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

Nordam, Tor; Letnes, Paul Anton; Simonsen, Ingve; Maradudin, A. A.

doi:10.1364/josaa.31.001126

Cited by 15 publications

(10 citation statements)

References 31 publications

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“…4(a) and (d), we observe a slight skew in the distributions. This is similar to results presented in other, similar work [2,21], and is due to the subtle differences between the distributions of p → p and s → s scattered light, as presented for in-plane scattering in Fig. 2.…”

Section: A Normal Incidencesupporting

confidence: 92%

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

et al. 2016

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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 10 −4 . * Oyvind.

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Section: A Normal Incidencesupporting

confidence: 92%

“…With the use of Eqs. (21) and (23)-(24), Eqs. (25b) and (25c) can be rewritten in the form (α = p, s, β = p, s)…”

Section: The Reduced Rayleigh Equationmentioning

confidence: 99%

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

et al. 2016

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“…The equations we need to solve are deduced from the general equations Eqs. (18) and (20) by applying them respectively at a 3 = + and a 1 = − and by using Eqs. (23) and (24) for the model of the field expansion.…”

Section: The Reduced Rayleigh Equationsmentioning

confidence: 99%

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

2018

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By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Selényi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Selényi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Selényi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.

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“…Recently, expressions similar to those that appear in Eqs. (A4) and (A5) were used to calculate the mean differential reflection coefficient on the basis of the numerical solutions of the Rayleigh equations for the scattering of light from a two-dimensional randomly rough perfectly conducting surface [39]. For the type of randomly rough surfaces considered here it is the case that R(q |k ) = (2π) 2 δ(q − k )r(k ).…”

Section: Discussionmentioning

confidence: 99%

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

Maradudin

Pérez-Chávez

Jędrzejewski

et al. 2018

Low Temperature Physics

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The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation. * aamaradu@uci.edu † Ingve.Simonsen@ntnu.no arXiv:1801.09951v1 [physics.optics]

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

Cited by 15 publications

References 31 publications

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

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

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

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