请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   ' @: L\" I5 F3 U
2. k0 = 2*Pi/lamda;
   7 ^5 j& I+ K/ H\" T
3. n1 = 1.4677;(*纤芯折射率*)2 T/ S. x7 f\" {! x9 F
   
4. n2 = 1.4628;(*包层折射率*)
   9 J' e' N8 L7 p( }5 V; E
5. n3 = 0.469 + 9.32*I;(*银折射率*)
   ! _7 t) y) R! k
6. a1 = 4.1 10^-6;(*纤芯半径*)
   2 e' d$ A! j: E& E3 Y/ \
7. a2 = 62.5 10^-6;(*包层半径*)' T: L3 t# n; d! r
   
8. d = 40 10^-9;(*金属厚度*)
   , O: D8 R+ e2 N+ ^1 z% W& i9 ]8 o
9. a3 = a2 + d;$ D8 f+ G8 G- f& w/ J& ]
   
10. mu = Pi*4 10^-7;(*真空磁导率*)$ {! x6 K3 X8 k* R\" @
    
11. epsi0 = 8.85 10^-12;(*介电常数*)
    9 e2 B2 b, R: B+ O5 \% N9 W. d
12. 
    2 N2 H, A& [8 g8 Z, [. @: V* _* l
13. n4 = 1.330;; q# c0 }9 I' Z5 t6 I8 Y# {
    
14. ! W1 H% R4 q/ T: r
    
15. neffcl = neffclre + neffclim*I;$ s' e1 A) z/ ]' N9 j2 O
    
16. 
    / u/ e$ g# ^  N( O; u
17. betacl = k0*neffcl;6 j3 C1 n3 o3 b4 C- R' \
    
18. omega = 2*Pi*299792458/lamda;, `& R7 }2 ~) E
    
19. . ]2 G% d8 S) ^/ B
    
20. epsi1 = n1^2*epsi0;+ G1 w, U4 M9 }% [: ]( D1 {6 o
    
21. epsi2 = n2^2*epsi0;
    * y- q) w. W0 P
22. epsi3 = n3^2*epsi0;
    4 G2 W+ ?+ _) g: h0 D
23. epsi4 = n4^2*epsi0;3 L: k( M+ l% s% c\" g5 Q* s
    
24. 
    5 T' A. E. d( X. x$ x
25. u1 = k0*Sqrt[neffcl^2 - n1^2];2 p4 d& m# t$ M
    
26. u2 = k0*Sqrt[neffcl^2 - n2^2];
      W3 v* P+ {1 h4 f: U5 e
27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    , u\" n9 b  l4 C' H) J
28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    0 r4 ]. s) S, ]8 |( n\" k
29. 
    ) v  r3 d. u$ s- G5 q0 @7 ?  V6 ]
30. Iua111 = BesselI[1, u1*a1];$ ]- A3 ^! S9 \1 y# R8 u\" ]
    
31. Iua121 = BesselI[1, u2*a1];% L% j* Z8 r% y
    
32. Iua122 = BesselI[1, u2*a2];0 w: o* E+ m; g, L0 |' a1 u7 a
    
33. Iua132 = BesselI[1, u3*a2];0 x( I# L3 D9 ^) ]! t
    
34. Iua133 = BesselI[1, u3*a3];9 @  c+ {! t\" V: B
    
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    : w1 k/ f% a, u6 p
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    $ ]9 p! X! q4 w4 [  B
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    6 C; F$ t: P! K$ h
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;+ x% b* n! h7 q/ s. d
    
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
      G9 H& D3 M+ U) d1 _' f2 x
40. ! F7 D( @' _' |  y
    
41. Kua121 = BesselK [1, u2*a1];
    9 a) ^& C# N: j
42. Kua122 = BesselK [1, u2*a2];
    : Q4 t1 X! i' r4 c3 m  {: @
43. Kua132 = BesselK [1, u3*a2];
      r* p  o( w2 ?0 t; B
44. Kua133 = BesselK [1, u3*a3];
    ' I: z7 @\" a5 I
45. Kwa143 = BesselK [1, w4*a3];6 W; _: F+ l) A5 v+ w0 }3 U
    
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    ( B  o2 ]4 s0 ?$ Z, ~: d
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
    ! h/ T8 n( ?. l4 S, `- Y4 r' b
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;9 s7 A% ?; o\" M3 Q  y5 @+ G
    
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    # }* W% s3 G7 B7 ]- T8 ]( Q2 {
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;7 D1 `' e( ^0 [$ Q( W' k9 A
    
51. ) s; ~( Z1 }' D) a) ]2 O( U/ Q
    
52. H1 = (betacl*Kwa143*
    2 i+ b4 }# t$ r8 r
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*+ ~- R* j% R: Y6 b& t3 S% n; m  h( y
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*) ]. O\" [9 V/ g* K2 F6 W
    
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*4 ^; j9 L# o' J# q5 _; E
    
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
    ' |% t- C( X4 c7 S
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*\" g0 {3 E2 Y3 s) k- X
    
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*- L! p* Y8 f  d
    
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: r+ u& D, ]3 Q  f( A$ j+ ]
    
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ( e8 ?% o' n3 o! {  j5 G) p( a/ d
61. 6 N, K7 |6 t5 M6 }4 i' @
    
62. H2 = (betacl*Kwa143*+ f9 K, k5 P# p4 }7 j
    
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    8 A9 K# b8 n6 x4 S\" o
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    . {7 Z  h# n  H0 J
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    & M! ~0 w\" q; q- [+ H4 H+ a
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    * @' {$ n) j- \  C% y3 [
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*  a  L8 w# O; z/ Y
    
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*& f* z+ f) G; M; O, J  H
    
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*+ \3 S9 i! N& U$ ?0 j
    
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);* n& I1 t: m* d6 n+ }: }; D7 X) t
    
71. & [# y# c( U& i' e6 i- Q  V\" o& S% d
    
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*; k, t1 r7 L' Z\" \  c
    
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    $ |% c\" i  P1 @. x* J9 O$ L
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*0 L1 \0 {' H8 E& h6 c$ E1 t* S
    
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*, r. i: Y\" o1 b7 J$ U
    
76.        Kua122 -
    $ F2 V' _' u; S8 u. z- ~
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 8 I0 P3 S, ]! f( M' u% R4 u- G
    
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    1 b* b) T  {4 C5 W% O3 x
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    # j( K. _7 @  W% l
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    - i# p6 ?: U1 _# @( s2 H
81. / B- Q& O\" S6 j: p
    
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*  v( \8 o5 t0 x- u1 @  B+ v
    
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    2 _- U! A# y# Z5 A1 s
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*. L% O5 Y\" y# O3 m\" c4 _
    
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*& T1 s2 c# J* D, j( i: `' h
    
86.        Iua122 - ! I$ ^* M- I- J# @) h
    
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    & J% `- e( j. K4 p1 t
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -   ~1 ]+ U* T- u/ s* \! ^: m
    
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    0 s6 _* T- S: ~\" \$ ?# \, [
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    . r0 c4 f. {/ I3 m9 u
91. 
    . ~- W4 B) D1 T. w3 {! g
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    - ^' ]2 ]% \8 P* G
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*- b3 Q1 E4 }& Z8 ~2 g
    
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    5 x  {7 E2 T' q/ C+ z
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -' s* d. ^* b0 H- S! _\" c
    
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    / A# U5 e# o- g% a
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    ! L) ~: t3 K* D( ~
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ) q\" H/ W6 W' E: f- n7 `5 z
    
99.       w4^2/u3^2*Kwa143*IIua133);6 Z5 d0 n- u: A$ r# z
    
100. 
     6 q2 B9 u' ]  p: O
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
     + D  a! C& Y$ V
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*  c1 M4 X, H- R- a- x* T
     
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*; `# r5 a1 I) w
     
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
     / b4 T( \8 r/ h% x! r+ @4 h
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     * O+ e3 N\" m! o4 [4 B
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
     ( D& i0 E9 _+ A2 T
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 1 n, U) ~& c5 J
     
108.       w4^2/u3^2*Kwa143*IIua133);
     8 W1 M4 k: \0 `* \( X0 K* z
109. ( K* n- H, L( N7 N9 M+ x, H
     
110. M3 = (betacl*Kwa143*
     8 F& |# L% t1 s& e2 I) A
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - : U; {* G% E% L8 H\" ]. g
     
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     . U4 h/ Z  a4 a
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - + L; ~7 k& }' L/ s* m% c
     
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*% M7 A1 ~' ^' G  _6 l
     
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     2 |' K; ^* U* a* `- e0 o0 g
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     * T9 W0 T+ l: q% p; V
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 0 v6 G% e% Y* ]2 D+ M
     
118.       w4^2/u3^2*Kwa143*IIua133);9 A1 ^1 R4 h& p8 g3 b
     
119. 
     / s9 t- [2 X! L' q1 M  c, S/ k
120. M4 = (betacl*Kwa143*# \# g\" h( l& _4 |# d3 b9 H1 |/ F
     
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -   b* S0 f  G6 Q6 J  P
     
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*, R\" j8 f7 Q8 R/ @# b
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
     . K, F9 x# ^; W, U. J
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*# O/ Y3 {( Y6 X& d/ S
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     $ F% S9 M* x8 k# X
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     . D1 O& n& h# _: \, W. v
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - \" Q% m$ c% i+ w# B\" S4 {2 ]: v
     
128.       w4^2/u3^2*Kwa143*IIua133);\" [8 v  }; H  x5 U
     
129. 
     7 N2 U3 K4 o% I
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;5 [% ^4 F* Z( n  E4 M' Q. j: b* U
     
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     * O1 N- w  J* r7 e/ c\" t  }
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     2 O4 i) _' h\" G. t
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     \" W: O+ X0 D+ u
134. % O+ ]1 ~7 D' |5 E, i( b
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;6 d- B4 }& C/ u& h; `) K
     
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;5 h0 k7 ^1 ~8 d+ e0 i
     
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     & P: ^, \  H( n8 |- y0 a
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
     6 z! Y  G2 B, i0 ^
139. 6 ?4 ?8 J\" F3 C1 K# Z0 ^1 C+ Z
     
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
     * C: Y5 _. g3 r
141.      V1*M4);# O) N5 K$ M+ p+ x* p3 f1 w7 l) l
     
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
     0 Z* H  l+ h& I
143.      V2*M2);
     % H2 Q: l7 B8 K8 S9 g$ I
144. ' Z+ ]6 O  y- `. \& Z& b9 _
     
145. x = xicl1 - xicl2;9 D4 Y. K5 `+ a6 q% G\" l- B$ {
     
146. x1 = Re[x];
     & D4 K  ]2 l/ G2 b% `
147. x2 = Im[x];9 h, \8 z% r1 A
     
148. 
     * b( n- p7 z& ~# \
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];0 n2 C7 \, W2 R3 H; w4 V& x2 g% G
     
150. ]* M+ r* y+ m7 C
     
151. * L7 E2 V  H0 I! R$ `$ N. N1 Q- L* E! ?
     

复制代码

代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
( l7 G- N1 b1 ]2 b5 @但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
8 d( g: Q; h0 Z; P, k: w换成
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
. Q! R  v; x0 d" \; ` ]
. B2 r$ p3 O1 x2 ^1 B$ J4 C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.

4 k! @& ]7 G0 f$ ^* W" `请问是怎么回事?

- Y- i' e% Z" ]3 q* b+ x