Coherent scattering from rough surfaces

Several topics pertaining to rough-surface scattering are discussed. Among them are the region of validity of the Rayleigh hypothesis, which treats the field expansion in a concavity in terms of only outgoing waves, and a solvable model for plane wave scattering from a thin-comb grating. Both involve periodic, deterministic surfaces. In addition, for an arbitrary deterministic surface, the T-matrix is shown to satisfy a three-dimensional Lippmann-Schwinger integral equation for a noncentral and complex "potential." Specializing this to a homogeneous Gaussian distributed random surface yields a one-dimensional integral equation for the ensemble average of the T-matrix (Dyson equation) which can be solved. The solution is compared to experimental measurements and illustrates the importance of multiple scattering in explaining surface scattering phenomena.

[1]  J. Desanto.  Scattering from a random rough surface: Diagram methods for elastic media , 1973 .

[2]  B. A. Lippmann,et al.  Note on the Theory of Gratings , 1953 .

[3]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .

[4]  R. F. Millar.  On the Rayleigh assumption in scattering by a periodic surface. II , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  John A. DeSanto,et al.  Scattering of a scalar wave from a random rough surface: A diagrammatic approach , 1972 .

[6]  C. Bouwkamp.  A note on singularities occurring at sharp edges in electromagnetic diffraction theory , 1946 .

[7]  D. Maystre,et al.  Sur la diffraction d'une onde plane par un reseau infiniment conducteur , 1971 .

[8]  E. Jakeman,et al.  Non-Gaussian fluctuations in electromagnetic radiation scattered by random phase screen. I. Theory , 1975 .

[9]  Raj Mittra,et al.  Analytical techniques in the theory of guided waves , 1971 .

[10]  John A. DeSanto,et al.  Numerical solution of a singular integral equation in random rough surface scattering theory , 1974 .

[11]  John A. DeSanto,et al.  Green's function for electromagnetic scattering from a random rough surface , 1974 .

[12]  W. Ament.  Forward- and back-scattering from certain rough surfaces , 1956 .

[13]  N. Cabrera,et al.  New method for solving the scattering of waves from a periodic hard surface: Solutions and numerical comparisons with the various formalisms , 1978 .

[14]  G. R. Ebbeson,et al.  Gratings that diffract all incident energy , 1977 .

[15]  A. T. Bharucha-Reid,et al.  Probabilistic methods in applied mathematics , 1968 .

[16]  E. Wolf,et al.  Resonance states as solutions of the Schrodinger equation with a nonlocal boundary condition , 1976 .

[17]  Scattering from a sinusoid: derivation of linear equations for the field amplitudes , 1974 .

[18]  P. Waterman,et al.  Scattering by periodic surfaces , 1975 .

[19]  G. Tommei,et al.  Diffraction and rainbow in atom-surface scattering , 1973 .

[20]  John A. DeSanto,et al.  Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries , 1971 .

[21]  J. L Uretsky,et al.  The scattering of plane waves from periodic surfaces , 1965 .

[22]  Herman Medwin,et al.  Specularly scattered sound and the probability density function of a rough surface , 1973 .

[23]  Kenneth M. Mitzner.  Acoustic Scattering from an Interface between Media of Greatly Different Density , 1966 .

[24]  P. M. van den Berg,et al.  The Rayleigh hypothesis in the theory of reflection by a grating , 1979 .

[25]  James J. Cowan,et al.  Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings , 1970 .

[26]  W. Miller,et al.  Atomic scattering from a sinusoidal hard wall: Comparison of approximate methods with exact quantum results , 1976 .

[27]  J. G. Zomig.  Physical Modeling of Underwater Acoustics , 1979 .

[28]  R. F. Millar.  The Rayleigh hypothesis and a related least‐squares solution to scattering problems for periodic surfaces and other scatterers , 1973 .

[29]  R. Newton.  Scattering theory of waves and particles , 1966 .

[30]  Uriel Frisch,et al.  WAVE PROPAGATION IN RANDOM MEDIA. , 1970 .

[31]  R. Hazeltine.  DIFFRACTION RADIATION BY A LINE CHARGE MOVING PAST A COMB: A MODEL OF RADIATION LOSSES IN AN ELECTRON RING ACCELERATOR , 2008 .

[32]  L. Rayleigh,et al.  The theory of sound , 1894 .