Numerical modeling of a influence of a nanoparticle pair on the electromagnetic field in the near zone by the vector finite elements method

Here we propose a mathematical model based on a vector finite-element method for modeling the distribution of the electromagnetic field in the near zone of spherical particles. This model has allowed us to develop algorithms for the appropriate software. The verification of the model shows that the discrepancy between the research results of the proposed model and the available calculation results based on analytical formulas derived from the Mie theory for homogeneous spherical nanoparticles does not exceed 10 percent. Calculations were carried out to determine the relative positions of a pair of metal nanoparticles at which the intensity of the electromagnetic field reaches the maximum value in the near zone. The advantage of the proposed mathematical model and approach consists in the use of tetrahedrons as finite-elements. The tetrahedron finite-elements allow one to approximate the heterogeneous structure of the nanomaterial with the accuracy sufficient for the practical use. Furthermore, in this way the continuity of the tangential component of the electromagnetic field in the entire calculation region can be achieved.