Transition operator calculation with Green׳s dyadic technique for electromagnetic scattering: A numerical approach using the Dyson equation

- Direct DDA method to evaluate the transition operator.
- Irregular and inhomogeneous particle scattering.
- Use of the Dyson equation and of the integral equation for the transition operator.
- No expansion on an explicit basis, real space approach and no boundary conditions.
- Outputs: electric field and Müller matrix.

A new technique to compute the transition operator for a single arbitrary shaped particle is presented, called Green׳s dyadic technique for transition matrix (GDT-matrix). It is based on the use of the volume integral equation (VIE) for electromagnetic scattering. By interpreting the transition matrix as a generalized potential in combination with the Discrete Dipole Approximation (DDA) method, it is possible to make a parallel use of the Lippmann-Schwinger and the Dyson equations to iteratively solve for the transition matrix and Green׳s function dyadic, respectively. Hence, there is no need to explicitly specify the boundary conditions and only an accurate spatial discretization of the particle is required, which is done by a sparse-octree volume discretization. Further no assumptions regarding the particle symmetry, homogeneity and isotropy need to be made. For the validation of the code, examples in 1D and 2D are investigated. Then, 3D results are compared with Mie theory for spherical particles. A cubic particle is also considered while for more complex shaped particles, a qualitative comparison against experimental results is provided for forward-scattering.