Resolution of the inverse problem in near-fiel optics.

Objectives
We want to retrieve physical properties of nanostructures (size, width, index of refraction) from experimental data obtained with near-field optical microscopes. This problem is known as the inverse problem.

Methods
Development of algorithms in order to solve the direct problem (FDTD) in near-field and use of evolutionnary strategies in order to explore the space of the solutions.

Results and prospects

We have developed a numerical solution in order to solve the inverse problem in near-field, based on a heuristic evolutionary approach. The main goal is to find the parameters of the sample leading to numerical results similar to the experimental ones. The starting point of the procedure is the reformulation of the inverse problem as a multidimensional nonlinear optimization problem. Evolutionary strategies are used for the search of the optimum of the solution function. These methods are based on random variations of the input parameters, with mutation, recombination and selection of the best elements. This procedure is iterated until a termination criterion has been reached. Results obtained until now are encouraging, as they allowed us to retrieve parameters like the width, the index of refraction of topographical defects. The distance of detection of the intensity could also be estimated. The proposed inversion method is a very versatile and efficient tool, which is practically independent of the method used for solving the direct problem, even if it is currently based on the FDTD method. The use of near-field experimental data should allow us to validate our approach for solving the inverse problem in a near future.

We have currently focused our studies to 2D structures and dielectric materials, but there is no restriction to the extension of the method to 3D structures and/or metallic materials.