Solving a scattering problem in near field optics by a least-squares method

Motivated by the Trefftz method, a numerical algorithm is proposed based on the least-squares technique for a scattering problem in near field optics. Fundamental solutions and plane wave functions are used to approximate the scattering field toward infinity and the local properties, respectively. Whilst evanescent wave functions are introduced to enrich the plane wave functions to capture the sub-wavelength feature of the field. The continuity across the element boundaries is enforced by minimizing a simple quadratic functional. The method needs not truncate the domain and could obtain high accuracy with even coarse mesh by increasing the number of basis functions. Numerical experiments are also presented to show the effectiveness of the approach.