请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;) B# a- C2 K) A4 _/ C
   
2. k0 = 2*Pi/lamda;
   6 R- c- Q: j2 {5 C4 r  x
3. n1 = 1.4677;(*纤芯折射率*)
   / Z2 {8 q; U# P
4. n2 = 1.4628;(*包层折射率*)
   ) H) ]7 V9 F: b# ~. h
5. n3 = 0.469 + 9.32*I;(*银折射率*)
   ( W6 H6 w% l' Y0 O+ L
6. a1 = 4.1 10^-6;(*纤芯半径*)
   5 H3 O  }3 ~) C3 ]
7. a2 = 62.5 10^-6;(*包层半径*)
   ) F$ F2 @+ J9 D
8. d = 40 10^-9;(*金属厚度*)) _1 f' C1 ]! d
   
9. a3 = a2 + d;
   7 J9 W3 K4 G\" V' I: j
10. mu = Pi*4 10^-7;(*真空磁导率*)
    ) @2 d2 a8 z/ I5 q/ z' P
11. epsi0 = 8.85 10^-12;(*介电常数*)
    ( |0 a4 {1 M5 Y3 ^# g8 _* e
12. 
    , w) `2 c2 t; i* T3 H
13. n4 = 1.330;: s8 b- K% v, o' }! w6 o# Q
    
14. : K9 p+ p5 Q0 A% P% M' M# n6 F
    
15. neffcl = neffclre + neffclim*I;
    ; b' u+ b! G5 y1 X& Z# k
16. 6 B, @( P- x2 S, x+ I  [- s
    
17. betacl = k0*neffcl;
    1 S* O5 m% _. C# a5 a8 r2 @! X
18. omega = 2*Pi*299792458/lamda;
    * W0 S  }2 s; Q2 Q# L$ u; x6 R$ H
19. 5 Y9 R2 k5 c6 L4 X0 |
    
20. epsi1 = n1^2*epsi0;' ~* M1 t; o# u/ i, h! @1 I2 u' [
    
21. epsi2 = n2^2*epsi0;
    6 e. F  i3 p# K, d
22. epsi3 = n3^2*epsi0;0 R9 N. `: {. U4 k  V# |
    
23. epsi4 = n4^2*epsi0;5 ?* c: V6 C; J) {. c
    
24. \" O; i. X8 G' P- ^6 ?8 @4 G- }! I
    
25. u1 = k0*Sqrt[neffcl^2 - n1^2];; U9 A- [\" Z. R% ]
    
26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    , [9 i/ {9 Y! r
27. u3 = k0*Sqrt[neffcl^2 - n3^2];* f9 X/ r  n7 f9 U/ Q) ?
    
28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    $ r9 e; V- A/ ?: N\" u: ]0 a
29. 0 I; E1 b+ `, O9 J
    
30. Iua111 = BesselI[1, u1*a1];) O/ H2 H1 X5 q5 m' J2 ?: e1 _
    
31. Iua121 = BesselI[1, u2*a1];' a; D* ^7 M\" @
    
32. Iua122 = BesselI[1, u2*a2];$ y( Q7 A0 s, S# L8 }2 I
    
33. Iua132 = BesselI[1, u3*a2];
    ' f/ f! S9 y% t$ f\" w
34. Iua133 = BesselI[1, u3*a3];- [5 i7 Z7 u# w6 {- g\" u; `
    
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;# Z' J, i% F9 K) h3 W
    
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;5 Y! w0 B! w( `2 T8 I, B: o4 P
    
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;5 ?8 @4 o- ]( N+ l$ t1 T9 i
    
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;4 G4 l8 O4 x$ i1 h\" o2 n6 U3 j
    
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;8 c9 _5 t, e7 W6 ]2 b  k  `6 b
    
40. 
    \" o/ ~  l3 W5 S8 o- D& z
41. Kua121 = BesselK [1, u2*a1];
    ( ]7 Z8 c$ V5 Z9 N9 P
42. Kua122 = BesselK [1, u2*a2];
    6 G+ q( u$ i  S) @
43. Kua132 = BesselK [1, u3*a2];2 j  r4 J0 g9 N1 m2 J, l) e
    
44. Kua133 = BesselK [1, u3*a3];
    - Q5 {3 ?5 g8 g; |9 h! ]1 s  d+ i% @
45. Kwa143 = BesselK [1, w4*a3];0 J, B& m! V4 K) a
    
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;/ p4 I/ b  Q& N+ c\" `; Z) f$ F2 N4 G9 j; i
    
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
    ; q9 b$ g. j& G7 G, P, b  B0 x. X
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;7 |7 Y\" D5 g/ S
    
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    ( \, ?7 t0 ^9 b- c
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;! s, {( {9 x; G+ d5 X
    
51. ; x9 f: L3 c# l! n% I9 J4 Y* V
    
52. H1 = (betacl*Kwa143*
    3 C- v  y; h+ i% h9 B
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*- v3 p* `! \, E- i+ t6 f
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    5 f0 F3 t8 z* S9 t4 M, Y) D
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*1 ~7 D$ K2 C& c
    
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*  F# ~, I\" e- n0 r$ W
    
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    # A, y5 [. t8 n, F
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*! \% Y4 L2 q! y3 g
    
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    # `2 M8 A$ A9 M  B: n
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& N* q9 u# K6 y7 _. d
    
61. 
    % y) E8 B8 N; g
62. H2 = (betacl*Kwa143*8 g0 R2 C2 L# v4 X\" ^5 R6 y4 Q$ t
    
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*7 f2 e  U# R6 Y1 ^0 R) @& a$ I
    
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*. O4 F4 E. b7 L\" {
    
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*7 c, x, Z9 @3 B$ R  F7 `
    
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    ' n9 S* o. g2 _' O# ]1 O
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*6 {6 w6 R) M1 u, t3 i5 ^$ R
    
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    : [/ ^4 a2 c' Z
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*. H* {- A% s\" w2 @; r
    
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ; X1 e, [% m& M$ q) N& C1 b
71. ; I\" x\" R, y3 t- N3 H  O% a# |
    
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*% e; V. J9 J  e( H3 M. j0 k\" D
    
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    6 m# H7 C9 I  P6 X; L& }
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
      x3 h/ m9 G' H' e( O
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*$ x\" Q: _1 [; t8 F
    
76.        Kua122 - ) }' F\" F# y8 M0 F2 Y( W
    
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    8 a. o. u* f' Y( ?) j8 c6 T2 T( |
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ! e# t+ y3 u2 {6 `7 l+ X
    
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 5 J( S$ [4 p; y6 `7 G3 E
    
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; i$ W/ L2 O$ b
    
81.   Q# G4 E4 ^& W\" |7 `/ P4 B
    
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    8 F1 L2 ]  n4 _\" ]9 ^1 @2 n
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*5 ~4 Q8 l) @1 I: m- o/ ~  D6 K
    
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    1 Y) N& ]# e- F6 R: E+ S  U0 c
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*, F- q# b0 o8 \
    
86.        Iua122 - ) l' X. z& i& v3 h2 j
    
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    ! R2 H' C/ T# Y/ z& X% j9 L( W
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - ' E' `) b$ K7 k
    
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 1 r  K8 h; H/ D+ p
    
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);* y$ H\" {+ J* p( a$ p! u! N
    
91. 
    6 R\" {( ~4 C3 n
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*\" J) V: l8 o' p3 P' e
    
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*' {8 R8 J/ `5 [9 r( }) [
    
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*7 U; v( Y* B! i3 g0 o. N
    
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -  S8 }1 S, o, y$ l/ `
    
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    8 `9 ?) }9 j1 w& v
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - % G8 b: Y4 c; U4 Y6 `
    
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    & [# q* {- a8 ~
99.       w4^2/u3^2*Kwa143*IIua133);. J* U4 g& b0 z& {1 g/ L$ h2 e
    
100. 
     ; @7 l2 _( ?- a' x
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
     \" l6 k' s- C8 g' `- R
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*0 M. g$ f1 s$ O3 d
     
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
     ! u) K5 v' ?6 J6 [8 \, e: p: Q
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -# }$ ?7 L. m9 U/ Q3 z
     
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     ; R% ?% z2 ~2 h7 s0 {& P( q. o
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
     - W- }8 I' w6 A% c) X7 L
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - + l0 n8 R2 l6 f0 F8 T
     
108.       w4^2/u3^2*Kwa143*IIua133);; [/ H, I! d. a\" v/ {- w) V
     
109. ! u& F( }/ b( K  [
     
110. M3 = (betacl*Kwa143*7 Y8 U0 U4 ?- d/ Q
     
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 3 W& s# C, [1 y\" A3 B$ U
     
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     \" \$ a2 s* w, ]- x6 Y, H
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - : Q& T9 O# J% N; f
     
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
     ! ~1 N1 z$ ^\" @; [  a8 A
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     3 g. |! D( D+ `. T4 p) m% s6 v
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*( S6 z# C! C' J- f  d3 d+ b: ~
     
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 2 H3 f6 @4 Q1 W7 ~) F( B
     
118.       w4^2/u3^2*Kwa143*IIua133);! n, D8 B1 l7 r0 ^
     
119. \" L; F8 G$ k2 H3 D) y) Q
     
120. M4 = (betacl*Kwa143*$ v5 m6 j* J* y
     
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
     7 L+ ^+ E4 y& V: M+ \
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*9 L- K: `* f' ^, X/ O/ _, _) `- J
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 9 `6 Z% `/ D3 U# D2 e; G
     
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
     2 w3 ?- z; a. z. }0 |: h
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     # d3 t\" _. I- z% W0 h7 I- y: b
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     ' m: N! Q* |, W$ o# k
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
     , W# i1 T3 T' I/ u
128.       w4^2/u3^2*Kwa143*IIua133);
     $ n# M1 v( Y9 g9 y) J. c( u
129. 
     : e6 U+ ^\" Z* x! R( P! V9 g
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;7 [8 [& P0 E/ T$ R- V5 a: T/ E
     
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     + W( a# L  j+ D8 u: \
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     * a+ ~0 I$ A6 y
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     / g. Y5 W% m' }* ^3 k
134. & p  f0 p' W8 W
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     , v+ ?& h/ H* G# ?# y3 ?
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;! w+ z% A1 b# d\" f' x( Q- w
     
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;7 Z2 w. L\" W' `, C/ |, W
     
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;2 A# u# _! k7 S; N1 H2 O0 M/ g5 r
     
139. 
     5 W) v% b: c: U% G/ A% r
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + $ R$ |2 Z9 O7 r
     
141.      V1*M4);
     ) k. W7 @% Q7 D2 C: d* u
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 2 i7 C2 q8 y8 Q
     
143.      V2*M2);
     5 c5 j- ~! Y: W# o4 W# A7 G
144. 
     ; Q( @& O* h$ M( W6 x\" f
145. x = xicl1 - xicl2;
     \" T  q! V  C\" |' P
146. x1 = Re[x];
     , q& Y1 J# Y- I5 L+ I9 i+ f& Y
147. x2 = Im[x];  C  J& E$ _\" b& M; o
     
148. 
     ; C! W7 y3 M( U6 Q7 [
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];\" [4 i+ C1 d: N9 _1 v7 U1 j
     
150. ]
     \" Q& Z- L% [9 w  G- r
151. . `. K+ v' m% ]& H! ^* |! M2 @1 G/ ~% d
     

复制代码

代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
换成
$ Q5 G& K; K9 x! L7 Q/ ZFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
& t: y1 H% T# }( t; Z5 ]; j ]
6 {9 v7 m7 H& C就会出现
- s; T% M+ b$ T9 Y% S- ?FindRoot::lstol: 线搜索把步长降低到由 AccuracyGoal 和 PrecisionGoal 指定的容差范围内，但是无法找到 merit 函数的充足的降低. 您可能需要多于 MachinePrecision 位工作精度以满足这些容差.
9 M- w3 T6 ]( J; \% J# {  T  u' @
请问是怎么回事?

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