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	郁闷 2015-6-6 15:06

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发表于 2015-6-2 12:57 |只看该作者 |倒序浏览

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lamda = 1.55 10^-6;
\" x( n1 E; o! k9 F
k0 = 2*Pi/lamda;; j/ G\" J\" `* ]; B9 g
n1 = 1.4677;(*纤芯折射率*)
/ d( L- R+ d9 L
n2 = 1.4628;(*包层折射率*)/ u& G. p5 n: E: a# [, `# K) X I
n3 = 0.469 + 9.32*I;(*银折射率*)
0 D. x: |( v, R- P4 I2 R/ u) Y
a1 = 4.1 10^-6;(*纤芯半径*)
2 S) i2 ]; v0 h c, v
a2 = 62.5 10^-6;(*包层半径*)2 A! K- k$ \' K' `$ y
d = 40 10^-9;(*金属厚度*)1 B4 @: n7 V6 f8 N6 `
a3 = a2 + d;6 R$ O5 U$ P% ]- q% l1 Z; M* q
mu = Pi*4 10^-7;(*真空磁导率*)
6 f/ q! W$ R' c. h9 K/ h
epsi0 = 8.85 10^-12;(*介电常数*); T+ }1 q6 p, ] Z4 [3 [3 n
; L, ]& D. T/ B7 A* t
n4 = 1.330;
0 H: E& f/ H5 H% D- j
- o4 m) t6 \- R7 `# T- T2 d: B R
neffcl = neffclre + neffclim*I;
4 x# k- J% K* e# A/ d: f, [9 Z
2 n' U1 y1 V8 W' ]! L+ W- k
betacl = k0*neffcl;/ m$ Q. K. } F S5 T
omega = 2*Pi*299792458/lamda;( l7 N+ e3 ?$ ?) D/ y
0 k8 U# u5 \0 T0 q0 l( h. N* \' P
epsi1 = n1^2*epsi0;
! f7 F, P* }/ y9 k5 X
epsi2 = n2^2*epsi0;& P% [/ Y1 b% ^8 k+ n/ o
epsi3 = n3^2*epsi0;6 a% K7 M& H+ I5 T! K1 M- d: @
epsi4 = n4^2*epsi0;/ A' e% P\" E: b
; J! g, E1 j9 M8 I
u1 = k0*Sqrt[neffcl^2 - n1^2];
/ Z- A2 w7 M: b: a
u2 = k0*Sqrt[neffcl^2 - n2^2];
u3 = k0*Sqrt[neffcl^2 - n3^2];
\" {- V* ^8 |$ T# Z/ c2 h
w4 = k0*Sqrt[neffcl^2 - n4^2];
7 T7 m\" `- t P7 i3 @
1 c1 ?9 P! Q6 @/ R) P* a
Iua111 = BesselI[1, u1*a1];3 k2 ~% f, @) e. g% G5 m0 p
Iua121 = BesselI[1, u2*a1];
* L- r) G/ t( u1 z: Q6 I
Iua122 = BesselI[1, u2*a2];
. F/ d+ ]* }: {( @! S/ `( _5 r
Iua132 = BesselI[1, u3*a2];
% G+ ^9 c$ d4 O1 y; f* w
Iua133 = BesselI[1, u3*a3];
; p, q8 \: H6 p' \
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
[) D% t. o- f9 g O\" E
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;' [3 W/ N) u) x
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
7 b/ H; B: f9 G) A7 S( S
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;; A% Z2 o' s4 M\" q( ?
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
4 t4 b8 _/ C7 A* [, C- k* ]( \
4 Y5 f: }& J7 q7 _
Kua121 = BesselK [1, u2*a1];4 W1 G8 `- x6 V7 W4 g, a
Kua122 = BesselK [1, u2*a2];
# q# ~4 X, V( c$ U! O
Kua132 = BesselK [1, u3*a2];% t( b8 d6 }4 j( M N) g
Kua133 = BesselK [1, u3*a3];
m8 u C8 f( W) S+ ~' Y! i. c
Kwa143 = BesselK [1, w4*a3];. Q9 z; M# G5 Z6 V
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;5 R\" h6 p8 O; q/ a( y
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;7 v4 L\" l7 V! @! o1 O4 n6 d& E2 b* C1 f
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
6 b: x/ I' U+ Q2 ^: x# d+ U4 l
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
) D6 s' `3 w( I B, m
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
: p! _\" `6 l- D& Z# b# E
2 l6 c. u8 h/ Q. s+ {
H1 = (betacl*Kwa143*
! C$ ~; Q* ^) k: |' U
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*7 {& z; ?+ k' S
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*) I2 o5 S& }, T\" L* H- ^' J9 ^ [4 A
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*! x9 E. p) U |, q* Z
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132** n2 s6 e+ p% F: ?8 \- \
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
9 z% Q! K7 k$ u5 }! R
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' ^' b* x1 H6 t1 l' b
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
/ f8 c/ J0 I( ?6 J3 | J8 _
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);, y/ i- |$ T v0 n
% y0 T4 E' G+ [* ^
H2 = (betacl*Kwa143*
0 x8 h1 `, m) H& s
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
# u% T2 J- v7 B! t6 Y- a) }9 h- j& X
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*- m- Y7 e\" f. r7 h
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
& Q0 D) ^7 G( z& D' N; k
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
; H+ p/ ^9 Y7 U9 x
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
1 S3 s) @6 U% O$ o# ]
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
q( }* e. N, U
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 w0 [. N. a! s3 A, T% D1 t- K# s& e
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);, h! S\" A' u( H$ z7 F3 U
; i; N0 f# w: L3 E
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*# p1 B, H/ ^\" i5 u n/ t% p\" O# n' ^
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
. M) h, X0 Y9 Q6 N9 U/ j& k, ?
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
+ q) t8 o2 Q! Z; R) S
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*: y% U1 E# w\" ~: w! o o( m0 @
Kua122 - + p% a C\" M) r+ b/ j/ {+ q' j% f; ]
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 7 ?) |9 C* D* L4 D' ?\" m
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
# n\" [! [$ ]6 ^. l2 s2 P& h
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
% y+ A5 w8 W! s
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);9 ?\" M9 w2 F- {8 l: J: ~. I1 C7 d2 e
$ Z3 p\" m! ^2 t( Z. z6 y
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
1 E3 z6 t- j' P: U g7 P
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
# u$ l* a- ~! W9 }* W\" m
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143** _4 W9 T4 Y4 I: n1 D/ X
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*5 ^. l2 P e& d) F* F
Iua122 - / h; Q1 [0 X* d0 c
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - / I# Y- Y( E! X8 e' k\" o
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - \" I6 U& H2 {( s% G% k
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 8 Y# j8 m- N7 B5 a& h8 `
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
7 r( a* B( T1 r5 g4 d2 P
2 L- u3 i- [- F4 p5 C
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
! d6 i3 G1 ~& g, N/ j, j$ k* u
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*; u\" H\" i$ H4 j, |
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*3 \6 \8 R) H/ E/ j6 Q8 }3 z' W+ s# @
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -8 M P/ |1 E! N( j+ i& }8 n# i
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
* {: C! N4 P- V+ J
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 4 H3 m9 ]# F. k( B) ]4 t& r
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - , M5 C* ?1 Y2 S5 k2 d; J
w4^2/u3^2*Kwa143*IIua133);) w' {$ n) c. T+ u( R+ f1 u
. I4 F. S3 x0 D: w: g: h; p
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*1 F5 V& Q, C* ^* @, M
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*# H @# J\" E$ y
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
. [% `1 ` Y\" a5 a. y
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
\" k1 g3 k% P\" C1 p$ J
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ' N6 ^0 H. ^0 c+ c7 R
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
: L$ g% D5 o! Z8 y& U% f. i
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
/ K6 C m% k# `5 p4 u6 \
w4^2/u3^2*Kwa143*IIua133);
( ~2 s! d, g+ [+ c1 ~
! ^* d' O7 N' c0 I9 ^
M3 = (betacl*Kwa143*3 M& z- o9 c/ F8 g& }- R$ s
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
/ Z! X& H; C I4 g9 M1 s- ]5 u: h
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
! ]7 w/ v2 A1 L8 w7 P. a
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
( r f- R# V& M1 M2 `, c( P( o
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
' U6 q5 Q( _) J\" z- m
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 5 q- f7 I( O0 K8 f* \
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
+ [/ P\" b6 c\" q2 P
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - & b/ A' J2 g% M/ U! k1 s
w4^2/u3^2*Kwa143*IIua133);1 [' ^, F, |- w3 T' H4 F* x
/ @/ V# W' W2 P, h
M4 = (betacl*Kwa143*
6 W- C8 W8 w# D: u1 x8 e) N( x
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
j* g: r7 B0 _7 i0 m
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
# Q) ? p) z v. T m& I
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
. P- n' e3 B ]8 k* s
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
. _2 b2 R, o& G: n ^5 d
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
, L; w6 d( V0 y
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
7 T8 J& c( B\" `2 i0 z ^
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
, N( i+ ^ K+ R2 u
w4^2/u3^2*Kwa143*IIua133);
( ~2 E\" d _ k+ W0 f. I9 y
& c5 S/ k9 t- {: O
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
5 N1 ~0 `2 G/ E$ I\" w( _( I# C
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
* j. f' T& j+ x2 C+ ^5 L& G
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;) _% H\" C: [) Q4 Q2 K0 N4 |5 l% ?7 H# z0 T
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
0 b0 R' T3 D& x; Z
9 ^1 A+ N* q9 V# Q
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;% j\" F+ z* a) s- M
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;- d2 ?# ^. F0 }# z S$ r+ k! E( Q4 [
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;2 R# x, L4 E( J6 q1 Z$ B
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;, q! N( N1 L, `9 _
0 L: R: p8 ~\" _/ J. e+ Q0 U) K
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 0 Y# \- `3 x\" O: Q4 F. j
V1*M4);( ?* T8 h+ s/ d) ^: U$ P
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
2 {! v1 F* b/ \7 R9 J, l
V2*M2);
6 y, A! E1 [ [) |7 V\" t, X- @
2 w, z, X4 L$ ~! N* n( k5 L
x = xicl1 - xicl2;
' ?; C: `: t' i$ J
x1 = Re[x];\" A! Q\" u4 N7 o, @9 `
x2 = Im[x];
: S& m, b/ |2 P# h/ v
) t* k2 n- j8 M
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];7 O1 `+ x& F/ k+ r7 q+ q' Z1 B
]0 L* @% a$ v, n F0 R( Y
2 w' t6 n4 p8 N! S3 L

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}}];
]
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.

请问是怎么回事?

zan