scholarly journals Wave Scattering by Periodic Surface at Low Grazing Angles: Single Grazing Mode

2000 ◽  
Vol 26 ◽  
pp. 1-41 ◽  
Author(s):  
M. I. Charnotskii
Keyword(s):  
Wave Scattering ◽  
Periodic Surface ◽  
Grazing Angles

On the Rayleigh assumption in scattering by a periodic surface

1969 ◽  
Vol 65 (3) ◽  
pp. 773-791 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Conformal Mapping ◽  
Plane Wave ◽  
Analytic Continuation ◽  
Critical Points ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elliptic Partial Differential Equations ◽  
Total Field ◽  
Periodic Surface ◽  
Plane Wave Scattering

AbstractIn treating plane wave scattering by a periodic surface, Lord Rayleigh (10) assumed that the discrete, outgoing and evanescent plane wave representation for the scattered field was valid on the surface itself. Recently, this Rayleigh assumption has been questioned and criticized. For the surface y = b cos kx on which the total field vanishes, Petit and Cadilhac(8) have demonstrated its invalidity when Kb > 0·448. The present paper discusses scattering of a wave, incident from y > 0, by an analytic periodic surface y = f(x) ( – ∞ < x < ∞), and shows that the Rayleigh assumption is valid if and only if the solution can be continued analytically across the boundary at least to the line y = minf(x). Conformal mapping and results relating to the analytic continuation of solutions to elliptic partial differential equations reduce the problem to one involving the location of singularities and critical points of a potential Green's function. Provided that the perturbation of the surface from a plane is sufficiently gentle, the validity of the Rayleigh assumption is established. For the surface y = b cos kx it is shown that the assumption is valid if Kb < γ, where γ is a positive number no greater than 0·448, the precise value of which is unknown. Possible extensions of the analysis to different or more general situations are suggested.

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