Abstract
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03\%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p- or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic) Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.
Highlights
Wave scattering from rough surfaces is an old discipline which keeps attracting a great deal of attention from the scientific and technological community
The structures of the angular distribution of the intensity of the scattered light depicted in Figure 3 are consistent with what was found by recent studies by using other numerical methods (Simonsen et al, 2010a,b)
Included are total time, time to setup the coefficient matrix of the equation system and the time to solve the equation system
Summary
Wave scattering from rough surfaces is an old discipline which keeps attracting a great deal of attention from the scientific and technological community. Examples include: metamaterials (Agranovich and Gartstein, 2006; Maradudin, 2011), photonic crystals (Joannopoulos et al, 2008), “spoof ” or “designer” surface plasmons (Pendry et al, 2004), optical cloaking (Pendry et al, 2006; Schurig et al, 2006; Baumeier et al, 2009), and designer surfaces (Méndez et al, 2002; Maradudin et al, 2008) These developments have made it even more important to have available efficient and accurate simulation tools to calculate both the far- and near-field behavior of the scattered and transmitted fields for any frequency of the incident radiation, including potential resonance frequencies of the structure
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