OBLIQUE INCIDENCE PLANE WAVE SCATTERING FROM AN ...

Progress In Electromagnetics Research, PIER 68, 2007265cylinder “i” can be expressed, respectively, asH s φ i(ρ i ,φ i ,z) = E ′ 0G k 0jη 0 λ 0−E ′ 0G hλ 2 0 ρ ik dHφ d i(ρ i ,φ i ,z) = E 0G′ jη d λ d−E ′ 0G hλ 2 d ρ i∞ ∑−∞∞∑−∞∑∞−∞A in H (2)′n (λ 0 ρ i ) e jn(φ i−φ 0 )nC in H (2)n (λ 0 ρ i ) e jn(φ i−φ 0 ) , (8)B in J ′ n (λ d ρ i ) e jn(φ i−φ 0 )∞∑nD in J n (λ d ρ i ) e jn(φ i−φ 0 ) , (9)−∞where h = k 0 cos θ 0 , λ 0 = k 0 sin θ 0 , G = e jk 0z cos θ 0√, k d = k 0 µdr ε dr ,√λ d = kd 2 − k2 0 cos2 θ 0 , η 0 = √ √µ 0 /ε 0 , and η d = η 0 µdr /ε dr .In the same manner, the φ components of the electric field can bederived using Maxwell’s equations as followE φ = 1 ( ∂Hρjωε ∂z− ∂H )z,∂ρ(where H ρ = −1 1 ∂E zjωµ ρ ∂φ− ∂E φ∂z).Thus the φ component of the incident electric field on cylinder “i”takes the formE incφ i(ρ i ,φ i ,z) = −hE′ 0λ 2 0 ρ e jk 0z cos θ 0e jk 0ρ ′ i sin θ 0 cos(φ ′ i −φ 0)i(10)∞∑nj n J n (λ 0 ρ i ) e jn(φ i−φ 0 ) ,−∞while the φ components of the scattered electric field and the electricfield transmitted inside cylinder “i” can be expressed, respectively, asE s φ i(ρ i ,φ i ,z) = −E ′ 0G hλ 2 0 ρ i−E ′ 0G η 0k 0jλ 0∞∑−∞∑∞−∞nA in H (2)n (λ 0 ρ i ) e jn(φ i−φ 0 )C in H (2)′n (λ 0 ρ i ) e jn(φ i−φ 0 ) , (11)