures in homogeneous media and located on dielectric substrates. In order to present structures that corroborate the conditions derived from such polarizabilities, first, the effect of constituent material on the frequency response of the nanoparticle is investigated. Then, the dimensions of nanostructures that satisfy the first and second Kerker's conditions are evaluated, while it is also ascertained that by varying the excitation wavelengths in an individual nanoparticle, switching between forward and backward unidirectional scattering can be achieved. This creates numerous attractive possibilities for the manipulation of optical pressure forces. Moreover, the influence of impinging direction upon the forward-to-backward scattering ratio is studied. Since, in many applications, nanoparticles are situated on dielectric substrates to make the structures more practically feasible, in this work, the effect of substrates on the Kerker's conditions are evaluated. It is shown that the presence of a substrate adds new dimensions of polarizability to the structure. Despite this new polarizability, two structures are engineered, here, which create strong asymmetrical scattering over a wide frequency range and wide angle of incidence.