The math formulation for this is here. It's on slide 17. If there are 9 (3 x 3) harmonics, each element of the scattering matrix will be 18 x 18. field_reflected = S11 * field_incident. The field vector is defined such that the x-components come first and the y-components come second, with the zero-order harmonic being in the center of each of the subsets of the vector. The field component field[i] is:
i = 1: (1, 1) harmonic
i = 2 (2, 1) harmonic
i = 3 (3, 1) harmonic
i = 4 (2, 1) harmonic
i = 5 (2, 2) harmonic (the zero-order in x- and y-),
etc. i = 1-9 corresponds to the x-polarized fields. i = 10-18 has the same ordering but represents the y-polarized fields. So S11[i, j] corresponds to the amount of the i-th harmonic reflected as the j-th harmonic. I
The math formulation for this is here. It's on slide 17. If there are 9 (3 x 3) harmonics, each element of the scattering matrix will be 18 x 18. field_reflected = S11 * field_incident. The field vector is defined such that the x-components come first and the y-components come second, with the zero-order harmonic being in the center of each of the subsets of the vector. The field component field[i] is:
i = 1: (1, 1) harmonic i = 2 (2, 1) harmonic i = 3 (3, 1) harmonic i = 4 (2, 1) harmonic i = 5 (2, 2) harmonic (the zero-order in x- and y-),
etc. i = 1-9 corresponds to the x-polarized fields. i = 10-18 has the same ordering but represents the y-polarized fields. So S11[i, j] corresponds to the amount of the i-th harmonic reflected as the j-th harmonic. I