理想导体圆柱对平面波的散射

1、理想导体圆柱对平面波的散射l.TMz极化假设TMz极化均匀平面波垂直入射半径为。的无限长PEC圆柱，波的传播方向为+尤,入射电场和入射磁场用柱面波展开，分别表示为E，c =& E e-jkx =si E e-狄pcos（p =代 E jnJ Qp）e泗z 0z 0z. 0nn=-coVx E* = a 9nj-n+ij （上 p + fl 9-j -n 尸（kp） e洒p jCOjJ, pnq jCOjl.一=-con=oo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Eg =& E a H（2）Qp）n=coHsco a工 H（2）Qp）竺M 性 H（kp）

2、p jcopi p dtp 甲 ,-n=-（4）根据PEC的边界条件,切向电场为0,可以得到E党0H=S从而得到展开项的系数为。j-nj （kp）ejp + o H（2） （kp）nn n-J （如）-Jn *H（2）（如）n=0（5）。冲，将系数带入展开式，得到散射=-00sea 0P CD|Ll psea =Eiy. jJnH耳（如）h（2）Qp）5sea =一00H（2）（ka）n（7）kE V . J （ka） / ） 9- 2 J-n、/，侦PJe泗=一00nu-H（2）（如）nn（8）对于远区散射场，k p- co, H（2）Qp）铝旦-jne-jkp ,则相应的电场和磁场 Jtk

3、p电场和磁场的表达式为H（2）（ka）”nEsca = -E 2 j-n 匕（）H（2）Qp）顷0、Escaz厂：2 j V J (ka)=E ie-jkp，n_7ejn(?兀 k pH(2)(ka )n =一3HscaPH sca中(10)(11)2 jV J (ka)八；ejk p，n rejn(? r 0 H(2)(ka )n =-8n=E 巨ej p 2 e泗n F k PH(2)(ka)n =3利用远区散射电场计算散射宽度(Scattering Width)为b = lim 2兀pPT3E scaEincJn牛)e泗H (2) (ka )n =8 n(12)c*c Compute T

4、Mz Scattering from PEC Circular Cylinder by Mie Series cc a INPUT, real(8)cOn entry, a specifies the radius of the circular cylindercfINPUT, real(8)cOn entry, f specifies the incident frequencycrINPUT, real(8)cOn entry, r specifies the distance between the observationcpoint and the origin of coordin

5、atescphINPUT, real(8)cOn entry, ph specifies the observation anglecEzOUTPUT, complex(8)cOn exit, Ez specifies the z component of the electriccscattering fieldcHphoOUTPUT, complex(8)cOn exit, Hpho specifies the pho component of the magneticcscattering fieldcHphiOUTPUT, complex(8)cOn exit, Hphi specif

6、ies the phi component of the magneticcscattering fieldcc Programmed by Panda Brewmasterc*subroutine dSca_TM_PEC_Cir_Cyl_Mie(a, f, r, ph, Ez, Hpho, Hphi) c*implicit nonec - Input Parametersreal(8) a, f, r, phcomplex(8) Ez, Hpho, Hphic - Constant Numbersreal(8), parameter : pi = 3.141592653589793real(

7、8), parameter : eps0 = 8.854187817d-12real(8), parameter : mu0 = pi * 4.d-7complex(8), parameter : cj = dcmplx(0.d0, 1.d0)c - Temporary Variablesinteger k, nmaxreal(8) eta0, wavek, ka, krreal(8), allocatable, dimension (:) : Jnka, Ynka, Jnkr, Ynkrcomplex(8), allocatable, dimension (:) : Hnka, Hnkrco

8、mplex(8), allocatable, dimension (:) : DHnkreta0 = dsqrt(mu0 / eps0)wavek = 2.d0 * pi * f * dsqrt(mu0 * eps0) ka = wavek * akr = wavek * rnmax = ka + 10.d0 * ka * (1.d0 / 3.d0) + 1if(nmax = 0) then ! Finite Distanceallocate(Jnkr(- 1 : nmax + 1), Ynkr(- 1 : nmax + 1), Hnkr(- 1 : nmax + 1), DHnkr(0 :

9、nmax)call dBES(nmax + 2, kr, Jnkr(0 : nmax + 1), Ynkr(0 : nmax + 1)Jnkr(- 1) = - Jnkr(1)Ynkr(- 1) = - Ynkr(1)Hnkr(- 1 : nmax + 1) = dcmplx(Jnkr(- 1 : nmax + 1), - Ynkr(- 1 : nmax + 1)Ez = - Jnka(0) / Hnka(0) * Hnkr(0)do k = 1, nmaxEz = Ez - cj * (- k) * Jnka(k) / Hnka(k) * Hnkr(k) * cdexp(dcmplx(0.d

10、0, k * ph)Ez = Ez - cj * k * Jnka(k) / Hnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0, - k * ph)enddoHpho = 0.d0do k = 1, nmaxHpho = Hpho + cj * (- k) * k * Jnka(k) / Hnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0,k * ph)Hpho = Hpho + cj * k * (- k) * Jnka(k) / Hnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0,-k * ph)enddoHpho

11、= Hpho / wavek / eta0 / rHphi = - Jnka(0) / Hnka(0) * DHnkr(0) do k = 1, nmaxDHnkr(k) = (Hnkr(k - 1) - Hnkr(k + 1) / 2.d0Hphi = Hphi - cj * (- k) * Jnka(k) / Hnka(k) * DHnkr(k) * cdexp(dcmplx(0.d0, k * ph)Hphi = Hphi - cj * k * Jnka(k) / Hnka(k) * DHnkr(k) * cdexp(dcmplx(0.d0, - k * ph)enddoHphi = H

12、phi / cj / eta0deallocate(Jnkr, Ynkr, Hnkr, DHnkr) else ! Infinite DistanceEz = - Jnka(0) / Hnka(0)do k = 1, nmaxEz = Ez - 2.d0 * Jnka(k) / Hnka(k) * dcosd(k * ph) enddoEz = Ez * dsqrt(2.d0 / pi / wavek)Hpho = 0.d0Hphi = - Ez / eta0endifdeallocate(Jnka, Ynka, Hnka)end subroutine dSca_TM_PEC_Cir_Cyl_

13、Miec#850209060305 0 5 0 5 1 1 -Angle (deg)图1 PEC圆柱的双站散射一TMz极化假设TEz极化均匀平面波垂直入射半径为1的无限长PEC圆柱，波的传播方向为+尤，入射电场和入射磁场用柱面波展开，分别表示为H inc =合 H e - jkx = a H e - jk p cos? = a H (k p)ejn?z 0z 0z 0nn =一3(13)Einc = a 孔 1 E nj-n+1J (kp)e洒-a 虬 j-nJ，(kpMp jO8 pn甲 jO8nn=-3n=-3(14)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

14、如下(15)H sca a H aH2)(k p)n =-3(16)=a &i 工 H(2)(kp匡-a 给乙 h(2)(kp)p jO8 p n。平甲 jO8n nn=一3n=一3根据PEC的边界条件，切向电场为0，可以得到E，nc + E sca0 工 Ij-nJ (kp)e洒 + a H(2)(kp) jO L nn n -(17)从而得到展开项的系数为。-n Ji ejn?，将系数带入展开式H(2) (ka )n得到散射电场和磁场的表达式为Hsca =- H E j - n J 、H(2)(k p )ejn? z 0H (2) (ka)nn=-8n(18)E sca pH1 E nj-

15、n J(k)、H(2)(kp)e泗 p n H(ka) n(19)E sca 中kH0 E j - n J (。I H(2) (k p)ej砰 jgH(2) (ka) nn=s n(20)对于远区散射场，kp s，H(2)(kp)业jne-jkp，则相应的散射磁场为 兀k pHsca - Hz02 j亍 J (ka)e - jk pn7ejn?冗kpn =3 H。)(ka)(21)Esca p12j e-jkp 尤 nn、e泗 w 0H(2) (ka )n(22)n=-sEsca =门 H中02 j 寸 J (ka)e- jkP 2 n 7 ejnpH(2) (ka )n兀k p(23)n =

16、一3则散射宽度(Scattering Width)为b = lim 2冗pPT3H scaH incn =一3J ka)n7r 泗H(2) (ka )n(24)c*Compute TEz Scattering from PEC Circular Cylinder by Mie SeriesINPUT, real(8)On entry, a specifies the radius of the circular cylinderINPUT, real(8)On entry, f specifies the incident frequencyINPUT, real(8)On entry, r

17、specifies the distance between the observation point and the origin of coordinatesINPUT, real(8)On entry, ph specifies the observation angleOUTPUT, complex(8)On exit, Hz specifies the z component of the magnetic scattering fieldOUTPUT, complex(8)On exit, Epho specifies the pho component of the elect

18、ric scattering fieldEphiOUTPUT, complex(8)On exit, Ephi specifies the phi component of the electric scattering fieldphHzEphoProgrammed by Panda Brewmasterc*subroutine dSca_TE_PEC_Cir_Cyl_Mie(a, f, r, ph, Hz, Epho, Ephi)c*implicit nonec - Input Parametersreal(8) a, f, r, ph complex(8) Hz, Epho, Ephic

19、 - Constant Numbersreal(8), parameter : pi = 3.141592653589793d0real(8), parameter : eps0 = 8.854187817620389d-12real(8), parameter : mu0 = pi * 4.d-7complex(8), parameter : cj = dcmplx(0.d0, 1.d0) c - Temporary Variablesinteger k, nmaxreal(8) eta0, wavek, ka, krreal(8), allocatable, dimension (:) :

20、 Jnka, Ynka, Jnkr, Ynkrreal(8), allocatable, dimension (:) : DJnka, DJnkrcomplex(8), allocatable, dimension (:) : Hnka, Hnkrcomplex(8), allocatable, dimension (:) : DHnka, DHnkreta0 = dsqrt(mu0 / eps0)wavek = 2.d0 * pi * f * dsqrt(mu0 * eps0) ka = wavek * akr = wavek * rnmax = ka + 10.d0 * ka * (1.d

21、0 / 3.d0) + 1if(nmax = 0) then ! Finite Distanceallocate(Jnkr(- 1 : nmax + 1), Ynkr(- 1 : nmax + 1), Hnkr(- 1 : nmax + 1)allocate(DHnkr(0 : nmax)call dBES(nmax + 2, kr, Jnkr(0 : nmax + 1), Ynkr(0 : nmax + 1)Jnkr(- 1) = - Jnkr(1); Ynkr(- 1) = - Ynkr(1)Hnkr(- 1 : nmax + 1) = dcmplx(Jnkr(- 1 : nmax + 1

22、), - Ynkr(- 1 : nmax + 1)Hz = - DJnka(0) / DHnka(0) * Hnkr(0)do k = 1, nmaxHz = Hz - cj * (- k) * DJnka(k) / DHnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0, k * ph)Hz = Hz - cj * k * DJnka(k) / DHnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0, - k * ph)enddoEpho = 0.d0do k = 1, nmaxEpho = Epho - cj * (- k) * k * DJnka(k) / DHnka(k) * Hnkr(k) * cdexp(dcmplx(0.d0, k * ph)Epho =