Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface

Abstract

The problem of scattering of electromagnetic waves from a set of cylindrical objects buried beneath a slightly rough surface is undertaken with the cylindrical wave approach as a method of analysis. The small perturbation method is used to compute the scattered field from a rough surface. Numerical results for a rough surface with a sinusoidal profile are obtained with asymptotic evaluation

Electromagnetic scattering by a circular cylinder buried below a slightly rough Gaussian surface

“…(2), assuring a finite illumination length, with a periodic rough surface. Compared to the numerical implementation presented in [28,29], the surface is now nondeterministic, as in the previous works the surface had a deterministic periodic profile, being described by a sinusoidal function.…”

“…L q1 l e −ilφ t J q n cq α q H 1 l n 1 α q L q2 l l q e −ilφ t J 0 q n cq α q H 10 l n 1 α q : (29) δ ml is Kronecker symbol, and l q n cq ∕n 1 or n 1 ∕n cq for TM or TE polarization, respectively. Moreover, it is G 1 l · J l ·∕H 1 l ·, and G 2 l · J 0 l ·∕H 1 l ·.…”

“…(1), n ∥ sin φ and n ⊥ 1 − n 2 ∥ q are the parallel and orthogonal normalized components of a general plane wave, respectively. First-order SPM solution is applied, under the assumption that the phase difference due to the height variation is much smaller than 2π, and the slope of the rough perturbation is much smaller than unity [29]. Mathematically, the conditions are formulated as jgζ cos φ i j ≪ 1 and j∂gζ∕∂ζj ≪ 1, respectively.…”

“…Moreover, Green's function of the rough surface has to be evaluated, with a further increase in the computational cost. In [28,29], a spectral-domain solution to the scattering of a plane-wave by a cylinder buried under a rough surface of infinite extension is found in the frame of cylindrical wave approach (CWA), combined with first-order SPM [12] to model a slightly rough surface. Numerical results are given for the case of a periodic deterministic surface with sinusoidal profile.…”

“…Numerical results are given for the case of a periodic deterministic surface with sinusoidal profile. The theoretical approach is implemented through accurate evaluation of the involved spectral integrals in [28], whereas an asymptotic solution is found in [29]. CWA is an accurate semi-analytical technique developed to deal with scattering problems from buried cylindrical objects.…”