Statistical method to describe the electromagnetic field on the surface of spherical particle of a 2D array

A semi-analytical statistical method has been developed for investigating the near electromagnetic field of a two-dimensional (2D) array of spherical nano- and microparticles. It takes into account multiple scattering of waves in the framework of the quasicrystalline approximation (QCA). Equations are derived to describe (i) ensemble-averaged and (ii) ensemble- and surface-averaged energy densities of electric and magnetic fields on the surface of spherical particles embedded in a light-absorbing medium. The method allows one to directly analyze the averaged fields at a known radial distribution function of the array particles. The calculation results are presented for local field enhancement at the wavelengths of the plasmon resonance of silver nanoparticles and the lattice-induced resonance of an ordered array of wavelength-sized silver particles at normal incidence of a plane wave. There is excellent agreement of the results obtained for the highly ordered arrays with small and moderate filling factors and the data of the numerical finite element method (FEM) for perfect arrays of nano- and microparticles. The developed method realization is significantly faster than the used realization of the FEM (up to 250 times).