Show description

Asymptotic of integrals with edge singularity. The total diffracted field H ( x ) is sought from the primary wave H 0 ( x ) incident on flat perfectly conducting infinitely thin screen S bounded by contour L. In this case, Green’s formula [27] gives integral representation of the magnetic field strength vector at any point x0 outside the screen: H ( x0 ) = H 0 ( x0 ) + ∫∫ (∇g × J ( x )) d S. 83)* given phase function Φ = Φ( x0 , x ) = r. 83 and with the same phase function are obtained for the radiation of aperture antenna in rigorous mathematical model [16,17].

At point M0, we have that g = 0, gξ1 = gξ 2 = 0. Now, we introduce the function γ (ρ), the so-called “neutralizer,” which is infinitely smooth all over the semiaxis 0 ≤ ρ < +∞, and 1, 0 ≤ ρ ≤ ε 0 γ (ρ) =  , 0, ρ ≥ ε1 where 0 < ε 0 < ε1 < R0 . Let us “split the unit” as 1 = γ (ρ) + [1 − γ (ρ)] in the integral I I = ∫∫ exp ( jk Φ) F d S = J + J . 74) 0 Here, J1 = ∫ ∫ exp ( jk Φ ) F1 dS , S1 = S ∩ {|x − x0 | ≤ ε1 }, F1 = F γ, J 0 = ∫ ∫ exp ( jk Φ )F0 d S , S0 S1 S0 = S ∩ {|x − x0 | ≥ ε 0 }, F0 = F (1 − γ ).

Let the perfectly conducting scatterer V to be bounded by closed surface S and let the Cartesian coordinate system origin to be placed inside the region V. We consider the object V as being illuminated by electric dipole, with vector-moment p that is localized at the point with radius-vector a = − a R 0 . 111) which is the plane wave field. 110) onto V. 110). 114) 35 Elaboration of Scattering Electrodynamics Theory follows the reciprocity principle for the complex scattering diagrams: q ⋅ E scat (r 0 |R 0 , p) = p ⋅ E scat (− R 0 | − r 0 , q ).