理想導(dǎo)體圓柱對(duì)平面波的散射

1、理想導(dǎo)體圓柱對(duì)平面波的散射l.TMz極化假設(shè)TMz極化均勻平面波垂直入射半徑為。的無(wú)限長(zhǎng)PEC圓柱，波的傳播方向?yàn)?尤,入射電場(chǎng)和入射磁場(chǎng)用柱面波展開(kāi)，分別表示為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灑p jCOjJ, pnq jCOjl.一=-con=oo散射場(chǎng)朝外傳播,因此，散射電場(chǎng)和磁場(chǎng)用柱第二類Hankel函數(shù)展開(kāi)，分別表示如下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）根據(jù)PEC的邊界條件,切向電場(chǎng)為0,可以得到E黨0H=S從而得到展開(kāi)項(xiàng)的系數(shù)為。j-nj （kp）ejp + o H（2） （kp）nn n-J （如）-Jn *H（2）（如）n=0（5）。沖，將系數(shù)帶入展開(kāi)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、/，偵PJe泗=一00nu-H（2）（如）nn（8）對(duì)于遠(yuǎn)區(qū)散射場(chǎng)，k p- co, H（2）Qp）鋁旦-jne-jkp ,則相應(yīng)的電場(chǎng)和磁場(chǎng) Jtk

3、p電場(chǎng)和磁場(chǎng)的表達(dá)式為H（2）（ka）”nEsca = -E 2 j-n 匕（）H（2）Qp）頃0、Escaz廠：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利用遠(yuǎn)區(qū)散射電場(chǎng)計(jì)算散射寬度(Scattering Width)為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)圖1 PEC圓柱的雙站散射一TMz極化假設(shè)TEz極化均勻平面波垂直入射半徑為1的無(wú)限長(zhǎng)PEC圓柱，波的傳播方向?yàn)?尤，入射電場(chǎng)和入射磁場(chǎng)用柱面波展開(kāi)，分別表示為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灑-a 虬 j-nJ，(kpMp jO8 pn甲 jO8nn=-3n=-3(14)散射場(chǎng)朝外傳播因此，散射電場(chǎng)和磁場(chǎng)用柱第二類Hankel函數(shù)展開(kāi)分別表示

14、如下(15)H sca a H aH2)(k p)n =-3(16)=a &i 工 H(2)(kp匡-a 給乙 h(2)(kp)p jO8 p n。平甲 jO8n nn=一3n=一3根據(jù)PEC的邊界條件，切向電場(chǎng)為0，可以得到E，nc + E sca0 工 Ij-nJ (kp)e灑 + a H(2)(kp) jO L nn n -(17)從而得到展開(kāi)項(xiàng)的系數(shù)為。-n Ji ejn?，將系數(shù)帶入展開(kāi)式H(2) (ka )n得到散射電場(chǎng)和磁場(chǎng)的表達(dá)式為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)對(duì)于遠(yuǎn)區(qū)散射場(chǎng)，kp s，H(2)(kp)業(yè)jne-jkp，則相應(yīng)的散射磁場(chǎng)為 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 =門 H中02 j 寸 J (ka)e- jkP 2 n 7 ejnpH(2) (ka )n兀k p(23)n =

16、一3則散射寬度(Scattering Width)為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 =