The analysis and synthesis of metasurfaces are important because of their emerging applications in a broad range of the operational wavelengths from microwaves to the visible light spectrum. Moreover, in many applications, like optical nanoantennas, absorbers, solar cells, and sensing, the presence of a substrate is apparent. Therefore, understanding the effects of substrates upon the metasurfaces is important, as the substrates typically affect the resonance behaviors of particles, as well as the interactions between them. In order to consider the impacts of substrates, this paper develops a method for the characterization and homogenization of substrated metasurfaces. This approach is based on independent studies of the electromagnetic behavior of the constituting nanoparticles, and the interactions between them. It uses image theory to calculate the interaction constant tensors in the presence of a dielectric substrate. Then, the contributions of the quasi-static interaction fields of the primary and image dipoles are considered as a homogeneous sheet of surface polarization currents. Finally, the closed-form expressions for the interaction constant tensors are derived. To show the accuracy of our proposed approach, the numerical results of the method are compared to other approaches, as well as with those generated by a commercial EM solver, which are all found to be in good agreement. Moreover, the effects of the refractive index of the substrate, the geometric characteristics of the particle, and periodicity of the array are also investigated on the interaction constants. We believe that this methodology is general and useful in the design and analysis of substrated metasurfaces for various applications.

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.

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