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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;
+ U1 Q# ~. L+ f) U6 v
k0 = 2*Pi/lamda; F, N2 N0 o6 x
n1 = 1.4677;(*纤芯折射率*)
+ f- t' g) V' F$ W
n2 = 1.4628;(*包层折射率*)
' S! r$ f; r5 {, c1 v! {- @
n3 = 0.469 + 9.32*I;(*银折射率*), Z\" l4 P: k! h
a1 = 4.1 10^-6;(*纤芯半径*)
; ^2 y! {2 S\" {3 L
a2 = 62.5 10^-6;(*包层半径*)
+ [4 C. I7 E5 P; ^$ r0 a2 \9 h) m- r
d = 40 10^-9;(*金属厚度*); r9 a6 p0 t: G, H
a3 = a2 + d;
( U1 h$ S\" K9 D
mu = Pi*4 10^-7;(*真空磁导率*)
/ l8 m) Y/ e6 W8 ]( I) u/ O. g: X1 |
epsi0 = 8.85 10^-12;(*介电常数*)
1 R9 H8 g5 O* C, p
z6 r( J+ W% ]# ^9 m @7 u) O
n4 = 1.330;
. S; T. I8 t: h/ ? D
8 P: C% v. s! L# c2 `% m
neffcl = neffclre + neffclim*I;
Q5 p6 v4 q& L+ C7 f
+ v4 G9 l% `) F. m5 ]: ]; z
betacl = k0*neffcl;
, M- ]. ^9 r\" ?\" g: W6 M
omega = 2*Pi*299792458/lamda;
& Z+ O& L0 i- S* w- p @ ]4 s* W
! c\" B: h8 ?1 f* `: m5 w
epsi1 = n1^2*epsi0;
$ D/ m# d6 q) m: P
epsi2 = n2^2*epsi0;. \$ B& V# A* H9 W; o0 V* T
epsi3 = n3^2*epsi0;
; ?+ Y' e- }1 J( R- l; S
epsi4 = n4^2*epsi0;
4 F; c, w7 F# b: }( g0 A
6 G% x, E' G M8 `5 ]
u1 = k0*Sqrt[neffcl^2 - n1^2];
0 P! ]' l' U. Q$ j' _! J- D
u2 = k0*Sqrt[neffcl^2 - n2^2];
f5 t\" w6 O( l7 y) F9 ?6 ]
u3 = k0*Sqrt[neffcl^2 - n3^2];
' k2 R; x5 e3 G! I$ R5 d7 g
w4 = k0*Sqrt[neffcl^2 - n4^2];\" P1 [6 N. L+ {5 c! z! X2 W7 e
& W1 |$ t' ]' E# n7 m
Iua111 = BesselI[1, u1*a1];
6 W0 a0 [* q7 L; n$ ]
Iua121 = BesselI[1, u2*a1];
; w0 c X. }( F a5 h, e
Iua122 = BesselI[1, u2*a2];3 g# N& `/ z8 e4 ?
Iua132 = BesselI[1, u3*a2];
, h9 _1 v8 n. a. R& }) n8 c
Iua133 = BesselI[1, u3*a3];6 q$ P4 q8 T/ l2 d. ?
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
, s+ \0 D1 ^8 G4 H( |+ }. e
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;\" \0 d$ @: P6 b B4 W% c
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
# p8 U8 U$ Y- @! _+ h
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
\" `3 T1 R! w+ c0 }( n* f
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
& x\" s' p2 M\" Q, B% n9 i7 y
. v' t7 g' Q& z4 y, g
Kua121 = BesselK [1, u2*a1];
$ c' Z! b2 M0 Y: Z% Z\" D2 f
Kua122 = BesselK [1, u2*a2];\" }- P1 G! L. @5 `* y' s6 |
Kua132 = BesselK [1, u3*a2];
) k% q+ _' D3 t
Kua133 = BesselK [1, u3*a3];
d$ L4 u8 _6 h0 `% x7 ]1 }
Kwa143 = BesselK [1, w4*a3];
! E3 U+ [% _/ g
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;+ P- R* T9 t7 {
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;# T- r( Q& F' N1 R0 b
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
\" ~' i\" |\" _; Q9 r& q* I
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
0 n. Q6 u7 E' w2 E0 E
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
# e0 V; V) R\" O4 y1 |4 Q% n3 g7 m- _
2 j9 ]5 ]8 Q5 v S! P0 e\" h* y9 H
H1 = (betacl*Kwa143*
z/ O& d, z: K& p. b' G
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
/ a8 K1 x7 u: J\" a% {( F+ d4 {% t+ W
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
, f2 X& Q) x3 H9 _
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*7 ^ i( `# l' H, i
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
9 E4 f\" T9 P& Q! a4 C
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*$ M7 h) h. b! d* [# [
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*5 [. |9 O- y/ G4 \( z; ^
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
. L- A/ E! d7 K3 Z. |& f7 |
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
\" [4 Q( G1 c8 \/ P# S! \
7 E8 @5 g: L1 t6 Z+ V, s( W
H2 = (betacl*Kwa143*% o7 T) D8 e* u2 d# o ~% ^2 b% w
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*) j- D- t/ o, }9 W( w/ T
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
\" t1 X5 {( [1 ^$ ` C
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*& [2 _' q: ]. j% t3 A5 L& O
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
. ~. p* g& l8 k; ?5 Q
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
2 Z( p( S8 S' V+ ~3 v5 N
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
R$ h/ ]( |3 ^% D
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, E( C. Q6 ]. r. e5 L; A
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133); ^% N3 L4 e. {0 T; R8 w I
$ c. A, j+ k: o. G2 t2 `- M
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
* P, x' Y9 {: Z& W, ?. I8 e2 @
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
9 h8 h/ b0 u% h. q; u! h
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
- i8 {/ _+ n% r! E$ R
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*7 T: H* x) l: q, d3 a: C
Kua122 -
5 K2 ^2 t, Q2 c }! W3 P2 K
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - & F! V e M* Z: h
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 0 ?1 q7 e: ?5 u c O' d
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 4 _, B* {. A# L+ }
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
6 ]/ F# k' N# O3 V: [( R; F
! G% M, ?7 M: H\" q( N9 }/ o/ _
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*4 X, p1 H, g& Z+ y
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*! _# V0 ]$ `- g% E1 D7 K! r+ p
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*: k7 x# _- T. H9 H8 J: ~
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
% U( O' t6 o( _7 _; M4 C
Iua122 -
' d. ?( @8 t. c
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ) v7 o5 |$ S# G' O K# y, _8 P2 F' }
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
0 Y5 j! N- F. w; ~\" A
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
8 H ]) s3 E9 N9 E7 U% A
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
: A |' |1 y) D5 P5 w
9 R& a3 a! S\" s
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*. m5 q, D; L, d% U: R0 i
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
( S( @* p, s$ N3 t7 ?
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
: i/ ~, u/ r9 v+ g1 [) O+ [+ O
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
- d: T7 {7 b& ?; W( b
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ?: t8 ]- y( H0 x% e% D9 k
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
1 Q1 t* a+ s/ Y9 a( j
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
7 ? ?: n3 k: @8 @- n& a/ P! c
w4^2/u3^2*Kwa143*IIua133);
8 M9 c. I) L4 o8 q
- z, |% k6 L$ i# O) T# S
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*: M* m/ z1 [! `# G8 T
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
, p, c4 L4 L5 P7 ~
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
, h) M, T: n( Y
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
0 I, M& _% q, C' o
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
! }4 i5 g0 g! M! b6 d H
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - : h- m* S$ J3 x7 K6 @4 h) @4 ^8 c
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 9 d3 K! r+ Y! V( z! Z5 ~! u
w4^2/u3^2*Kwa143*IIua133);2 S$ j. b% b9 g, H0 q+ t; @7 u\" E# ]
8 I8 F: y% l0 \/ p% h
M3 = (betacl*Kwa143*; ?. ~7 [: G1 C\" _. r$ u) M: Q8 T q
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
6 j6 [' v; g: w, V1 R ~4 v
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143* V. H- j/ |+ t1 q F
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - # B# Q8 |/ b; W% `
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*9 s9 \: m4 K, V( _
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - , \& T8 o* X5 o3 g+ P, r
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
0 s8 C3 s0 Z! K
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
2 n6 z) y z$ a. [3 H+ v$ ]6 k3 R
w4^2/u3^2*Kwa143*IIua133);8 w' }2 m0 q4 L7 E' n0 O
$ W+ O+ P. I\" Y8 x$ X: R
M4 = (betacl*Kwa143*
. J- P: [# I- T+ L4 l
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - # A7 s3 W( [\" w4 z8 h8 k0 _2 X
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*1 W# m* X( O C+ w7 Z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
$ S( s P2 h. ~# y% Q# D
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*; D1 s0 E# @! j
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
0 E+ V: b\" R2 I, X' M8 s6 L' h4 O\" d
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
7 \# x# Y* z7 I. h. w
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
% V: [/ T! k# w! Y! h. H, f/ A
w4^2/u3^2*Kwa143*IIua133);\" {1 D# u' T7 c9 t/ C
\" y2 M9 [% H* P\" V9 ?. c
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;3 T; I- b2 p* Q
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;% w\" Y( p1 l' i2 p7 S+ S z. A
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;! T% M4 y9 g8 J& f
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;$ }2 j& B4 q+ _ |+ Q1 b6 I5 B% d; |
\" R/ t3 B% J8 [- x. ^& |5 I* _) F5 m1 }
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;/ n7 h% ?1 U5 f- p
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;, k( j( g9 i# G$ f% W7 H
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;9 D6 ]' E: U$ F- o% J) W; l! @
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;& N( P/ S6 |. g' l3 s& V
6 q9 X: o: ^+ u2 p0 h) X
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 4 q1 l/ C3 S' Q# _2 Y& O$ f
V1*M4);' A Y$ N, H4 w# F. r9 V2 [& S
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
0 V$ _1 a\" q$ _ r8 r
V2*M2);
# L& g* |$ [# f\" o
1 D* a5 z/ w\" m1 U0 u: o4 f5 v+ Z
x = xicl1 - xicl2;- D5 q2 E j+ s1 q- Y* P* C7 a
x1 = Re[x];
/ z+ _ ?9 X4 d. m! L
x2 = Im[x];
: p! \. y2 y& y0 _8 |. {) E
0 ~$ m# E5 k+ X9 D- V3 Z
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];; p7 ?7 |\" u/ t- F4 {4 m
]
8 ?3 X8 ]4 C2 D
8 M' U1 G. |9 ?8 O* \7 _\" {2 ^1 x

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