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Waves Random Media 7 (July 1997) 395-434

X-ray scattering from a randomly rough surface

T A Leskova-+ and A A Maradudin++
-+ Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 142092, Russia
++ Department of Physics and Astronomy and Institute for Surface and Interface Science, University of California, Irvine, CA 92697, USA

Received 20 August 1996

Abstract. On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory , where is the dielectric function of the scattering medium. The magnitude of for x-rays is in the range from to , depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in . The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric - dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.

URL: stacks.iop.org/0959-7174/7/395
DOI: 10.1088/0959-7174/7/3/010
PII: S0959-7174(97)77361-8

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