Frequency and time domains interactions in nanophotonics

In this thesis, we discuss the problems of scattering and optical manipulation related to nanosystems of different complexities. The multipolar decomposition method is used to represent scattering processes in nanosystems as a series of elementary excitations with well-defined properties. By knowing these properties, one can not only explain unconventional optical phenomena at the nanoscale, but also predict new effects related to light routing, near-field enhancement, optical manipulation, and others. The main focus of the present thesis lies in the theoretical description of such phenomena. In the first part we discuss optical phenomena in the frequency domain. At the first level of complexity, the problem of scattering from isolated nano-objects is analysed by the Mie theory and Cartesian multipoles. The relation between excitation of multipoles and induction of the optical force is discussed. It is shown that, upon excitation of an isolated metallic sphere with two crossed planewaves, an unusual transversal force is induced. We demonstrate that the multipolar approach can very accurately approximate the behaviour of this force and explain the additional peculiarities observed in simulations.Then, we investigate the problem of scattering by more intricate dimer systems. The response from a dimer made of metal and dielectric nanospheres is studied using the coupled dipole method. For such a system it is shown that the electric and magnetic dipoles excited in each nanosphere can be enhanced or suppressed by varying the interparticle distance. In particular, it is demonstrated that a dielectric nanosphere - an object with a strong magnetic response in the visible range - can completely lose this property upon approaching a metal nanoparticle. We also consider scattering from a more intricate system made of metal and dielectric disks stacked one on top of the other. It is shown that by tuning the geometrical parameters of this system, such as height, radius and disk spacing, one can achieve a configuration with dominating magnetic dipolar response. The second part of the thesis aims at studying the dynamics of scattering effects as well as the dynamics of optical forces in the time domain. Unlike the traditional approach that consists of looking at the time-average scattering or time-average optical forces, we study the oscillating parts of these quantities. In this context, we discuss the dynamics of optical forces acting on a film under planewave illumination. We derive the fundamental equations that govern the dynamics of the optical force as a function of time in this case. From the derived equations, it follows that a simple continuous-wave laser can temporally pull the films towards the source of radiation. These developments allow us to deduce the analytical equation giving the amplitude of the temporal beating force acting on objects of arbitrary shapes. The thesis also includes an investigation of the dynamics of linear and second harmonic signals scattered from plasmonic structures under pulsed illumination. A decomposition of the linear scattered signal into eigenmodes is performed and, subsequently, it is demonstrated, how the interference of those modes affects the second harmonic response. Finally, we suggest an efficient way to reduce the calculation time of the second harmonic response.