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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