Models of near-field spectroscopic studies: comparison between Finite-Element and Finite-Difference methods.

We compare the numerical results obtained by the Finite Element Method (FEM) and the Finite Difference Time Domain Method (FDTD) for near-field spectroscopic studies and intensity map computations. We evaluate their respective efficiencies and we show that an accurate description of the dispersion and of the geometry of the material must be included for a realistic modeling. In particular for the nano-objects, we show that a grid size around rhoa approximately 4pia/lambda (expressed in lambda units) as well as a Drude-Lorentz' model of dispersion for FDTD should be used in order to describe more accurately the confinement of the light around the nanostructures (i.e. the high gradients of the electromagnetic field) and to assure the convergence to the physical solution.