Rigorous Dyson equation and quasi-separable T-scattering operator technique for study of magnetic response from ordered and disordered non-magnetic particles’ ensembles at electromagnetic wave multiple scattering

Abstract

An exact Dyson equation for averaged over electromagnetic crystal unit cell propagating total wave electric field is derived, with supposing the incident wave electric field to have the Floquet property. The mass operator related to periodic structure effective tensor dielectric permittivity is written as double Fourier transform from electric field Tscattering operator of the structure unit cell. The Lippmann-Swinger equation for the unit cell T-scattering operator, written in terms of the unit cell T-scattering operator in free space and the electric field lattice tensor Green function interaction part, is resolved by quasi-separable method. This recently presented quasi-separable approach to unit cell Tscattering operator enables one to consider unit cell containing several particles, with coupling between them directly inside the cell as well as through the structure via above lattice Green function interaction part. The obtained quasiseparable unit cell T-scattering operator is applied to study double diamagnetic-paramagnetic narrow peak in artificial periodical material with unit cell including the coupled plasmonic particles. Actually this magnetic phenomenon is appeared as combination result of space-group resonance between two small dielectric spheres and plasmonic resonance inside a single sphere. Studying the magnetic response of disordered media, we use Dyson self-consistent exact equation for ensemble averaged wave electric field inside dense discrete random media, with a random mass operator having been put under averaging sign. The random mass operator was written in terms of particles’ correlations functions of all orders and particles’ clusters’ T-scattering operators. We discuss comparison between the unit cell T-scattering operator of periodic discrete structure and a cluster T-scattering operator of random discrete structure and consider the above double diamagnetic–paramagnetic peak also in random discrete structure of coupled small plasmonic dielectric spherical particles.