请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   1 \# g4 F# i) j9 f5 }  v* \$ h4 M
2. k0 = 2*Pi/lamda;
   0 L1 N+ R9 W* B
3. n1 = 1.4677;(*纤芯折射率*)\" J  f$ [5 e) o. a
   
4. n2 = 1.4628;(*包层折射率*)
   % D1 w% o- n% h) t  Z' t: R& }* }; b
5. n3 = 0.469 + 9.32*I;(*银折射率*)2 q; t! T0 }8 Q' f5 ~, y; O
   
6. a1 = 4.1 10^-6;(*纤芯半径*)
   ! B) |) C% r2 H/ S
7. a2 = 62.5 10^-6;(*包层半径*), o; D8 ]+ `! K
   
8. d = 40 10^-9;(*金属厚度*)
   8 t9 V\" K- B7 E! @! G3 H
9. a3 = a2 + d;* r7 c& Q6 r& ?3 T( p
   
10. mu = Pi*4 10^-7;(*真空磁导率*)+ g* h8 W  j, f% m- v2 d
    
11. epsi0 = 8.85 10^-12;(*介电常数*)8 `  X\" M7 v3 |1 _  F1 b
    
12. 
    \" r7 R+ O, m1 g. U) d
13. n4 = 1.330;
    - z: {# Y\" k) A1 Y! m( u3 D\" J! K
14. + B9 H5 v6 q! c% [7 T# @* Z
    
15. neffcl = neffclre + neffclim*I;) G  d\" N/ B- r5 S
    
16. ! N* Z7 d0 o7 a3 M! t2 k& M
    
17. betacl = k0*neffcl;. ^8 z' Z4 B9 a- D- q  ?; P0 t
    
18. omega = 2*Pi*299792458/lamda;
    - e, t$ {# {. m7 F; y) C& n
19. 7 r! q- F# t* ]$ x7 r$ P, R6 _
    
20. epsi1 = n1^2*epsi0;+ }* P2 I. ~: H) @
    
21. epsi2 = n2^2*epsi0;
    1 _' D7 Z7 l% W\" H& J* v
22. epsi3 = n3^2*epsi0;
    9 H/ D+ E' m4 z
23. epsi4 = n4^2*epsi0;
    ! d& Q5 K# ]. e( t' `
24. 2 y4 U& T- j* ?
    
25. u1 = k0*Sqrt[neffcl^2 - n1^2];
    - b1 V\" N. ?$ C' L4 u; [
26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    0 T# G6 ?1 I6 u/ |: {
27. u3 = k0*Sqrt[neffcl^2 - n3^2];6 {2 v! I2 |% z* f
    
28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    \" b4 r- }$ h  ?! w\" V
29. 
    7 x) }* [\" ^8 e' w
30. Iua111 = BesselI[1, u1*a1];
    3 ^7 m; Z6 m! L! c
31. Iua121 = BesselI[1, u2*a1];
    4 \! t$ |\" l' ~6 A
32. Iua122 = BesselI[1, u2*a2];
    # J- E5 N* ]( K& t5 O4 T
33. Iua132 = BesselI[1, u3*a2];2 d0 `/ z\" n) Y! Y/ A# t  h) [
    
34. Iua133 = BesselI[1, u3*a3];
    * N5 L) |# u( ?9 m! g
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    * E/ t4 w' k4 _# F- [2 e% G5 D
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    2 P% X6 m/ j, N/ Y! Y+ W\" v
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    # J' q3 w  P$ o- t0 T' L3 H
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;$ B: b- w/ ]8 O0 [7 T, v5 d$ w% H4 G
    
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;\" |* Q' y- ?2 z' j/ C\" {, n+ o
    
40. - _: T' ^5 I0 f
    
41. Kua121 = BesselK [1, u2*a1];6 o. r- B* H; z$ p# \/ E
    
42. Kua122 = BesselK [1, u2*a2];
    # E4 y+ R8 @3 Q. K4 u) j% a) |
43. Kua132 = BesselK [1, u3*a2];, K0 r+ M' s9 e8 [( F2 V
    
44. Kua133 = BesselK [1, u3*a3];( [# ^% r/ C0 k) A/ H- p
    
45. Kwa143 = BesselK [1, w4*a3];' g$ {2 H. G) B4 r- y
    
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    $ n- k1 H5 x- n) |8 u# s) f1 p4 d
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
      U' F6 L, Z; p3 [' G8 k
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    ! P( P, A; X  I) T
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;\" L' ?6 O  ?' t3 u. F  g' \
    
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;& R, p$ H\" {5 E4 Q* ^
    
51. 2 v8 J3 x9 a) P' f: l. q
    
52. H1 = (betacl*Kwa143*9 D, \( U* A4 ~: R
    
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*0 t5 w  T; P  X4 b+ B
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    7 G- |8 C. O! \1 {) B) ?
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" B9 H* X$ F8 y0 i% \
    
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*2 `3 m, m# V2 v1 i
    
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    2 J9 f% D  l6 d
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*7 O8 [! ]2 _6 q! v( k% H0 Z  }
    
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    - A, u' l; @; Y' ]* J
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! O& Y3 F) R( ~5 ?
    
61. 
    - t- E2 R5 A1 X
62. H2 = (betacl*Kwa143*
    % |& w\" d* }/ c1 N
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*) S  C# T( ^' q2 A4 i
    
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    , }$ D\" w4 l/ i# S- o
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    2 @7 G2 G0 `$ b3 l, g$ i' U# M
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*- }  j0 o: u6 h6 `
    
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 F5 b& E1 r! ]  M2 n! J& W; J$ c
    
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*) P$ C# m3 W. e& K2 C6 P
    
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    7 n( X, A8 Y5 c
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    - ~9 z5 a1 H+ K\" x1 w! {
71. 
    2 x# G4 i* Y2 h% u% s% V7 q
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*' E* p2 F6 \4 [) ?
    
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    & P9 o6 F: B9 _
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*( G% i% s, d& y2 J) T# \
    
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*# C( b( p+ f, U
    
76.        Kua122 -
    7 l! D& C) F1 {0 V
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - , h7 u+ @/ P& ?3 a5 p5 D' W+ g+ i
    
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ; H; Z: X# s, Y3 v- u# v
    
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 1 D5 N: u' m$ p6 o/ C
    
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    4 p' a\" m  r, U: X* f  L6 f
81. 6 S/ F0 Y1 I/ i: ]. e\" S
    
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*0 @$ k! @% k. Y% I- F
    
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    ' _6 Q4 ?+ ]4 \7 t7 D1 G5 m3 M
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    0 U+ W( g' i: Q' U, E7 h0 V
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*7 L0 p0 Z& F1 ~$ H# S\" s2 q
    
86.        Iua122 - , h1 I0 o  {% }6 c, Q4 M4 @
    
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    / W9 }/ z3 @3 k1 X6 x& W: ^
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    $ W3 ^* `3 ~5 I( O, ^
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    ' r3 S  w/ F0 @9 s\" N% M; z) [
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    $ C2 n4 p, {9 p2 o
91. 
    # p% U. ]! _& \& B% `7 F
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    \" y) ~0 [- d/ r0 @: C3 j5 _
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*: F2 k' U6 k! P5 `6 W+ Q
    
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*. K- n\" t4 }- R! F/ @- Y
    
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -+ U& n5 \5 e6 \- q; o# B4 G) N
    
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    8 ]* k, G2 @0 x% p. @! f
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    $ c  ~( U& U) U1 K  r8 A
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - : C3 P7 a/ k1 K2 o: ^* s
    
99.       w4^2/u3^2*Kwa143*IIua133);) |' ], z7 n9 F) T. `/ g2 S0 C  [6 X# ]
    
100. 8 B+ h* s! m+ o( M4 c% s
     
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*- T3 i% t5 \; u4 D! d. A) m
     
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
     3 G& G5 c. k7 i' Z7 U6 K6 d  p% }- j/ q
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*1 @: a  E' I) G6 G( j6 D
     
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -) j  l+ S% a' k% i% V\" j
     
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     ( n3 P. _. c: p\" }
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
     9 J' h& i4 s. Q1 W% q( p8 A
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
     ( g: _* P& Z8 j\" V4 [2 q
108.       w4^2/u3^2*Kwa143*IIua133);! J& n/ ^4 j( c: u
     
109. 
     4 ?3 c% e/ n  l7 m0 ^$ i
110. M3 = (betacl*Kwa143*: z9 ~3 n\" p% M! x
     
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - : Y2 G1 h# R5 ?; s2 V. K  L: Y
     
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     ' j: O9 J8 z/ w5 O
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - . p- L5 @! G: A* E$ x3 F
     
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*% \9 v7 S) ~% K; Z\" M& p
     
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     9 K2 L; T4 G$ G$ F
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*5 i' ]/ s. d, @' |$ n2 y8 o
     
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - , [! V, o( G( U& V
     
118.       w4^2/u3^2*Kwa143*IIua133);
     \" D4 v2 s* o/ D: `\" p8 K/ Q
119. 4 N+ j: l4 c( i3 Q( Y+ ]2 b
     
120. M4 = (betacl*Kwa143*5 t# A% ?8 j2 l1 d1 R8 w
     
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - * ], Z2 n( z) a) O' k
     
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*% ^5 [7 C2 L9 `% L, Z( s! V
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 8 k0 b& E! V- A/ g' t( E. Q
     
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*+ z: ]4 T9 y% C
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     , w5 ?& ?' H7 |
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     ; y2 e$ e. [1 Z/ Z
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 3 A* M5 n' T$ v( O# ^; B2 h$ a
     
128.       w4^2/u3^2*Kwa143*IIua133);
     # r6 ]+ |( m7 T* k. B. {
129. \" ^& [2 g, [$ y9 Z5 }
     
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;2 M3 J7 Q( f1 {
     
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     / Q7 Z' D, _1 j& ]7 V& R
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     ' Y: j; c7 g. ]. N
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;  R( ?' ]& _\" ]1 {5 \2 J) l% A
     
134. $ t\" _5 r$ S  z\" x3 y! Y1 O
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     * R3 a8 q\" O2 S
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;  c8 F! h2 y$ S8 }& M
     
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;6 j+ j% B. Y( t! m
     
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     % j& ?! g7 P' G  P+ [/ U
139. & C# [7 ~4 Y3 S( k4 M
     
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
     6 X\" m% f2 G8 E7 p  J/ D
141.      V1*M4);% i3 I) y1 }) V
     
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + - T! j* C\" G0 o; y7 K- j, K; C, [9 X8 q
     
143.      V2*M2);4 N& z+ d. S& d
     
144. 
     ' E) ]5 G, r/ P9 v, v
145. x = xicl1 - xicl2;
       O3 r/ q4 W! }% O, n4 l/ C) f
146. x1 = Re[x];
     $ [$ H2 O! E- G0 |9 r
147. x2 = Im[x];4 [/ ?5 a$ v; o( {; H
     
148. ; e# {& g+ l# g% O, ~7 i0 g
     
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];, p6 L2 V0 t5 f# |7 j% |1 ?; C; @
     
150. ]  _* T  m! g4 U/ ?
     
151. 2 u3 {) U3 e  o( o
     

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}}];
' j1 e/ i  C; V4 i, q$ r换成
3 G2 O! b1 W! D& T' ?' X0 cFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
]
/ ?+ f3 X% l& T  u5 W; f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.
; x, P8 Q6 O  L4 @# @# p/ u' H
请问是怎么回事?