请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   $ p( ]  Y$ ]  _! T
2. k0 = 2*Pi/lamda;; J# p8 e5 Y3 I2 d
   
3. n1 = 1.4677;(*纤芯折射率*)# x, ^( q3 f1 m- M/ P4 O* D
   
4. n2 = 1.4628;(*包层折射率*)
   7 ?- A3 Q, U) ^\" }' `$ o6 H* U
5. n3 = 0.469 + 9.32*I;(*银折射率*)% m% y8 g& U- e+ u! @
   
6. a1 = 4.1 10^-6;(*纤芯半径*)! P) h) _; g- c, u8 ~* Q
   
7. a2 = 62.5 10^-6;(*包层半径*)
   8 C; ]- M  t7 o) u+ k$ S
8. d = 40 10^-9;(*金属厚度*)) m6 h& q4 k5 S; c\" R
   
9. a3 = a2 + d;1 T+ z9 D! x* C0 N* v% C
   
10. mu = Pi*4 10^-7;(*真空磁导率*)
    . r8 V4 ]- H+ e' y5 p/ i* I
11. epsi0 = 8.85 10^-12;(*介电常数*)
    ' ^0 l/ q3 L1 q/ _8 g/ j7 @9 W
12. . y# Q0 g: m2 j( r, L' ~
    
13. n4 = 1.330;
    4 u7 E7 n  F# G4 B2 `* j9 ^+ i
14. 5 W+ V3 l7 m1 N5 h3 h, O: `
    
15. neffcl = neffclre + neffclim*I;/ B# d. f, R% A+ b. T
    
16. 
    1 D! V- l7 b0 u
17. betacl = k0*neffcl;, f\" U# ^! ]9 E* l  E
    
18. omega = 2*Pi*299792458/lamda;% Z( c+ y; T8 x( f! h, l$ M
    
19. . \' F; a# Q, X- b\" e\" x6 H; ^
    
20. epsi1 = n1^2*epsi0;5 }3 k3 b( r* {
    
21. epsi2 = n2^2*epsi0;
    ( h( X7 ^3 L% g  M( M
22. epsi3 = n3^2*epsi0;  i% r, ^' P) K: _+ L$ w% `/ H6 z
    
23. epsi4 = n4^2*epsi0;, o7 ~7 |; ^% I/ O
    
24. , {# L, R* l, l* G
    
25. u1 = k0*Sqrt[neffcl^2 - n1^2];; m$ ~; l  H& ~  `* r0 n
    
26. u2 = k0*Sqrt[neffcl^2 - n2^2];4 [0 S  R\" I$ y
    
27. u3 = k0*Sqrt[neffcl^2 - n3^2];3 H\" {+ k0 ~* V/ i: Y% l
    
28. w4 = k0*Sqrt[neffcl^2 - n4^2];8 ]& W2 |5 T  x1 ?) b& [( x' t
    
29. ) O: ]5 u; G, |' v
    
30. Iua111 = BesselI[1, u1*a1];
    6 u+ Z6 m1 H. C! M) f2 E0 A( x5 }1 N- B
31. Iua121 = BesselI[1, u2*a1];9 E9 z7 ], j& r3 x4 U8 @) F( s5 E
    
32. Iua122 = BesselI[1, u2*a2];' u1 C8 }) G/ }( D- H; p6 m
    
33. Iua132 = BesselI[1, u3*a2];
    3 N' b\" U: G* C: j4 ]# q( O
34. Iua133 = BesselI[1, u3*a3];4 N9 w\" M6 z  K+ V- s# p! q
    
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    7 a5 Q* \4 U+ Y7 I
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    - R4 t$ o& Q5 c3 a1 p- ]5 y
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    1 K; F' s- e& Y1 b% }1 n
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
    5 F+ M5 v2 F9 v\" L- o
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;+ K7 F0 w7 f1 ?4 F' k' W
    
40. ) |! R2 J% ]+ H) E  K
    
41. Kua121 = BesselK [1, u2*a1];$ u! r+ s) n8 v
    
42. Kua122 = BesselK [1, u2*a2];( o* m  p\" L5 X7 l) v& a) I; Z
    
43. Kua132 = BesselK [1, u3*a2];9 @7 i5 s- o9 X4 w4 s4 ^
    
44. Kua133 = BesselK [1, u3*a3];% T+ w- P* H2 q8 g$ V
    
45. Kwa143 = BesselK [1, w4*a3];, \* V# s* |7 a\" J
    
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;0 J: u1 A5 {$ }& A
    
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
    0 x5 o' d; D% m+ v* J- H4 W
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;5 Q' H. P& A6 Z
    
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;  C: |\" a+ k. c! y3 U
    
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
    7 _2 G0 X! B- v  s/ x# z1 x
51. 9 n8 C4 O0 b; h' O/ u* K6 m4 `
    
52. H1 = (betacl*Kwa143*) w7 D# e5 f6 N! }4 X9 }( u3 v0 l
    
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*0 D6 a% L- b2 F
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    + B2 k1 @$ j. `( C1 B9 E7 w% U
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    0 b% t4 f6 e% ?0 d7 P2 T
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*$ X  o\" ^8 ^6 B5 d/ n
    
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ( V/ j4 Z  \9 ^& Q: N' Q% i
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*, T5 E9 ]4 U( U% j3 Z3 y
    
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*8 a* R) O- \2 o* e2 n& J: m
    
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    9 t5 ^. a# p+ S\" ]7 |  O
61. 2 A& d8 L6 b& r4 S
    
62. H2 = (betacl*Kwa143*8 i* I; q* l9 Z. O
    
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*6 s; H1 g! |8 L
    
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*9 @\" y6 g$ ~& ]# s  D) U
    
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    0 w6 @  W  c7 O7 p7 N3 A; Z, w
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*! ?& r, }4 Z1 K4 o8 g7 v
    
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    & A+ S8 L. M/ ?3 [3 E
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    2 f, @. V) a& }% g2 A
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    4 N0 W% c4 K. }: e9 p6 I# u
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ; A9 o4 N& |! w+ x0 G
71. ; Z. R' w$ I5 q. d+ w5 e
    
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*+ _. S( G# o7 S+ g3 q
    
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*) J\" A5 C; l& s2 e8 ^, Q; |
    
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 H/ Z; E7 u6 I3 g- g
    
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*6 Z* i) z$ h' f
    
76.        Kua122 - 5 R1 l8 E  U3 _  \0 R
    
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    # O6 T& k3 i\" T2 z  a\" p
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 9 \. x' v8 ?' P8 h\" A9 {2 [4 |
    
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - , W1 C* C+ @4 m# s
    
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    - l) N' X1 p8 \6 |# ~$ s
81. # h& M+ B6 T( n$ @* B! M* c2 z
    
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    / ~* h+ K; P' e1 @
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    3 o6 U4 y& p! X\" A
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*! k$ f: y; X. g
    
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    3 F/ \3 ~/ D  J4 ?5 ^# r& d; w
86.        Iua122 - 2 J. S- M; b- e8 Z
    
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    + E: z) i/ E: Z# T4 f( j
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    ( S3 ^$ e& U5 V* z! Z5 v\" s
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ) s) F7 Y% l* q
    
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    2 y3 l8 {8 v8 L/ @8 ]# T
91. 
    $ F1 W# w8 s2 P
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    9 R8 V. i$ H- k2 c
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    + Z# n$ `) S0 ?; F6 `# r
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*. w. r8 |0 f0 n( E( x
    
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    % L6 T2 V3 y* v
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ! d\" Y$ O2 ]* }( P* j3 i  {0 o
    
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    4 s1 {' z0 w) P# F( j' R! b
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    * s1 T\" R$ ^4 O% O3 U4 {
99.       w4^2/u3^2*Kwa143*IIua133);
    , U/ v: {* |2 g9 \
100. 
     5 ?& S; T\" V% Z$ s7 y5 H
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*/ ]  K$ b* `+ X) |- H4 P; B3 u
     
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*: n\" }# N0 I, z7 C# K' ]! M7 G5 N
     
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*+ u  L8 x7 Q( K% Z) _0 K! g, i! U
     
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
     % F\" k3 i  {1 Q! l4 S7 y0 Q
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     0 P. J$ ^1 \+ N1 r
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - ! r5 Q! a4 Q3 `, m
     
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - $ n$ j3 l( e6 ], _1 B2 w) z3 Z
     
108.       w4^2/u3^2*Kwa143*IIua133);( ?7 Y\" y! t7 h
     
109. 4 ?. M- D8 b, k/ k
     
110. M3 = (betacl*Kwa143*2 u9 F/ Z# c% h/ [
     
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
     & ~, w9 c+ z3 m- m, D1 m
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     ' S2 @, ^$ c\" y% i' V5 N
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 5 d! \\" R: ?1 _) e9 u, w2 A2 T5 `* a
     
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*5 U5 z# E# ^7 J4 ^$ I
     
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - . U5 w) O' I2 ]( M$ O0 O$ r: E
     
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*5 l7 p- ~: F- z. J! f
     
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
     9 v* e3 c) ~\" z: u  T& h  B' D8 u' Q0 n
118.       w4^2/u3^2*Kwa143*IIua133);
     + h6 }1 t& ]8 g1 {( K& v
119. 
     6 A/ ~  a+ j, d( a5 J( w; M, G; v6 f
120. M4 = (betacl*Kwa143*
     \" c( m1 k3 g+ l# ^8 R& ~: l
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
     & V, n) g5 h+ D6 y$ s
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*) @\" H8 V5 D\" L5 M( o1 x
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - & L: z8 x6 w% e- z1 j5 r6 _: o
     
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*3 v; p# L' [- j6 D\" x
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ; a% U0 I; x& r\" s
     
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*( i9 X$ S4 P( y
     
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - $ m( G, ^8 o- V- u8 k' X
     
128.       w4^2/u3^2*Kwa143*IIua133);( ^  v' v. t+ ^! K
     
129. # c7 B& o4 l- P7 r
     
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     \" u  `& O5 b' D0 O; T
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;. s5 W% T! E+ E9 K: L! {
     
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;( u9 T) [( p0 N\" J, a% x
     
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     \" {) i, R5 B5 D8 V3 J1 H7 S
134. . J2 U7 n+ D5 K8 W9 i
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     5 @\" M! a! V+ ^; {
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     5 a9 n/ Y. Z8 |/ Z4 x5 G; n8 l
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     ! z0 U3 \\" x8 w& b6 I; [
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     ; J1 [. W' T, \( H  o% c1 q2 R
139. : {) J* n7 w7 E\" f\" Z% j
     
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 4 X. r- J  Z  k; |) g
     
141.      V1*M4);
     ' R2 Q' [9 [0 K% Y, I- ?  n
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
     ' i4 ]! r+ j! }. b8 t- S( h
143.      V2*M2);
     . s# M5 m/ ~\" j7 {* \& u, X/ w- O: ?8 O
144. 
     1 F\" z2 m4 B/ F. @2 A3 v8 d$ N
145. x = xicl1 - xicl2;
     - H, K\" d: _\" _$ x3 f* U. b8 [4 S. x0 u0 M
146. x1 = Re[x];\" v1 H3 F9 t2 W& L
     
147. x2 = Im[x];
     ' {' ~- Y, b1 h
148. 
       L0 O5 A+ ]( h0 x2 v) \. S& W
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];+ P+ i+ a\" [+ w7 e\" h\" C3 c
     
150. ]
     ; K' [4 z2 F! R: B- h2 Z6 q
151. 
     2 u# h* s, i8 u% F0 Y* a* e

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
' l9 a! e# A0 E5 D: |' gFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
& D% R5 u( {( q! K ]
$ n- m/ ~' a$ X就会出现
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.

请问是怎么回事?

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