均匀介质圆柱对平面波的散射(Mie级数)..doc
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均匀介质圆柱对平面波的散射
1. TMz极化
假设TMz极化均匀平面波垂直入射半径为a的无限长均匀介质圆柱,相对介电常数为εr,相对磁导率为μr,波的传播方向为+x,入射电场和入射磁场用柱面波展开,分别表示为
(1)
(2)
散射场朝外传播,因此,散射电场和磁场用柱第二类Hankel函数展开,分别表示如下
(3)
(4)
透射场则由柱面基本波函数的线性组合表示,由于透射场在介质内部均为有限大,因此
(5)
(6)
根据介质表面的边界条件,切向电场和切向磁场连续,可以得到
(7)
(8)
求解方程组,从而得到展开项的系数为
(9)
(1 0)
令,将系数带入展开式,得到散射电场和磁场的表达式为
(11)
(12)
对于远区散射场,kρ → ∞,,则相应的电场和磁场为
(13)
(14)
c**********************************************************************
c Compute TMz Scattering from homogenerous lossless dielectric Circular
c Cylinder by Mie Series
c
c a INPUT, real(8)
c On entry, a specifies the radius of the circular cylinder
c epsR INPUT, real(8)
c On entry, epsR specifies the relative permittivity of
c the homogenerous dielectric circular cylinder
c MuR INPUT, real(8)
c On entry, muR specifies the relative permeability of
c the homogenerous dielectric circular cylinder
c f INPUT, real(8)
c On entry, f specifies the incident frequency
c r INPUT, real(8)
c On entry, r specifies the distance between the observation
c point and the origin of coordinates
c ph INPUT, real(8)
c On entry, ph specifies the observation angle
c Ez OUTPUT, complex(8)
c On exit, Ez specifies the z component of the electric
c scattering field
c Hpho OUTPUT, complex(8)
c On exit, Hpho specifies the pho component of the magnetic
c scattering field
c Hphi OUTPUT, complex(8)
c On exit, Hphi specifies the phi component of the magnetic
c scattering field
c
c Programmed by Panda Brewmaster
c**********************************************************************
subroutine dSca_TM_DIE_Cir_Cyl_Mie(a, epsR, muR, f, r, ph, Ez, Hpho, Hphi)
c**********************************************************************
implicit none
c - Input Parameters
real(8) a, epsR, muR, f, r, ph
complex(8) Ez, Hpho, Hphi
c - Constant Numbers
real(8), parameter :: pi = 3.141592653589793
real(8), parameter :: eps0 = 8.854187817d-12
real(8)
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