Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy

We present a technique based on the use of coherent confocal microscopy that can be used to estimate, to within a scale factor, all of the elements of the second-order susceptibility tensor of a single pointlike nanoparticle under permutation and Kleinman symmetry. An estimate of the three-dimensional position of a nanoparticle is also obtained. A forward model for the problem is presented and a method for solving the inverse problem is demonstrated. The approach is tested through simulations which show that the position and the elements of the susceptibility tensor can be robustly retrieved using this method.