  We investigate theoretically and numerically the light focusing by
finite-size silicon nanostructures. The structural element is a sphere
supporting dipole and quadrupole resonances of both electric and magnetic
types. Our analytical model is based on the coupled multipole model (CMM) when
the optical response of every particle in the structure is associated with the
excitation of its multipole moments generating the secondary (scattered) waves
in the system. Since the focusing effect is reached due to the interference
between the incident and scattered waves, it is possible to control and
optimize its efficiency by managing the spatial positions of particles. In this
work, we study the applicability of the CMM and zero-order Born approximation
(ZBA) for the electromagnetic field simulation in finite-size many-particle
systems at the single-particle multipole resonances. The CMM and ZBA are
verified by comparison of approximated results with the results obtained from
the T-matrix method. We discuss the application of the developed approach for
focusing structures composed of nanospheres arranged in rings and
multi-objective optimization of their focal length and focal intensity via an
evolutionary algorithm. We demonstrate the strong optimization potential of our
calculation scheme, based on the ZBA, for designing effective ultra-thin
metalenses.
