OBLIQUE INCIDENCE PLANE WAVE SCATTERING FROM AN ...

Progress In Electromagnetics Research, PIER 68, 2007263is expressed in the (ρ i ,φ i ,z), cylindrical coordinate system for e jωt asEz inci(ρ i ,φ i ,z) = E 0e ′ jk 0z cos θ 0e jk 0ρ i sin θ 0 cos(φ i −φ 0 ) e jk 0ρ ′ i sin θ 0 cos(φ ′ i −φ 0)= E 0e ′ jk 0z cos θ 0e jk 0ρ ′ i sin θ 0 cos(φ ′ i −φ 0)∞∑× j n J n (k 0 ρ i sin θ 0 ) e jn(φ i−φ 0 ) , (1)−∞where E 0 ′ = E 0 sin θ 0 , θ 0 is the oblique incident angle as shown in Fig. 1and E 0 is the amplitude of the incident electric field component. Theparameter k 0 is the free space wave number, φ 0 is the angle of incidenceof the plane wave in the x-y plane with respect to the positive x-axis,and the J n (ξ) is the Bessel function of order n and argument ξ. Thesecond expression of the incident field component is in terms of thecylindrical coordinate of the ith cylinder, whose center is located at(ρ ′ i ,φ′ i ,z) of the global coordinate (ρ, φ, z).zincEφθ 00IncidentwaveyxFigure 1. The parameters describing the obliquely incident E-polarized plane wave on a simple cylinder.The resulting z component of the scattered electric field from theith cylinder and the transmitted z component of the field inside thecylinder material can be expressed, respectively, asE s z(ρ i ,φ i ,z)=E ′ 0e jk 0z cos θ 0∞ ∑−∞A in H (2)n (k 0 ρ i sin θ 0 ) e jn(φ i−φ 0 ) , (2)∞ (∑Ez d (ρ i ,φ i ,z)=E 0e ′ jk 0z cos θ 0√kd2 B in J n k 0 ρ ik02 −cos 2 θ 0)e jn(φ i−φ 0 ) , (3)−∞