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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;% z4 U# h. e- Z% X6 N2 t
k0 = 2*Pi/lamda;
. n1 B' f3 Z. u\" k7 _
n1 = 1.4677;(*纤芯折射率*)
) c, s- n) Y) G$ ~\" n- }2 `
n2 = 1.4628;(*包层折射率*); e0 w* c% c! X/ q! k$ g$ P
n3 = 0.469 + 9.32*I;(*银折射率*)
# s; }8 N+ D+ W% C' C/ L
a1 = 4.1 10^-6;(*纤芯半径*)+ |/ z# w- S- |7 l
a2 = 62.5 10^-6;(*包层半径*)
1 q. j\" f, Y) R- M `+ w
d = 40 10^-9;(*金属厚度*)- P, U# [8 z' }: J: n! O
a3 = a2 + d;% F0 f G9 x; ^1 ]5 X
mu = Pi*4 10^-7;(*真空磁导率*)
$ f4 x& `/ _# v9 R# N T: a+ g
epsi0 = 8.85 10^-12;(*介电常数*)$ L( n4 b0 t/ O* J* J
, k% C, Q3 H/ X9 F3 w0 O1 p
n4 = 1.330;1 J8 U5 J$ P h\" e0 F
! ^1 [2 n, q) {5 C/ o4 B1 j
neffcl = neffclre + neffclim*I;# E; x( W; T' H
, r% M2 J' x- Q0 n7 w
betacl = k0*neffcl;0 N8 U+ y a' Q0 m
omega = 2*Pi*299792458/lamda;# E3 l: k% p* c; t- G! e
o9 k: k, P% \0 }3 p8 s5 @' g0 R8 o! Y* M
epsi1 = n1^2*epsi0;, H$ t* I7 ~\" ^: P
epsi2 = n2^2*epsi0;8 E\" g _8 n0 G) A0 B1 @! C
epsi3 = n3^2*epsi0;' P. ?+ @# C6 _7 j1 {\" W
epsi4 = n4^2*epsi0;
& R# y4 b( B0 X# e8 ?
: U2 f4 s\" @( o3 r) y0 O
u1 = k0*Sqrt[neffcl^2 - n1^2];: a3 K- x3 S& X+ g9 D; H9 {0 C9 ~6 y
u2 = k0*Sqrt[neffcl^2 - n2^2];1 O5 d1 P) [* C6 w8 T
u3 = k0*Sqrt[neffcl^2 - n3^2];
; r9 U; q' Y! g$ u; L
w4 = k0*Sqrt[neffcl^2 - n4^2];, E4 v# _% j) ^' a7 N% i+ b
7 o6 `6 k1 a0 f8 I
Iua111 = BesselI[1, u1*a1];
. j0 r/ Z9 j- Q) h) E4 z
Iua121 = BesselI[1, u2*a1];
/ o0 ]) W$ @' [; |: b& Z& Z; d
Iua122 = BesselI[1, u2*a2];2 i' v. Y9 h' ^6 [& N5 x: f5 B
Iua132 = BesselI[1, u3*a2];
5 L4 `% M+ j: T1 U; h/ V- G
Iua133 = BesselI[1, u3*a3];5 _5 u0 E6 P! R' T: [3 v
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
) P$ h9 N* T+ `
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
6 ~\" _3 T4 i. O( c7 D- @% @4 @
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
( Z/ a9 S+ }, C# W6 f) y# @
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
- h' v* w* Z! A- ?
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
9 i\" `3 } I0 t, x
1 q' A: O\" `$ p5 B
Kua121 = BesselK [1, u2*a1];
$ c0 U( K) s3 w\" L/ h! Q
Kua122 = BesselK [1, u2*a2];
: m; w1 W! j7 m, I$ [% W
Kua132 = BesselK [1, u3*a2];! z$ t7 z+ v- D1 E
Kua133 = BesselK [1, u3*a3];& b$ L6 w+ r! q0 X\" A% I. y4 i
Kwa143 = BesselK [1, w4*a3];) Y7 f; K2 V' u8 }- v
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
4 r8 f2 {$ e& b* [
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
0 r! J' G3 p% e. [7 z7 w5 c
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;% G: o/ c$ P! X) l5 E\" g
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
9 t8 X f* U8 ]2 R
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
8 I. t( N1 m1 F
0 z1 ?3 U0 P$ v% ^5 x2 v\" m
H1 = (betacl*Kwa143*
1 E8 D6 u @! l0 m# c# ?, l; \
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
0 n7 X3 C- V3 S% _
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
( _. R! l9 Q2 e2 [) T$ M' g
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*4 }; V4 P4 H- C9 T
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
/ _9 J4 `, J4 ?, y( M8 V1 K
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*& U1 N) a; h( _, p2 J
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*2 @6 a4 `+ z0 |3 c3 I$ r# E) ?6 t
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
6 B/ `6 e& B K4 R2 F. t; a
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);% Q# I% X6 e; e, G+ p& p
3 G! k6 C( U, @- J
H2 = (betacl*Kwa143* i1 g\" ?) |9 Y
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
5 y/ O9 H0 O' P Q; b8 y- `0 U9 M
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*( E! \8 D# d: i9 N' B( {7 K! J
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*- }4 G' r$ u* h, t9 U
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
9 X1 L1 N# Z+ g
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; Q0 I. q7 _! z3 h1 B
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*) Z9 M2 @; t7 j# V* o
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
% m2 U$ \6 X9 `5 d
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
8 z+ p* [# \4 {; d+ t. u
& W, |5 I5 _. N1 O9 e( G) Z ? F
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
2 s( N7 q* P, ^- b' m
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*2 z; X5 [* ? z+ `9 I3 Y
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*; g9 e& C\" ` X) T- p- J' l- [
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
6 E: S C C9 o! T1 W
Kua122 - 8 W0 z2 N8 b# P# n& ~/ Z
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
8 A& y7 m* ] z7 ~
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
% Z5 \, x, x9 u0 Q/ n
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
0 O9 v+ V2 n) ]) h% r
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
D2 m\" E$ d5 B& s/ H\" \
) ]: R! F' z8 j\" H3 F# d
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*0 k& B9 ?2 W$ r7 [# {3 U+ u0 z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
. Z3 q/ ^% ]. l1 @
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*, Y* i K% M8 O
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
3 O$ z6 N+ h# b4 b
Iua122 - . ?5 F/ }% U9 W+ v9 x; ?' A
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
5 M/ \; ^: V/ ?8 {
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
9 U9 C9 g( Z% M3 D$ c; K
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 9 a6 X/ D0 c$ @\" s, \5 \) D
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);' t* S' V\" i( r- b2 a& \( y( Q) o
8 s, h7 g$ e% U' D @
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*/ b% G) ~, O' G! b\" Y3 ~8 k
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*6 j3 b1 g* x( q) O3 H
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*: G$ L% N6 d: i. V
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
7 E( o* R5 `$ k3 v; o5 ?
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
3 u6 U* H\" j& [
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - \" p# } o4 r\" D7 r& p% S( E
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
) z( X+ w2 t$ L
w4^2/u3^2*Kwa143*IIua133);$ R% M8 f! x8 j
1 r7 Z3 i+ J: e1 r* D
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*6 f8 I' ?5 R, r- n8 I1 ~
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
a5 k. l( n4 s! r! |# o
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
1 @* e+ H: c/ C- {! B5 n$ A
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
8 V& w9 @3 W\" I- w3 h3 N! Q
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
9 u2 Q3 \' t7 }6 C6 z4 f
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 0 \, M5 e( L; T8 y
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
* V, a3 w+ r+ H5 o% y
w4^2/u3^2*Kwa143*IIua133);
: ~' ~& C- `4 H/ @' N e; a3 y4 {
' q& e A- C I
M3 = (betacl*Kwa143** n$ R; C\" a4 @; \
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - & A) C- {- t/ E2 K: T2 ?
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
! t. g( D: b1 X& a1 D5 E
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
2 ~& w; i\" ]# i- Z M+ f8 ?% h
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*6 z$ b- b1 h6 Y8 l' F4 Q\" f; O, J
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
% ]\" b3 ]9 |- B( V4 n& _. ?/ D
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*, z4 Q; Y* ~, U/ P( s) S. O4 M; C
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - & b. @; h) C+ b x6 u
w4^2/u3^2*Kwa143*IIua133);, J0 z( X, ]3 \3 N1 _
# [/ u\" g! S$ p% x$ ` h6 ?
M4 = (betacl*Kwa143*) `6 x8 Z\" R1 e
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
% d. z! m2 S! @9 l ^ L
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*5 l2 S# c: g! V- l$ `
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
% f5 ]: ~! z. K7 U
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*2 I5 U; P; d% m
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
: u$ ~9 r$ A7 [) t% j+ f3 v
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*3 N6 o2 U0 ~/ R/ W! P3 r
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
8 J8 l1 ^7 ~! M, Y% A0 ]6 q; K
w4^2/u3^2*Kwa143*IIua133);\" V1 j$ L\" v+ Y$ M+ t( s
8 O' S5 C% Q1 q6 v
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
- c; A2 u3 K( n U8 K: x) f0 |) k
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;% i& X Y! W, ^1 s/ U
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;7 ]: s4 ^- Q6 i5 b) f
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
( \& L/ s5 k6 l
! o! l% P$ [9 g( c0 W7 ~5 f- X
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;1 S6 g4 ~* Q+ b7 o# K1 v7 f; \
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;' K& n1 a8 ^ ?
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1; t( B; u& \* [
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
\" }\" i! |/ C* I4 G( K! R; ^+ B
l4 ]# Z7 ]. ~8 s( `) ^, |
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
, l' y: _3 y' K\" C& Y
V1*M4);# ?9 j- n/ }+ Z4 Y
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
, w* F\" l' H% L' q: A
V2*M2);
$ f6 t y3 {1 W\" k
7 X' W; I, O3 S. Y\" {% C4 a* v
x = xicl1 - xicl2;- v/ C: j+ @8 I, y! ]
x1 = Re[x];
' x: V d9 V- ~1 i
x2 = Im[x];' E! G, n9 }$ _ V; {* s7 J2 F( b8 S
. T$ G* P8 c' \/ q6 F- B' z7 n
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];5 S( V- T( R# {9 T. K
]
8 N6 M% u# Y+ U% c j) V' t
7 B! n( n( x+ ?, R' J; E

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