请问FindRoot外面套一个For循环的问题

cxy623157929

1. lamda = 1.55 10^-6;
   ) r8 k8 f5 g7 ^+ U: J
2. k0 = 2*Pi/lamda;! b7 q7 y9 Q+ r\" e$ K. m
   
3. n1 = 1.4677;(*纤芯折射率*)
   7 \2 h% S- N' Q\" {7 U! x9 r
4. n2 = 1.4628;(*包层折射率*)
   / h% H8 f% {9 C+ w\" o
5. n3 = 0.469 + 9.32*I;(*银折射率*)
   5 Y& {5 W. a( ?8 ~3 T
6. a1 = 4.1 10^-6;(*纤芯半径*)& t' A3 l0 O( [
   
7. a2 = 62.5 10^-6;(*包层半径*)
   ; {' B: @4 v) q0 i* }0 {$ a
8. d = 40 10^-9;(*金属厚度*)
   \" F, y' W1 n, Z% U% y8 h
9. a3 = a2 + d;0 ?6 z; |1 M0 f# T1 b
   
10. mu = Pi*4 10^-7;(*真空磁导率*)
    1 n3 {4 }# ]% l' ?
11. epsi0 = 8.85 10^-12;(*介电常数*)
    % x3 u) o/ B- l$ s
12. 3 M+ ~. J5 }1 W; S' _
    
13. n4 = 1.330;5 p5 k' B/ R% \
    
14. 
    & R! E; N, H3 P* ]' d! F' @
15. neffcl = neffclre + neffclim*I;3 N% I3 e  d5 t% z9 w  N
    
16. # {  n5 C2 v8 o- I7 `
    
17. betacl = k0*neffcl;
    5 ~  s/ s% @! K% j4 g5 b5 \6 O/ |4 U% A
18. omega = 2*Pi*299792458/lamda;5 F7 ?! ?) G; q. T. |0 S
    
19. ; D& b* ?  W) G
    
20. epsi1 = n1^2*epsi0;
    ( G* A/ B* i2 a; `+ `
21. epsi2 = n2^2*epsi0;/ W( o% Z\" h3 O& W
    
22. epsi3 = n3^2*epsi0;
    ) a( z0 Z/ i- l: e, L
23. epsi4 = n4^2*epsi0;
    , [8 q$ G\" T9 B1 c
24. 
    . T& K. `4 n& M) K2 Z( `, e9 X1 S0 ]
25. u1 = k0*Sqrt[neffcl^2 - n1^2];
    , ?/ }& \; O6 i& ]  E
26. u2 = k0*Sqrt[neffcl^2 - n2^2];! T4 g  n. O. s% y/ ~  i7 h
    
27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    . b! N% K) l+ m1 b3 F- {
28. w4 = k0*Sqrt[neffcl^2 - n4^2];7 v) j' Q6 X! l3 Q# `2 K: |3 \
    
29. 
    , @! S* L# D1 v
30. Iua111 = BesselI[1, u1*a1];
    0 x3 E( a! ?6 q5 }# e( v* a
31. Iua121 = BesselI[1, u2*a1];
    / P5 s) K, L7 S( R3 s3 m$ Y
32. Iua122 = BesselI[1, u2*a2];
    * B; \4 T- V\" d; O1 J# J' \
33. Iua132 = BesselI[1, u3*a2];3 q4 R  [5 }0 a/ A( D& H+ l
    
34. Iua133 = BesselI[1, u3*a3];* S, X& A* d% Q* a  e
    
35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    * U; I& o0 L4 e
36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;\" b  h; W/ g4 c4 a6 I- ?
    
37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    / ~: z2 g) t' e1 d8 v
38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;2 C$ c( e3 ~- u; Y7 I* ?, u
    
39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    1 k* V) T$ K: K$ B8 F7 C5 q7 Z( V
40. % M# I( J1 u% P- ^2 y\" J- C
    
41. Kua121 = BesselK [1, u2*a1];
    * d$ L0 U  f* n1 `! `. x
42. Kua122 = BesselK [1, u2*a2];. }! Z/ V% Y, Y$ @9 Y# d' r4 G
    
43. Kua132 = BesselK [1, u3*a2];
    0 R6 \- j  M  q: ]2 ~3 @
44. Kua133 = BesselK [1, u3*a3];6 _, _5 c. j- V, V  h- y
    
45. Kwa143 = BesselK [1, w4*a3];
    5 M\" r7 r, _& z' m: v
46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    $ z' ?0 x3 C& b' }  b0 U  S
47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;6 f: P$ f. G; Y9 k
    
48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    8 T( Q9 _1 D3 i
49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    % ?4 V, {; I2 E% W8 ~; W  V3 ~
50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;) U2 C% B: p+ q
    
51. 
    6 V2 U9 @; ?) d7 u2 ~3 T: r
52. H1 = (betacl*Kwa143*& s0 ]# d& T# {4 M2 \# W0 G. y9 L: s
    
53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*! W) X- M! m; i2 w- E, {
    
54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*4 K$ S' b% g4 @9 ~4 Y+ T
    
55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    ; c& C. X* [8 g2 Q1 t8 @
56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
    1 O\" \' B  T0 v. J% J\" ?
57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*- R$ b8 c, M: L6 W) c! B
    
58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    , g- z$ x4 W1 E; ~( F
59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ; U% W; ^; [9 D2 V- p
60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    1 `8 l# F) A4 T/ x, {2 o8 L+ K
61. 
    3 Y4 [  n6 W* L; q2 l
62. H2 = (betacl*Kwa143*  I, @# r+ n- t( _3 |2 q7 v4 F7 [9 U
    
63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*7 M4 T# B& P# K' ?) x/ C. E6 q
    
64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*; H# j# Y\" o! A6 |: r! a\" G) e
    
65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*1 K: m\" Y7 t, c6 A1 H' _! y/ C
    
66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    * n# e- K! H( F$ v5 W; }
67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ) Y$ O\" M7 _; z. r
68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' E& @% l5 V' H2 c\" |5 R
    
69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*4 r+ {4 I\" q& z- e: H
    
70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);5 v# D4 M* g5 }
    
71. 
    0 w& J' Y8 u% N
72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    2 h* `7 X- p. m7 p3 d* n; Q0 E
73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*% v- M) ?) g$ [8 R4 x
    
74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*5 X5 Q, K% A% F8 P3 ^8 Z0 {
    
75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    2 ]3 T6 d; _. |- \- A1 c! j
76.        Kua122 - ( u& j+ C1 `0 |/ E
    
77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -   f) }8 U7 L+ M4 l: G- T7 b
    
78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    6 |, g1 Y0 v. j  ]$ k+ e
79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    , r, u8 Q# i4 y4 `
80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! b* |' [0 i' c( z& E
    
81. 
    0 w- E2 E- I8 o2 l5 R+ x$ q: D2 J% a
82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    , Z* x$ w- i* z! s
83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl** C% o! \, t( _, J
    
84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 H\" z1 }\" S# L) X' }6 g\" o
    
85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    * @/ `! u1 b% f( w7 C\" o
86.        Iua122 -
    4 e6 k9 B. n/ }1 j. D/ ^! c' I+ d
87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - - A+ O4 {/ j2 B
    
88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    ( P: K6 j; i& h$ X1 a
89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 5 j0 i$ c2 W( y, S
    
90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    . U- U! I+ J# v' b) z+ |
91. 6 S8 u. e  S( i! f0 b8 ?
    
92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*+ P1 B& x6 f& s9 q' x
    
93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*2 B$ y5 a- f\" w, L1 G8 g( {
    
94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    ; a8 d, t! Z  g( q4 G6 O. k7 |
95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -9 [, V- x5 U( F- V
    
96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    $ O' y7 ^3 w: b5 \' [
97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    . }* B% Q# P3 _
98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    5 _0 y+ u/ L% Y2 Q0 V( \
99.       w4^2/u3^2*Kwa143*IIua133);7 I7 m2 F$ U6 W
    
100. 
     : D5 d- N\" m/ d\" @, ~: b6 X\" v  K
101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
     , Q4 w  i) P' l
102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*& ]' E' ^4 v' K\" j4 k* b/ L8 O
     
103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
     4 @9 Z( a0 _2 q1 n- a% e- j! y0 d
104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -% v! J  G  l\" H: y- ]9 X
     
105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
     ( C% Y' S) z! i; ]* J
106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - ) x5 h0 X' S\" e
     
107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
     . e( p8 V, `9 K% n1 H+ G5 ~0 u% V) J: R
108.       w4^2/u3^2*Kwa143*IIua133);
     $ w& L2 C/ I* I7 h9 s+ T! u
109. 9 ^/ z+ h9 L* |% J4 q# M
     
110. M3 = (betacl*Kwa143*, Q$ d  A' l; t$ u% v
     
111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
     . o7 R6 a( J, H& M
112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
     ! ~+ Z. p* Q7 K' P
113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
     # _7 @1 B( h( r8 J% @
114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
     & K! }* K8 p; D# Z
115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
     $ H8 a# V& k0 K1 {6 G6 F
116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*# y/ s. m; U: H* E, F$ d! B
     
117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
     , l. r: e7 r9 C3 ?/ c# e. G
118.       w4^2/u3^2*Kwa143*IIua133);% R2 Z\" P/ Y2 O% A) K: ?
     
119. - ?/ l; i# B6 v4 D9 A* l2 [
     
120. M4 = (betacl*Kwa143*
     \" l8 S: m0 M2 R; y- v* |$ {% o% F
121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
     , Q, @8 o1 Q\" s! i( U9 P
122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*( ^; Z2 \- X, \+ P4 u
     
123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 4 Y( H9 f$ J% w9 \, @\" ^2 J
     
124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*/ W\" t( z\" n8 R4 b* C
     
125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ; T* o  e( I/ H1 s2 z+ N9 u\" r
     
126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
     1 F1 e+ i8 t8 I( w
127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
     1 g' z# o' W# a7 ?
128.       w4^2/u3^2*Kwa143*IIua133);
     4 a; [# e/ B6 U
129. 
     & F8 B: j& u' V6 p! e
130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
     2 [  d  E0 ?/ |% g2 i
131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;6 u. Q. U% y. W* r, R6 f8 s+ l) M4 J
     
132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
     . U: y/ a2 S0 a7 `, l
133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;: U5 o; ~, D* `9 O& U/ e- G# d) L
     
134. . k, ^8 r' e) t
     
135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;+ \* u  T9 a! ?3 M2 B
     
136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
     $ ?5 Y3 p  G1 C, j' e  H
137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;! s6 G; V, {! W4 w0 A
     
138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;3 x# y4 E+ K; N! b' T- Y
     
139. % A: S6 p. c0 L0 D# S
     
140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +   j3 y( A! `- a8 S, c
     
141.      V1*M4);0 j: j8 N% G) V  ~6 `) G
     
142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + \" g2 B$ K! I' w6 ]
     
143.      V2*M2);; u( W4 g2 F! i0 n8 ?- C
     
144. 0 \: I- [& [( W' U
     
145. x = xicl1 - xicl2;
     3 h- F5 D9 T4 t; ~1 Z
146. x1 = Re[x];
     7 ~0 [/ J8 `$ |\" {! u+ E
147. x2 = Im[x];
     $ H) v6 v5 ]: O8 j  q( i% P/ V9 T
148. # B3 A2 J2 E) N; L
     
149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
     ; g: p& z) O* ]! k
150. ]
     6 C) R9 ?) E. ?, [
151. & C& c7 ^8 @% V8 O0 e- k0 Z
     

复制代码

代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
8 e+ ~5 F* Q) p- ^; l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}}];
5 }! Q& y* P, v3 G+ l ]
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.
, E1 m- C' c/ D0 l/ T$ ^. U
2 C4 S: b& B7 i# F请问是怎么回事?