Disorder effect in a 2D array of spherical particles on the electromagnetic field on their surface

The influence of disorder in the spatial arrangement of identical, homogeneous spherical particles of an infinite two-dimensional (2D) array on the energy density spectra of the electric and magnetic fields on their surfaces under normal incidence of a plane electromagnetic wave is studied. The consideration is based on a semi-analytical statistical method (SASM) developed by us. Radial distribution functions based on the hard-disk model are used to simulate particle arrangements in arrays. We wrote a formula for this function describing the perfect azimuthally averaged lattice and analyzed in detail the energy densities for different deviations of particle centers from the nodes of the perfect lattice. The calculation results for a partially ordered array and imperfect and perfect lattices of silver (Ag), crystalline silicon (c-Si), and titanium oxide (TiO₂) particles with sizes of 50 and 300 nm are presented in the wavelength range of 0.3-1.1 µm for a host medium with a refractive index close to that of water. They demonstrate the contribution of the disorder effect to the optical response of the system and allow finding the optimal characteristics of lattice-induced resonances for energy densities on the particle surface. Such data are necessary for solving problems of increasing the efficiency of converting light energy absorbed by the system into other types of energy. The spectra of energy densities obtained under the SASM are in excellent agreement with the data of the numerical finite element method (FEM). To complete the picture, the near-field data are accompanied by far-field data for the incoherent component of the light.