请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   2 H6 U0 `( X! t1 @
2. k0 = 2*Pi/lamda;/ {6 C7 S6 c! A
   
3. n1 = 1.4677;(*纤芯折射率*)
   ( Q- L3 p! X' t; @
4. n2 = 1.4628;(*包层折射率*). }+ P4 {5 ]0 R# h! K' r
   
5. n3 = 0.469 + 9.32*I;(*银折射率*)' U9 x+ Y3 i6 v\" }1 Q
   
6. a1 = 4.1 10^-6;(*纤芯半径*)# U/ K% j) \& ]- M$ ]0 z9 B\" Q
   
7. a2 = 62.5 10^-6;(*包层半径*)1 |3 {7 Y: P8 ^! b6 n$ `
   
8. d = 40 10^-9;(*金属厚度*)
   / \- m/ l7 f- ^+ S) d1 _' b( A
9. a3 = a2 + d;) Q1 q) i6 P' a: {3 Q
   
10. mu = Pi*4 10^-7;(*真空磁导率*)
    . @1 l7 V9 |9 [; C5 |2 }
11. epsi0 = 8.85 10^-12;(*介电常数*)/ V* c2 J( R6 @- I  j4 t/ m
    
12. 4 k. [. N  m1 k: c& r$ V
    
13. n4 = 1.330;
    8 }' ]+ D% Z5 _. K# {
14. 
    - s8 Z' f! W  ]+ ~! m
15. neffcl = neffclre + neffclim*I;2 L0 x/ n1 l  ]
    
16. 
    5 r5 L( Y% W* K/ p8 P& \0 j( Z% k
17. betacl = k0*neffcl;
    ; m9 S9 F; I' f5 d8 z1 A
18. omega = 2*Pi*299792458/lamda;. P4 w' N1 X, b% z( L- |
    
19. 2 ^& J+ |# `9 ^6 t4 A9 r/ X
    
20. epsi1 = n1^2*epsi0;! b9 W: {  k: Y/ p% v
    
21. epsi2 = n2^2*epsi0;
    ! M: P8 U' K- p% ~
22. epsi3 = n3^2*epsi0;# Q. ]; S, x3 _) S
    
23. epsi4 = n4^2*epsi0;1 e( B+ Z. k8 R3 o( B# a
    
24. 
    2 o4 W* F& B1 C! P
25. u1 = k0*Sqrt[neffcl^2 - n1^2];
    4 U\" p& \# h# S2 A& U
26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    4 A! P, l) N% _7 |
27. u3 = k0*Sqrt[neffcl^2 - n3^2];0 ^+ n' B/ p4 f9 D. A+ r\" a
    
28. w4 = k0*Sqrt[neffcl^2 - n4^2];\" v% z1 L( y/ H1 l\" X\" \$ B
    
29. 
    6 @* e# ^* _: n$ M
30. Iua111 = BesselI[1, u1*a1];
    6 J9 i) f- N# Q/ C& Y7 q$ k
31. Iua121 = BesselI[1, u2*a1];
    * T% q- g% j/ j! V! P: D/ S
32. Iua122 = BesselI[1, u2*a2];0 S: p: N% a# r7 W
    
33. Iua132 = BesselI[1, u3*a2];
    % R9 x; q0 b9 i0 K+ U
34. Iua133 = BesselI[1, u3*a3];
    4 z\" I: k! t- D
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    & c1 M2 T2 B2 ^
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;) g2 G+ K/ Q6 }* J
    
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    % e% n$ P7 s5 }* f3 E! j
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
    7 x, Z: d$ j3 m* n$ u  Q  v
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    1 A9 l# H% O1 _5 [) E. Q% q
40. % w0 Q. K$ I6 x6 q+ i
    
41. Kua121 = BesselK [1, u2*a1];0 f) ]1 ^% ~( a/ X) f\" V
    
42. Kua122 = BesselK [1, u2*a2];& S* W* c2 P0 e6 b/ A
    
43. Kua132 = BesselK [1, u3*a2];  F  t0 i- K4 q5 ]
    
44. Kua133 = BesselK [1, u3*a3];
    8 S& p2 R# I1 n9 y
45. Kwa143 = BesselK [1, w4*a3];
    9 `) ?, r8 B4 _( W
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    % i; Z! J1 e8 o0 m( s) J3 ?7 S. ~
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
    / i\" n+ @( B  I' ^% f( {
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    - C% X+ a$ Y1 E( C' n
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    3 z! I3 c0 ?( r' _
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
    * j- j3 E1 ^+ u
51. 
    6 _+ N- ]9 \1 l- y/ B
52. H1 = (betacl*Kwa143*
    9 n7 u; y% x* r5 j
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    & {: W# i0 \( a\" `3 i
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    ) {% |, {& I8 S6 r' @7 X1 ~% F8 D
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    & U4 W% Q7 U\" }& k9 _/ J; A
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
    % ~* a& D; q! e( c& A' o' ?
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ' V$ ^) _\" Z% Y! ^1 k\" M- m\" W
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    6 B$ N# e  e- r2 L  [* D  B
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    6 S$ i! i+ E- G\" D, a, G# l
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);: _- N9 x- {. ?. f
    
61. 0 F/ ?5 y8 F: V2 e) q5 P
    
62. H2 = (betacl*Kwa143*7 _, P2 ~6 B& `; u* M! L+ d
    
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*- D* {; V/ `! Z! [7 i. M
    
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    7 z6 i& S: v6 U$ Z
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    6 H; `/ S0 n. m/ A5 l6 X3 p
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    , q# ]5 N* a6 a4 z. c* a
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    - S( M( N: I# [; n/ R% W\" `
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*3 h1 c+ q) ~' m6 K; @& y/ X; a( F
    
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    * L& T( l! y+ N8 i/ T7 T
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);, S' ?! ~  P' h! G3 C\" {' @; L4 B\" M
    
71. 
    ( T, H: V1 x4 l1 |
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*2 G2 G( f$ i; E( e# f
    
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*. B+ S% r: F5 k1 D# I& H0 o) y+ c; P
    
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    % w3 J8 ]0 r: p5 C0 ?' f# A
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    3 ~1 v0 |  t) ^/ \
76.        Kua122 - . J0 T0 Y7 S  e7 ^) S
    
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    - k- t* s5 J3 Y; E2 T  Z
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    $ Q% F* \  C# N0 Q, ]
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - , t( L$ i( Y! Y) e
    
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    - b* B% v0 F& e8 f: d
81. / }6 x, c\" ~. d1 F
    
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    ( w: ?+ Z& \$ ^7 `( ~+ K
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    1 B! C, Z( E# R
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    \" u$ a  T  F5 @2 \
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    0 H! r7 f' T6 Q! z7 Q3 y
86.        Iua122 -
    , _2 \6 i; x+ f* A( x
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - + P7 x' `\" c. n& k; K3 N- y
    
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - + H! u+ _& k! }+ `& l
    
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % l7 F1 Q: I0 B0 I& ^* a8 O
    
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    4 U/ e: q/ I3 d) a: }2 Y2 `/ G  m
91. 
    7 S+ \8 B. A0 g& U+ v- ?7 C
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*' r2 O# U: G1 N' ]* }
    
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    4 q  z; b5 _3 `4 E4 n( H6 l# ~
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*5 c4 f: ^3 m* q1 d
    
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    % N$ L  V0 |- q$ f' o
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    / z6 V1 Q# x0 I2 o8 [  p2 Q! @7 l7 `
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    ' V/ g& K4 K  T* P0 ~' @& g: p# f
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    # a) v( k# j& s) T\" g
99.       w4^2/u3^2*Kwa143*IIua133);. p4 o+ ^! x+ f. g( m
    
100. - O! u' s* h: S4 P5 o! t( A0 Q5 t
     
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*4 G  O( z' ^0 j! V- c
     
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*6 t% n! h4 @/ s: P: n1 [3 R
     
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*+ z! z4 E) B1 u* A4 X
     
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -9 C5 S  d0 z' j2 i% J/ l
     
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     ! O4 C6 g$ B9 m' F' j2 D7 ?) ?/ \
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 4 ^: Y4 ?) [, i7 M\" D* @; |4 x
     
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
     ' @+ D4 W0 B& E- i3 u4 m$ ^1 T2 L  k
108.       w4^2/u3^2*Kwa143*IIua133);+ g0 b% U& p3 h
     
109. . R* v  e1 d# H3 f/ r
     
110. M3 = (betacl*Kwa143*
       O\" B# |2 y% y* X. s5 k
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
     0 ?, k0 K% ]4 s0 T
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*2 @3 |4 e5 V: Y0 Z: l: D* }& ~
     
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
     ) ?: y. q) N4 ^
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
     . A2 A% s- b8 ^\" ~7 n) p5 Z( p
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     3 }3 a' H3 \& t% ]9 q
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     ( K# Q& o  f0 a
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -   \; F/ k; P  f9 G5 K7 L
     
118.       w4^2/u3^2*Kwa143*IIua133);6 M8 C6 i# g% [$ b. H* ^' X3 g3 O
     
119. 6 [7 ?6 q0 z) f1 E2 x1 P/ `
     
120. M4 = (betacl*Kwa143*; `1 f# D/ F8 y/ ^% t5 x. x8 m
     
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
     9 J7 @1 M* W# }) a8 h9 {  b
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
     : F9 s3 r- N, T  D
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 4 t- U8 Z& x. b7 v
     
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*2 W, n) ~% n( Z! i1 O: l9 [
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
       Q+ D  Q\" w* _: g  G( r
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*( S% N% b; L$ a' G5 u\" J5 k
     
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
     * m9 s' z2 P# y& W
128.       w4^2/u3^2*Kwa143*IIua133);3 P* s2 v8 v7 _9 t( _) ?
     
129. . K1 f1 I$ v+ r+ @\" }1 K
     
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;- j! t7 R9 e! @4 `1 T
     
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;& c$ t! i4 N- j4 ~; m
     
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;' K% e8 H* n5 o4 _) G' W  ^( ^
     
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;! `% P- M2 c& [+ t! {3 B
     
134. 
     / B8 Y' Y: y. v( k- V( g
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;: e8 {8 z3 q( N
     
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;7 `+ O, M( @' ~9 Y# z; q
     
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     + b5 s+ ]2 n5 b5 ~3 e0 k8 A
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     ! g, }, a1 J4 ^# ?
139. ) M9 F& ~& y1 C: ~2 z
     
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 3 H- }; j) n: |7 f$ ^
     
141.      V1*M4);
     9 d' `  H  [# e! v: _
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
     0 ?( c2 J! Z2 f6 i/ S
143.      V2*M2);4 g; d6 O, ~8 V8 T0 J$ Q  T
     
144. 
       s. _8 |( k. o
145. x = xicl1 - xicl2;  z' l% ?' q& Z2 U' F
     
146. x1 = Re[x];
     ! n# y1 h3 q* a6 a! u+ k
147. x2 = Im[x];2 S! {+ _4 s+ ^' `$ b\" k0 ^
     
148. 7 Y# h! [( e# r, h! O9 l6 N' }
     
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];0 X6 K* a5 s% ~$ Y+ V
     
150. ]1 t  x+ s+ @\" c9 M\" ?
     
151.   ]) L- }3 ~+ `6 R) h% Y* b+ U1 ?
     

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
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
]
1 R0 O. n: d5 n, F- [# 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.
- J, \; K. T4 p6 c- v) }
请问是怎么回事?