Tor Nordam

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

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. In the papers included in this thesis, we apply this formalism to study the scattering of p- or s-polarised light from two-dimensional dielectric or metallic randomly rough surfaces, or from two-dimensional randomly rough thin dielectric films on metallic substrates, by calculating the full angular distribution of the co- and cross-polarised intensity of the scattered light.We present calculations of the mean differential reflection coefficient for glass and silver surfaces characterised by (isotropic or anisotropic) Gaussian and cylindrical power spectra, and find a good match with experimental results, as well as results obtained from another numerical method. We also present a numerical calculation of the Mueller matrix for scattering from rough surfaces, based on the same method.We investigate the optical phenomena of enhanced backscattering, enhanced forward scattering and satellite peaks. Enhanced backscattering is a well known phenomenon, and is used as one among several indicators of correct results. The phenomenon of enhanced forward scattering has not previously been investigated in two-dimensional systems. We demonstrate its presence, and provide an explanation for why it is qualitatively different from the same phenomenon in one dimension. Regarding satellite peaks, there has been a dispute in the literature, where one group found they should be present in scattering from a thin dielectric film on a metallic substrate, while another group found they should not. We have demonstrated their presence, and shown how the one-dimensional phenomenon of satellite peaks become “satellite rings” in the two-dimensional case.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 discretisation. We also perform a numerical investigation of the range of validity of the reduced Rayleigh equation for scattering from two-dimensionally rough silver and perfectly conducting surfaces.The advantage of using a numerical solution of the reduced Rayleigh equation, rather than a rigorous numerical method such as the surface integral method, lies in the required computational resources. The main limitation of these methods for considering two-dimensionally rough surfaces are their memory requirements. To calculate the scattering amplitude for a typical system studied in this thesis, by the reduced Rayleigh equation, requires 12 GB of memory. To solve a similarly sized system with a rigorous method requires one or two orders of magnitude more. The limitation of the reduced Rayleigh equation is that it can only be applied to weakly rough surfaces, due to the assumption of the Rayleigh hypothesis.

Numerical Simulations of Scattering of Light from Two-Dimensional Rough Surfaces Using the Reduced Rayleigh Equation

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.

Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface

A nonperturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of p- and s-polarized light from a dielectric film with a two-dimensional randomly rough surface deposited on a planar metallic substrate, has been carried out. It is found that satellite peaks are present in the angular dependence of the elements of the mean differential reflection coefficient in addition to an enhanced backscattering peak. This result resolves a conflict between the results of earlier approximate theoretical studies of scattering from this system.

The scattering of light from two-dimensional randomly rough surfaces

We present results, obtained by rigorous computational approaches, for light of p- and s-polarization scattered from two-dimensional, randomly rough, perfectly conducting, lossy metallic, and dielectric surfaces. The perfectly conducting surfaces we study are characterized by an isotropic power spectrum of the surface roughness and by an anisotropic power spectrum. The mean differential reflection coefficient and the full angular distribution of the intensity of the scattered light are calculated for the perfectly conducting and metal surfaces. From the latter calculations it is found that the computational approach used in these calculations conserves energy in the scattering from a perfectly conducting and from a lossless metal surface with an error that is smaller than 0.5%. Finally, we presents results obtained by a numerical, nonperturbative, solution of the reduced Rayleigh equation for the scattering of p- and s-polarized light from two-dimensional randomly rough, metallic and dielectric surfaces. We show that the results for the metallic surface are in good agreement with results for the same metallic surface obtained by the rigorous computational approach.

Numerical studies of the scattering of light from a two-dimensional randomly rough interface between two dielectric media

Author(s): Hetland, OS; Maradudin, AA; Nordam, T; Simonsen, I | Abstract: The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered light. These results are obtained for both the case where the medium of incidence is the optically less dense medium, and in the case where it is the optically more dense medium. Optical analogues of the Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than

Numerical solutions of the Rayleigh equations for the scattering of light from a two-dimensional randomly rough perfectly conducting surface

10^{-4}

Numerical studies of the transmission of light through a two-dimensional randomly rough interface

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Impact of climate change and seasonal trends on the fate of Arctic oil spills

We present rigorous, nonperturbative, purely numerical solutions of the Rayleigh equations for the scattering of p- and s-polarized light from a two-dimensional randomly rough perfectly conducting surface. The solutions are used to calculate the reflectivity of the surface, the mean differential reflection coefficients, and the full angular distribution of the intensity of the scattered field. These results are compared with previously published rigorous numerical solutions of the Stratton-Chu equations, and very good agreement is found.

Coherent effects in the scattering of light from two-dimensional rough metal surfaces

Author(s): Hetland, OS; Maradudin, AA; Nordam, T; Letnes, PA; Simonsen, I | Abstract: The transmission of polarized light through a two-dimensional randomly rough interface between two dielectric media has been much less studied, by any approach, than the reflection of light from such an interface. We have derived a reduced Rayleigh equation for the transmission amplitudes when p- or s-polarized light is incident on this type of interface, and have obtained rigorous, purely numerical, nonperturbative solutions of it. The solutions are used to calculate the transmissivity and transmittance of the interface, the mean differential transmission coefficient, and the full angular distribution of the intensity of the transmitted light. These results are obtained for both the case where the medium of incidence is the optically less dense medium and in the case where it is the optically more dense medium. Optical analogues of Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the former case. For p-polarized incident light we observe Brewster scattering angles, angles at which the diffuse transmitted intensity is zero in a single-scattering approximation, which depend on the angle of incidence in contrast to the Brewster angle for flat-surface reflection.

Experimental and numerical studies of the scattering of light from a two-dimensional randomly rough interface in the presence of total internal reflection: Optical Yoneda peaks

We investigated the effects of a warmer climate, and seasonal trends, on the fate of oil spilled in the Arctic. Three well blowout scenarios, two shipping accidents and a pipeline rupture were considered. We used ensembles of numerical simulations, using the OSCAR oil spill model, with environmental data for the periods 2009–2012 and 2050–2053 (representing a warmer future) as inputs to the model. Future atmospheric forcing was based on the IPCC’s A1B scenario, with the ocean data generated by the hydrodynamic model SINMOD. We found differences in “typical” outcome of a spill in a warmer future compared to the present, mainly due to a longer season of open water. We have demonstrated that ice cover is extremely important for predicting the fate of an Arctic oil spill, and find that oil spills in a warming climate will in some cases result in greater areal coverage and shoreline exposure.