Computing the optical near-field distributions around complex subwavelength surface structures: A comparative study of different methods

Some 15 years ago, optical topographic signals with subwavelength resolution were obtained independently by several experimental teams. Since this exploratory period, a growing number of experimental configurations have been proposed and continuously developed. Simultaneously, this research field was supported by different theoretical works, aimed at developing our understanding of the interaction of optical fields with mesoscopic objects. Over the past three years, several theoretical frameworks have been proposed (Green's functions, field susceptibility, boundary conditions methods, multiple multipoles expansions, etc.). In this paper, an attempt at a careful comparison between two classes of numerical models is presented. Using the same test object, we discuss and compare the numerical solutions issued from a reciprocal-space perturbative method (Rayleigh approximation) and the solution originating from a direct-space integral approach (Green's function or field susceptibility). The discussion is given for different values of the relevant experimental parameters. The convergence of both approaches is investigated.