Response of periodic systems to electromagnetic fields: multipole expansion, microscopic charge-current density, polarization and magnetization

Polarization and magnetization fields are central concepts in the theory of light-matter interaction, because they describe the distribution of charges and currents induced in the material medium due to an application of electromagnetic fields. Here I develop strategies to treat polarization and magnetization fields in periodic structures and I analyze the radiation spectrum emitted by them. The methods are based on the multipole expansion of charge-current distributions and on its extensions to account for the motion of charges between lattice sites. In the first part of this thesis I treat the optical response of 2d nanoparticle arrays, with the focus on collective effects that arise due to higher order multipolar response. First, I evaluate the interaction constants that describe the collective radiative interactions between nanoparticles in magneto-electric quadrupolar arrays, in an approach that gives the radiative damping in an exact analytic form. Then I find the radiation spectrum from an array of gold spheres with large electric quadrupolar response. The spectrum is dominated by surface-lattice resonances (SLRs) which are of a mixed multipolar character, with significant contributions from multipoles that would be negligible if the sphere was isolated. I link the SLRs to an excitation of the normal modes of the array, and propose a simplified model of the normal mode dispersion relations to explain the SLR properties. In the second part of this thesis I develop strategies to describe charges and currents and polarization and magnetization fields in regular solids. The formalism is based on gauge-invariant dynamical equations of electron Green functions. I derive and categorize the descriptions of dynamics introduced via Peierls transformation of the Green function. Then I apply the formalism to treat the linear response of an insulator to electromagnetic fields. I find the microscopic charge and current densitites in a form such that their expansion around lattice sites follows in a natural way. Restricting myself to static and uniform fields I introduce microscopic polarization and magnetization fields, and derive all the response coefficients within one formalism that makes no reference to energy or thermodynamic potentials.Ph.D