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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 |正序浏览

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lamda = 1.55 10^-6;' e$ J' M' J/ n\" ^3 U$ m
k0 = 2*Pi/lamda;; U( Y! {8 ^7 o
n1 = 1.4677;(*纤芯折射率*)
6 `9 b6 |$ V- g! U: F* i1 @6 }
n2 = 1.4628;(*包层折射率*)% d& j\" Y* O9 y; b/ H% M' g/ c
n3 = 0.469 + 9.32*I;(*银折射率*)\" W) M* ?3 o* b( H: ~' Q( n
a1 = 4.1 10^-6;(*纤芯半径*)7 Q9 R3 `: ?. x! [9 w% z
a2 = 62.5 10^-6;(*包层半径*)* \1 E\" l1 J9 L$ R6 Q
d = 40 10^-9;(*金属厚度*)# }' c' }# p0 X4 S
a3 = a2 + d;
* M3 m: a% y2 d$ ?
mu = Pi*4 10^-7;(*真空磁导率*)! M7 \: F0 k; y6 {- \. b6 F
epsi0 = 8.85 10^-12;(*介电常数*)
' m/ @, J+ c; u
3 s `# A; @3 I0 k8 ~3 V2 ~) h
n4 = 1.330;
, W. S0 H3 D' A' V6 k q8 A0 S8 h
\" [4 m6 I2 Q8 b* h& N0 h/ E
neffcl = neffclre + neffclim*I;$ G( H. V' o% f: v- \
+ q- g8 B3 z& d% e& f8 ~
betacl = k0*neffcl;
# I& R$ e\" o+ W! \8 u
omega = 2*Pi*299792458/lamda;. H# G' n8 d) H7 x: \
1 \/ b! S+ Q4 H1 U. @& e$ E
epsi1 = n1^2*epsi0; X' b% |* J6 j& y
epsi2 = n2^2*epsi0;* [# W# E/ J, E/ b! B
epsi3 = n3^2*epsi0;4 T& l; ~- q0 }# g) t' _5 u, V! k
epsi4 = n4^2*epsi0;4 r3 w* I8 y# o4 T
8 A0 S) U* i- o4 I0 o
u1 = k0*Sqrt[neffcl^2 - n1^2];
1 c5 |# [; u3 @( u4 i7 q4 h
u2 = k0*Sqrt[neffcl^2 - n2^2];; e$ A& Q# N\" R; O- F$ {
u3 = k0*Sqrt[neffcl^2 - n3^2];! Q/ a9 G( w3 x: P! f' r3 E
w4 = k0*Sqrt[neffcl^2 - n4^2];9 q! b0 B+ N% V% _\" `( y# e
8 n$ s9 t; t1 g& I! B6 ?
Iua111 = BesselI[1, u1*a1];* r4 j\" }# _: D( ^6 F
Iua121 = BesselI[1, u2*a1];
% V! u* H9 M/ k4 _: G; v
Iua122 = BesselI[1, u2*a2];
\" L6 g; \+ l( |+ ~6 B! M
Iua132 = BesselI[1, u3*a2];& [% X( i' E. {) ^1 x+ o/ R
Iua133 = BesselI[1, u3*a3];
, ]2 R6 I8 J0 f4 M8 G# Z8 Y9 C
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
6 L! n3 ?; t# N- ^# \' N) r% O: X0 _/ U
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;\" `7 F8 u$ T5 q\" ]% \
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
( C3 [; S0 N# N0 X0 j& g) P
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
) e- M, d3 y8 P ^
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
: X1 k2 E$ Y$ r5 O5 m, z
5 p: M/ a P4 W0 h, H, ~
Kua121 = BesselK [1, u2*a1];
+ I; r3 b p. x+ L: ~
Kua122 = BesselK [1, u2*a2];
, L+ }- [& y4 Y
Kua132 = BesselK [1, u3*a2];( L* g. a! G6 G* R
Kua133 = BesselK [1, u3*a3];
2 P5 p! w! z: d4 e$ s0 T
Kwa143 = BesselK [1, w4*a3];) g& j* q9 [5 F
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;( E; i8 f; @# B# R
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;1 Y% I1 G+ B) i5 I6 |% O y
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
6 Y% q! r, Q, b, A1 `
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
+ g% `7 y4 e# k3 M/ `% a F9 T
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;( }- l# [2 W4 Q! R8 M
/ h3 S$ j; }+ t1 @( ^, b. N
H1 = (betacl*Kwa143*8 p6 }9 e8 J5 G5 C\" T' S
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*/ c) ~/ A' T# |5 w+ Y& A8 w) e9 o
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
& y& S; z) Q) n4 C9 B
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
! J: m) ?, X, |& t1 @; D1 R$ D
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
, y* j+ B0 ~ G3 B9 g( M: s
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*' d1 c2 j: }1 H3 v2 Y' ?( h
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*& w0 \3 [ L, q
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
4 e4 t( t6 S! ?; h5 L4 w
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! m; j, I- D. Y3 e. n: C8 h0 r
; d+ U, w! h: o: r, M
H2 = (betacl*Kwa143*5 z. o6 g+ P+ U$ u7 Z% t3 F
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
& A. C. W4 y$ O6 ]) l% H1 y& |
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*\" g; d: P; d7 S) Z0 r% A& n
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*8 U* n\" K\" |7 p* ?6 P9 |9 s
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
3 b; O& `0 p. x( x- o2 |. r
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
. d% g0 g7 S8 }+ N9 p
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' R A( ^, b7 A# F& h( G
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*! a* W! S4 t+ M+ ?( Z }( G0 V
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
' U* F5 I C0 ?0 j1 l
6 a2 W4 w7 w! N2 `& s% a- w
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
6 p# p$ O# f/ ~
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
0 K: v: {3 _ C* f- z+ t
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*5 _. N$ {6 @* Q; w: d! [/ O
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 k! @: J) W( O
Kua122 - 4 E8 c2 P9 |- O- ^( S, J: `7 T
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - * {& J ?5 A\" Y: s `
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - / S* U\" n% o+ q* w5 V
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 8 _( {; R! b6 W
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);0 w/ Q6 d: Y8 G6 `
\" D! A) s\" C* c4 Z
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
, X' t) e5 I7 @* A# P5 d
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*# A& E `! F+ l$ t. u% j) o/ S
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 p- F2 I& S# k2 x
Iua122 - 7 i( l- M' H, \, A5 B6 m U
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
& i8 v- _! I3 T; r7 `
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - \" g5 w5 e a8 U9 |
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 2 s- Q8 T* h2 I: |; W1 ]4 F
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
% d: j$ M$ @& i6 n3 v- O
$ q5 H. R3 z& ]! ]/ T
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*/ w( | J0 k c$ }- h$ S4 K
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*, W3 C/ B! n; ?+ h% F6 L
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
2 d1 A! q8 h, W, _3 V# v
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
6 \' J5 M' Q( h
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
r7 F\" w6 ^! z8 U; V, b
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
* Z% z2 b& ? }* H3 S
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 1 d' x0 q4 t- V\" X7 A, B
w4^2/u3^2*Kwa143*IIua133);
3 \3 W0 L( a' c3 `( }
) W, q+ [: [- o. P% F. a
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
: }2 t/ k/ X; u: j& e0 @# O3 {. `\" A
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*# K! n* Q. v- b% X
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
. G% m; ^7 w- m$ r\" W
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
1 w/ \2 Q/ ~6 o( r: B: r* I* d
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 7 h6 v' j/ y8 Y' D( D7 z7 U
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
1 x+ ^' X9 g( `# \+ Z% ^2 K5 i; m
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
8 n) ?' ?; \3 t
w4^2/u3^2*Kwa143*IIua133);
3 T% w8 Q) o$ o7 [8 i
2 ?, [% A! ?# n* z) b5 S
M3 = (betacl*Kwa143*
* l* S6 [2 Q/ \4 |
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
- Y7 l: o' F* k$ |; y3 T
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*& n/ I+ n d) C4 S3 w0 ^
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 8 |% [/ W; \3 N1 b
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
0 H8 ]6 o h1 y9 e `+ R
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - , k0 Y8 v0 M8 u8 ~5 t+ U( e
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
# h9 ~1 L' z3 Z0 g6 d5 [: r
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - # A3 G$ q8 n5 r& t6 J: @# f. W. Q
w4^2/u3^2*Kwa143*IIua133);7 l$ S\" H3 _( q) E
9 d9 n% m [4 P0 d
M4 = (betacl*Kwa143*
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - : s+ \; u4 k! z% w3 @/ _ I
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
1 E% Z( K' P- A9 d/ U5 V
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
, s/ m8 |0 ]* v\" B' O
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
( {3 J( Y1 X4 Z3 ?' {6 S$ l
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - * S! @6 a1 h$ \
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
9 c! P- p' j4 H+ d6 y
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
5 m' c+ Q* T3 H+ {& {
w4^2/u3^2*Kwa143*IIua133);7 y* S$ T& h* P- L9 Z& g
4 Z) t: {+ }$ P2 i: ~
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;6 f1 G$ i3 u' o/ z
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;( t7 A; U\" ] j3 V) H
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
: L& X& N2 ^4 i- E, ~\" H( E
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
/ m' ^/ ?! I' J) F
- w* x+ L x- ~$ Z- W
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
1 Q3 W\" L) Q+ [) q* |
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;4 r/ a4 J7 S2 X4 [) o
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;7 n4 c% A z m7 Q1 o) l' W8 W
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;) h1 q' a4 M; A/ E
2 `% ]: n* h( g! Y/ B
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
2 | {4 o/ M7 x5 j
V1*M4);2 }' V8 J. }) f: O: h
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
' c6 w7 V) F! j2 Q9 m
V2*M2);
\" c; _1 j S$ c% |/ P' j
# `3 K; t0 }# K' x% T\" y8 s- c
x = xicl1 - xicl2;
% g* v2 g3 [2 C( c5 G X' `3 z
x1 = Re[x];
2 n. W8 ~6 D% G& W
x2 = Im[x];$ o2 N2 G8 t( |8 c* a( v
0 z! t! j/ b6 S/ j7 e/ y! {
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
$ K$ }' J7 h9 A. y) c
]8 B1 |: n\" Z9 b3 G+ d2 S% {
7 ?$ ~9 H/ U- b8 ?$ Q, _- h

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