A least square T-matrix method for non-spherical dielectric particle compared with Waterman׳s T-matrix method in the near and far field

•We analyze the scattering field of non-spherical particles in the far and the near field.•Waterman׳s T-matrix diverges in regions far inside the smallest particle circumscribing sphere.•A new least square T-matrix method is used to calculate convergent results in the near and the far field.

A T-matrix method that minimizes the sum of the least square errors of the dielectric and magnetic boundary condition at the scatterer surface is presented in this paper. To evaluate the quality of this method, it is numerically compared to Waterman׳s T-matrix method. For this comparison, two scattering configurations are used, a prolate spheroid and a Chebyshev particle of the order 3. The convergence of the scattering field is discussed in the far and the near field. Outside of the smallest scatterer circumscribing sphere both methods produce the same scattering field. Inside of this sphere, only the least square method converges at the particle surface. In our examples, Waterman׳s T-matrix method diverges in regions far inside the circumscribing sphere. To show this, the boundary conditions at the scatterer surface are proved.The least square method can be used to calculate scattering quantities in the whole region outside, but also inside the scattering particle. A least square error of the boundary condition was introduced as an additional absolute convergence criterion.