The Born series applied to the Lippmann-Schwinger equation is a straightforward method for solving optical scattering problems, which however diverges except for very weak scatterers. Replacing the Born series by Padé approximants is a solution of this problem. However, in some cases it is rather difficult to obtain an accurate Padé approximant. In this paper we aim to understand the cause by studying the scattering by a cylinder. We find that there is a strong connection between eigenvalues of the Lippmann-Schwinger operator that are close to the real axis, the occurrence of a near-resonance, and the problematic behavior of the Padé approximant. The determination of these eigenvalues provides a general method to obtain, for any given geometry, materials for which near-resonances occur.@en

We use a rigorous vector Born series to solve electromagnetic scattering by a diffraction grating. To deal with possible divergence of the Born series, we compute Padé approximants of the Born series to retrieve the solution regardless. Besides results of the Born-Padé method for an example grating, for which the Born series diverges, we show analytical expressions for a two-layer grating in the case of s polarization. This gives insight into the convergence behavior of the Born series as function of the angle of incidence, for instance.

@en

We present the realization of a vectorial perturbation method based on the Born series applied to strong electromagnetic scattering problems. We present the general theoretical formalism and show a semianalytical implementation for scattering by diffraction gratings. We are particularly interested in the strong scattering regime, where the Born series is known to wildly (namely, exponentially) diverge. By applying Padé approximation to the vectorial Born series, we are able to obtain accurate results from divergent Born series. The method we present has the inherent benefit of being close to the actual physical mechanism behind the formation of a scattered signal, as the solution is built step by step from a sequence of multiple-scattering events. This helps in the understanding of signal formation, which is a key element in inverse scattering problems that are relevant to optical metrology, among others.@en

Electromagnetic scattering is the main phenomenon behind all optical measurement methods where one aims to retrieve the shape or physical properties of an unknown object by measuring how it scatters an incident optical field. Such an inverse problem is often approached by solving, several times, the corresponding direct scattering problem and trying to find the best estimate of the object which is compatible with a set of measurements. Despite the existence of numerical methods, a powerful way to solve those direct problems would be to use a perturbation approach where the field is expressed as a series, known as the Born series. The advantage of a perturbation approach stems from the fact that each term of the series has a clear physical meaning and can unveil much more about the scattering process than a purely numerical approach can offer. This method is however unpractical under so-called strong-scattering conditions because the corresponding Born series strongly diverges. In this work, we will show how to solve this problem by employing Padé approximants and how to treat electromagnetic problems well beyond the weak-scattering regime. This approach can represent an important building block to the application of the Born series to direct and inverse problems, with potential applications in superresolution, optical metrology, and phase retrieval.

@en