Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces

We calculate all the elements of the Mueller matrix for light scattering from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations. We foresee that the ability to model polarization effects in light scattering from surfaces will enable better interpretation of experimental data and allow for the design of surfaces which possess useful polarization effects.

Figure 1

Color-level plots of the contribution to the Mueller matrix elements from the light scattered incoherently as functions of $q_1$ and $q_2$ for angles of incidence $({\theta }_0,{\phi }_0)=(2^{\circ },{45}^{\circ })$. An ensemble consisting of $N_p=10000$ surface realizations was used in obtaining these results. The elements, ${\langle M_{ij}\rangle }_{\text{incoh}}$ ($i,j=1,2,3,4$), are organized as a matrix with ${\langle M_{11}\rangle }_{\text{incoh}}$ in the top left corner, ${\langle M_{12}\rangle }_{\text{incoh}}$ top row and second column, etc. The white spots indicate the specular direction in reflection.

Figure 2

Same as Fig. 1, but now for angles of incidence $({\theta }_0,{\phi }_0)=({25}^{\circ },{45}^{\circ })$.

Figure 3

The incoherent contribution to the diagonal Mueller matrix elements, ${\langle M_{ii}\rangle }_{\mathrm{incoh}}$, in the plane of incidence (parameters as in Fig. 2). The vertical dotted line indicates the backscattering direction. The lines, from top to bottom, correspond to $i=1,2,4$ and 3.