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

Abstract

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.

Substrated inhomogeneous metasurfaces analysis using interaction constant method

“…According to the figure, the center-to-center distance, a , between any adjacent particles is 150 nm, and the permittivities of these noted materials have been taken from 30 , 31 . In 12 , we discussed the effects of the materials on the polarizability tensors of the particles; while as mentioned in 12 , the main polarizabilities of the plasmonic nanoparticles with symmetrical shapes, such as nano-spheres or nano-cylinders with dimensions considered in this paper, are the electric polarizabilities. In contrast, high-index dielectric nanoparticles include both electric and magnetic polarizabilities.…”

“…Metasurfaces have widespread applications in the fields of antenna and communication engineering 1 – 12 , 32 , 33 . In most applications, metasurfaces are fabricated on dielectric substrates to improve the structures’ mechanical robustness, and to make them more favorable for practical applications.…”

Special scattering regimes for conical all-dielectric nanoparticles

“…After some simple algebra, one can obtain the following conditions for the multipole amplitudes: www.nature.com/scientificreports/ Further, taking into account the equations (27)(28)(29), we obtain the ratios between the multipole contributions for each of their combinations (see Supplementary S2): For all the above combinations, phase differences between multipoles can be obtained. Transverse phase conditions are:…”

“…Nowadays, the Kerker effect plays a crucial role in dielectric nanophotonics, giving rise to a variety of fully transparent phase-tailoring "Huygens" metasurfaces [22][23][24] . As a next step, the so-called generalized Kerker effect was introduced; this effect allows one to observe an interference picture between resonantly excited electromagnetic multipoles of different orders [25][26][27][28] . Expanding the possibilities of the usual Kerker condition, it allows governing the scattering directivity via the interplay of multipolar channels.…”