请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   $ ~  N- ]0 N% G
2. k0 = 2*Pi/lamda;$ n- m' ]6 J4 T+ G
   
3. n1 = 1.4677;(*纤芯折射率*)
   + ~2 D4 l: I1 `4 \; L
4. n2 = 1.4628;(*包层折射率*)1 h8 C; x5 L1 _# K
   
5. n3 = 0.469 + 9.32*I;(*银折射率*)1 Q1 ^7 b5 ~' E
   
6. a1 = 4.1 10^-6;(*纤芯半径*)
   \" e$ Y: i& f; t9 S
7. a2 = 62.5 10^-6;(*包层半径*)\" }: u0 H$ @4 X( M
   
8. d = 40 10^-9;(*金属厚度*)  L5 u/ T7 j; t$ h7 V
   
9. a3 = a2 + d;
   6 ~; S# Z, \& M1 ~
10. mu = Pi*4 10^-7;(*真空磁导率*)3 n  O9 d  u& h; h- _1 p: `- Y
    
11. epsi0 = 8.85 10^-12;(*介电常数*); N/ f+ o( p/ q! W
    
12. 
    + l. Q& M$ m; f- I
13. n4 = 1.330;8 ?/ @  M' v( B/ M\" z( C: a
    
14. , A: [5 d' e$ }3 M
    
15. neffcl = neffclre + neffclim*I;$ S! C& v6 N. e/ r# [% c
    
16. & n6 W2 v1 p, V' ~
    
17. betacl = k0*neffcl;% ]$ r/ G' l' ~
    
18. omega = 2*Pi*299792458/lamda;9 |$ d* _9 j/ a$ E4 h
    
19. 
    . L) E9 l2 M' ~% q0 s; f+ Q
20. epsi1 = n1^2*epsi0;2 d2 t0 z) G7 t4 }7 G
    
21. epsi2 = n2^2*epsi0;8 o& m: V4 ~; [1 R! C& X
    
22. epsi3 = n3^2*epsi0;
    ( V+ |8 D* M, K; O' y- i. a4 O
23. epsi4 = n4^2*epsi0;  w/ D! L5 U7 L8 t2 S4 T
    
24. 
    9 {( C6 Y; |7 A# R2 }! y# p
25. u1 = k0*Sqrt[neffcl^2 - n1^2];. t$ H& W6 Q. Q
    
26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    5 b4 O8 H; n5 S3 m\" ~
27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    4 }: E/ e; {, Q3 O/ g
28. w4 = k0*Sqrt[neffcl^2 - n4^2];  e) k+ {9 ~$ |5 P) g/ a% _
    
29. & ]+ d* ?) q9 M
    
30. Iua111 = BesselI[1, u1*a1];, g$ ~! w) N. c
    
31. Iua121 = BesselI[1, u2*a1];
    , s. T( m0 ~4 Q0 l* M9 K
32. Iua122 = BesselI[1, u2*a2];
    : G% e; y9 Q0 J3 H: ~: v/ B1 C. h
33. Iua132 = BesselI[1, u3*a2];
    4 V- c$ @9 _7 l+ F+ ?0 |& d9 _2 ]
34. Iua133 = BesselI[1, u3*a3];
    6 x8 K& [1 j) b8 \0 u
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;+ b2 t8 Z+ w* I  [1 p2 n, ?7 W
    
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;& L' p# W* U7 U2 Q
    
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    3 Y3 i; Z+ w$ T7 f: e# V1 u
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
    ' P8 x: E* _, M! T/ ]
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;& l; y; L& E* C/ }
    
40. 3 [8 X6 e& [2 p0 q
    
41. Kua121 = BesselK [1, u2*a1];, q' i0 v1 U+ F
    
42. Kua122 = BesselK [1, u2*a2];( |+ V# p5 r; A1 O, n
    
43. Kua132 = BesselK [1, u3*a2];
    ( a1 ^7 z' u& l4 k6 z2 T7 N
44. Kua133 = BesselK [1, u3*a3];
    $ x& n7 N9 [8 T+ j
45. Kwa143 = BesselK [1, w4*a3];
    ' R& b, r% E) {& p* e. C% Y
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;6 |\" n% r& S) z3 l0 J6 A/ k
    
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
    6 }  Y! c4 v# x3 c7 O6 h
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;) W0 z. w5 H1 t- u7 [4 V. L, U
    
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    6 f# r: x0 @: |+ n; m5 m
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;5 F7 H/ \6 S* y1 L# k2 ^
    
51. 
    % ]( F  v3 e* E\" M7 g
52. H1 = (betacl*Kwa143*
    * f* W# o7 J: U' u# w6 ^
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*0 f; ]1 I9 I, a8 y' W- K/ W
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*& L# K0 j$ i  z$ t& d+ \3 ?6 m
    
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*& T2 V2 T7 n! V' A
    
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*+ r( q; X! Y8 p/ E6 L* j! b( M8 X
    
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*% U5 N8 f1 k. d5 r9 s' D
    
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*5 ~4 j. ]& F$ |& Z, {1 W3 u
    
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*. s+ r\" {# A# z9 [3 ~0 B$ G. _& W
    
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; a$ r; q0 P, X4 W- r6 c
    
61. * Y+ L4 K  i+ J8 b
    
62. H2 = (betacl*Kwa143*
    . r! B  G4 p' O& Q; L\" X. V
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    7 ~, Z0 Y; Z/ R5 F9 r. T\" s$ g# c
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    : `+ g5 [7 m6 w! y2 j9 y
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*7 y: g$ V6 |! A* R/ l
    
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    . m. F1 y, g. M9 }  F
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    % b* B- N& C: H/ w
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*. e7 Z: J  q% D
    
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    + {2 |0 j9 w8 P% x
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 F3 z3 G' k# F
    
71. % @3 i6 _( |/ j
    
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    % d: Z0 h) ~2 f1 Z/ v0 Z
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*/ {7 e7 U/ K  b5 @1 K
    
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    4 s9 }9 c7 Q9 u6 D5 H
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*: Z& l3 R, d4 \) w5 z, G
    
76.        Kua122 -
    1 H% r\" v4 k# d4 }# k' o& c
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - - l  w6 r6 z) D- Z- L- J
    
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - # F: D6 w0 J+ r! X0 C
    
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    2 y% R\" j4 t& m: I2 t
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    1 c) a2 Y7 @% R+ \' g% n1 l- S5 b
81. 
    $ `: {+ B- E$ I4 h: ]* g6 e\" u# d
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*& N7 p5 z( v$ j! O\" `
    
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    - @' x4 S  _0 L$ z
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    : e, ^7 r; a, X
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    6 g. M) S\" s/ T# C7 @0 ~3 t
86.        Iua122 -
    2 N\" J# v# d! Z
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
      z8 W) h7 R0 i! F' K( g\" u
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    * K* u% I! A5 [& L/ w% Z
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 2 q6 _9 ?0 K5 r) U  C6 }1 I0 H
    
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ' d: t, W' D4 |0 ^! q! K. g! a
91. 
    ' h5 Q  J* C9 b4 p
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*# u' w( y: ?0 V3 T. B
    
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*$ w8 N3 E6 \; }2 j7 M
    
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    0 w\" m' T\" W& D
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    / n5 e1 `6 G2 g\" |% f3 M
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    5 ?1 E, p4 n7 |; ~6 b0 o
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - # x7 {\" s\" d5 [0 G8 U7 r
    
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    : a( G* \! ]* ^# g& l\" {6 s
99.       w4^2/u3^2*Kwa143*IIua133);4 _! K( i, t3 }) _: v+ D! @
    
100. 
     8 c$ ~$ n( w2 ^; q( B
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*0 t* \- x( B- W9 J
     
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
     \" J  y$ a+ r# s
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*! {2 S$ \/ ?6 ^
     
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
     0 S5 b' Y6 c2 K, O# b8 w
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     - I3 v- G: S4 e$ h4 w
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
     : S: ~& g\" U3 X
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
     7 P/ ~5 q4 u3 L# w4 }
108.       w4^2/u3^2*Kwa143*IIua133);
     0 I1 @1 x( F( s  l7 K
109. / ~* H, L8 |8 |
     
110. M3 = (betacl*Kwa143*
     , D- C3 z! b6 H5 K1 ?1 E
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - # o4 v- q4 }4 d
     
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     8 n5 E( Q\" L9 K+ T! K- H2 v! V
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
     2 E+ F9 |# ?; z, H% m
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
     * H* f4 i, {# I3 \
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - . w- L# ?7 t! B/ N
     
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*+ Y9 F$ O4 d, O% k
     
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -   T' a, ^8 j( a9 W
     
118.       w4^2/u3^2*Kwa143*IIua133);
     ( X& b' o1 z# R( q# H) `9 Q4 O
119. 0 o; _2 N9 m  i, @
     
120. M4 = (betacl*Kwa143*
     6 C0 }# J9 d& R/ w
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
     : Q! ?) R& x% d+ y  C
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*+ Z# e' {* A& w
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
     ) F8 ^( z\" U& N
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*: W; \\" [/ z: G  c/ p( D; l9 L6 J; k
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ) D5 |, g; J( i( x! F) \
     
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     5 j4 L+ e/ T7 L: W\" @( ^9 h
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 9 e7 T  C/ M8 k* y& f  ^6 U0 F( j9 q! Q
     
128.       w4^2/u3^2*Kwa143*IIua133);9 e\" Z  T& \- ~; l1 r7 ]
     
129. 
     ! N) ^9 Z5 v1 l
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     4 I& y; U\" O1 ~2 X: p% C, R
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;5 y8 h3 `$ A, y
     
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;6 P% H9 O: u- y
     
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;  A4 B& P/ b2 U9 z! w8 J; a: {
     
134. 6 D/ e' A. x  \* x9 K
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     4 R0 k& ^1 i! \+ o; [7 h6 i
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     / y* }. l. ~4 c7 N
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;) O6 O/ ^) [3 o, o( @) c
     
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     8 M9 w4 O1 l: Y, m! I1 O* o+ A- p! v
139. 
     $ `! P  D3 ~\" r\" ~0 f6 }% S2 s
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
     / m7 v/ z6 F' c6 X
141.      V1*M4);
     ( x' z( [* \# l\" C% A
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 7 R* Q' G$ P5 a% `\" F/ y) S' k
     
143.      V2*M2);\" \- n' j$ w- N; u( M\" g
     
144. 
     3 s- Y& Z& V( t) }
145. x = xicl1 - xicl2;8 Q2 F  D$ o% e7 |( [1 r
     
146. x1 = Re[x];
     - Q! x3 p$ i3 G& J& Q1 P
147. x2 = Im[x];' Q) n5 g8 R+ D! Z) a+ ?
     
148. ' I- [1 |& ~2 k* w
     
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];\" Z\" g4 S- X. ^
     
150. ]/ z5 C+ G, F+ E( E1 V
     
151. 
     / W( y/ h2 Y7 J

复制代码

代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
1 F5 ?7 `4 g, `' f% W8 S! F但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
/ T( h" f) Z. |1 N) C9 m换成
6 N* u% X. W$ |+ T" ^1 L0 p+ ?: yFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
3 p- I6 \$ z, Z: w- H FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
" a$ g0 U. P& b% L) q' _1 n8 O ]
, }  C" D3 V' L" y就会出现
3 ^1 c' W# k0 _' Y7 M% o! sFindRoot::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: f* P: n" g' O5 D( {% h6 M% a
请问是怎么回事?