1 Computation of the Field Enhancement by Small Facet Angles of Metallic Nanoparticles: Adaptive Remeshing for Finite Element Method F. Mezghani, D. Barchiesi, A. Cherouat, T. Grosges, and H. Borouchaki Project Group for Automatic Mesh Generation and Advanced Methods Gamma3 Project (UTT-INRIA), University of Technology of Troyes, France Abstract— The accurate calculation of the electromagnetic field enhancement around nanopar- ticles that exhibit facets with small angles is of interest to characterize their efficiency, given the experimental reproducibility of such structures. The finite element method is efficient to com- pute the enhancement of the field intensity at the surface of nanoparticles although the numerical results strongly depends on the mesh of the domain. An adaptive remeshing method is shown to be robust where the classical refinement method fails. The adaptive refinement method uses a posteriori error estimator with interpolation method of the physical field of interest, based on the residual method. The strategy of this method is to remesh the domain of calculation on the basis of the map of the physical and geometrical size that will ensure compliance with the initial geometry and the accuracy of the physical solution. The numerical application shows that the intensity enhancement computed near the vertex between facets with small angles (5 ◦ ) can reach 23%. 1. INTRODUCTION The outstanding optical properties of metal nanoparticles are used extensively in nanoscience [1]. As a matter of fact a huge local electric field is generated under excitation by an electromagnetic field (laser source). This field enhancement due to plasmon resonance in metallic nanoparticles produces a light source of nanometric size that is of interest among all in biology and nanotechnology applications, such as cancer therapy, drug delivery, fluorescence or spectroscopy enhancement. The optical response depends strongly on the size and on the shape of the nanoparticle [1, 2]. Therefore intense research activities occur on the synthesis of nanoparticles with control of their size and shape, and on related simulations of the field enhancement for their optimization. In some experimental cases, the shape of gold nanoparticles exhibits facets that are related to their mode of elaboration [3, 4]. Consequently an accurate method of calculation of the field around such nanostructures could help to their optimization. The finite element method is suitable for the calculation of the electromagnetic field around complex geometries. It allows the control of the accuracy while ensuring the convergence of calcu- lation through the adaptation of mesh. The adaptation of mesh can use various types of methods. These different techniques of adaptation lead to the refinement (or coarsening) of the mesh to meet the accuracy target deduced from a physical or geometrical estimator of error [5–7]. However the efficiency of the remeshing loop for the FEM depends on the error estimator and the adaptation strategy. In this study the remeshing process uses the interpolation of the physical solution of the problem obtained from the Finite Element Method at step t to calculate an approximation of the solution on the new mesh (step t + 1). An a posteriori error estimate enables the generation of a size map associated to the mesh elements. Then the construction of an adapted mesh conforming to this size map and the interpolation of the solution between the new and old meshes is repeated until the desired accuracy is obtained [8–11]. The application of this technique for electromag- netic modeling was shown to be efficient [8–11] but the calculation of the field enhancement near facets with small angles has never been investigated despite the fact that experimental shapes of cristalline structures exhibit such pattern. The purpose of this study is to evaluate accurately the field enhancement produced by the apex of the triangle constituted by two adjacent facets. The problem is hard, the angle between the considered facets being 5 ◦ . Indeed this problem cannot be solved with Finite Difference Time Domain (FDTD), Discrete Dipole Approximation (DDA) nor Green’s tensor methods that are not able to give the field enhancement exactly on the surface of nanoparticles with accuracy and therefore to describe such small changes of slope in the shape of the nanoparticle.