Multipole optimization of light focusing by silicon nanosphere structures

Abstract

We investigate the applicability of the coupled multipole model and its modification in the framework of the zero-order Born approximation for modeling of light focusing by finite-size nanostructures of silicon nanospheres, supporting electric and magnetic dipole and quadrupole resonances. The results based on the analytical approximations are verified by comparison with the numerical simulations performed by the T-matrix method. Using the evolutionary algorithm optimization, we apply the developed approach to design silicon nanosphere metalenses with predefined focusing properties. The obtained results demonstrate a strong optimization potential of the suggested calculation scheme for engineering ultrathin metalenses.

Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

“…The first term in (31) is responsible for the energy emitted by the excited source at infinity in free space, and the last term is responsible for the presence of the transparent prism.…”

“…It should be emphasized that multipoles are increasingly more involved in practical optics. They are most actively used to determine the contribution of various harmonics (dipoles, quadrupoles, among others) to scattering by a local obstacle [6,31].…”

Rayleigh anomaly induced phase gradients in finite nanoparticle chains

“…1,45 However, this numerical method acts as a black box such that important aspects of the physical dynamics remain clandestine. While approximate iterative solu-tions exist, [46][47][48][49][50][51][52] which may give some insight into the underlying physics, a closed-form solution for the problem is generally non-existent. In the following subsections, we first discuss the existing analytical solution for infinite chains, and then derive an approximate closed-form solution for finite chains.…”

Multipole Born series approach to light scattering by Mie-resonant nanoparticle structures

“…In nanophotonics, one can analyze the optical response of an ensemble of many nanoparticles in a perturbative manner (see Fig. 1) [23,24,25,26,27,28,29].…”

“…This method is based on constructing a convergent Born series and replacing it with a finite sum that successively approximates the interaction between particles where the accuracy depends on the number of terms included in the sum (i.e., on the Born approximation order). Born approximations of different orders have been used to simulate tip-substrate interaction [23,24], calculate polarizability of a non-spherical particle [25,26], model the antireflective properties of nanoparticle coatings [28] and optimize metalens design [29]. The applicability of the Born series method, as well as its convergence, are determined by the strength of electromagnetic coupling in the system.…”