Solving the problem of divergent Born series by Pade’ approximants

Master student Thomas van der Sijs of the Optics Group has published the paper: “Electromagnetic Scattering beyond the weak regime: Solving the problem of divergent Born series by Pade’ approximants” in Physical Review Research.

The paper introduces a new rigorous method to solve electromagnetic scattering problems in the strong scattering regime. Conventional methods such as FDTD, FEM or integral equation methods require computing the solution of a very large set of linear equations. In the paper Pade’ approximants are applied to solve the long standing problem of diverging Born series. In the proposed method only simple small systems have to be solved for all grid points separately inside the scattering object. This can be done in parallel, so that the method is very fast and requires very little computer memory.  The new method is not only useful for forward scattering problems but will also be very important for solving inverse problems, in particular to quantify the possibility of super-resolution by multiple scattering.  

Thomas will continue as PhD in the Optics Group in the framework of the Synoptics Programme.


Comparison between the results obtained with the new method (right) and the analytic solution (left) for the scattering of a plane wave by a cylinder of silicon in air with radius 400 nm, equal to the wavelength.

T. A. van der Sijs, O. El Gawhary, and H. P. Urbach 
Phys. Rev. Research 2, 013308 – Published 13 March 2020