Fabrication of one-dimensional random surfaces that display enhanced backscattering for only one specified angle of incidence

Mikael Ciftan; Tamara A. Leskova; Alexei A. Maradudin

doi:10.1117/12.446732

23 October 2001 Fabrication of one-dimensional random surfaces that display enhanced backscattering for only one specified angle of incidence

Mikael Ciftan, Tamara A. Leskova, Alexei A. Maradudin

Author Affiliations +

Proceedings Volume 4447, Surface Scattering and Diffraction for Advanced Metrology; (2001) https://doi.org/10.1117/12.446732
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

The phenomenon of enhanced backscattering in the scattering of light from a randomly rough surface is the presence of a well-defined peak in the retroreflection direction in the angular dependence of the intensity of the light scattered diffusely from the surface. A striking feature of this phenomenon is that it occurs for any angle of incidence. Suppose, however, that one would like to have a random surface that displays enhanced backscattering for only a single, specified, angle of incidence. Such a surface could be useful, for example, in situations where one wishes to position a source (and hence the detector) at a specified direction with respect to the site at which the scattering surface is situated. In this paper we show how a one-dimensional random surface can be generated that produces an enhanced backscattering peak for only a specified angle of incidence when illuminated by p-polarized light whose plane of incidence is perpendicular to the generators of the surface. This surface is defined by a power spectrum (the Fourier transform of the surface height autocorrelation function) given by g(Q) = (π)/(4(Δ)k)[θ (Q-k₁+Δk)θ(k₁+Δk-Q)+θ(Q-k₂+Δk-Q)θ (k₂+Δk-Q)+θ(-Q-k₁+Δk)θ (k₁+Δk+Q)+θ(-Q-k₂+Δk)θ (k₂+Δk+Q)], where θ(z) is the Heaviside unit step function, k₁= k_R-k₀,k₂=k_R-k_{0, k(subscript R} is the real part of the wavenumber of the surface plasmon polariton of frequency ω supported by the planar vacuum-metal interface, and k₀ is related to the angle of incidence measured clockwise from the x₃-axis by k₀=(ω/c)sinθ₀. An explanation is provided for why a surface defined by this power spectrum produces enhanced backscattering at only the angle of incidence given by θ_s=-θ₀, and it is confirmed by numerical calculations of the angular dependence of the intensity of the light scattered diffusely from it.

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Mikael Ciftan, Tamara A. Leskova, and Alexei A. Maradudin "Fabrication of one-dimensional random surfaces that display enhanced backscattering for only one specified angle of incidence", Proc. SPIE 4447, Surface Scattering and Diffraction for Advanced Metrology, (23 October 2001); https://doi.org/10.1117/12.446732

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