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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) = ()/(4()k)[ (Q-k₁+k)(k₁+k-Q)+(Q-k₂+k-Q) (k₂+k-Q)+(-Q-k₁+k) (k₁+k+Q)+(-Q-k₂+k) (k₂+k+Q)], where (z) is the Heaviside unit step function, k₁= k_R-k₀,k₂=k_R-k_{0,k(subscriptR} is the real part of the wavenumber of the surface plasmon polariton of frequency supported by the planar vacuum-metal interface, and k₀ is related to the angle of incidence measured clockwise from the x₃-axis by k₀=(/c)sin₀. An explanation is provided for why a surface defined by this power spectrum produces enhanced backscattering at only the angle of incidence given by _s=-₀, 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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