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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;& Q4 B\" W$ E\" ^' s; B0 y& U- t$ G
k0 = 2*Pi/lamda;( c) j) R6 p. N
n1 = 1.4677;(*纤芯折射率*)
& ?. ~5 U$ w+ C0 y/ c' I# a- v
n2 = 1.4628;(*包层折射率*)
2 q8 ?- p0 w+ o7 D8 J( R$ H
n3 = 0.469 + 9.32*I;(*银折射率*); Z& E5 d+ Q7 I
a1 = 4.1 10^-6;(*纤芯半径*)
5 K0 {, k) s2 B9 A8 k6 K4 a
a2 = 62.5 10^-6;(*包层半径*)
7 ]9 U& S! h) P, w9 V
d = 40 10^-9;(*金属厚度*)\" h* E4 t: B, F5 i1 Q
a3 = a2 + d;
1 G1 U/ {\" b, t' d6 y0 Y+ A- J C0 M
mu = Pi*4 10^-7;(*真空磁导率*)& [8 S3 G7 d3 c2 s1 H x' p
epsi0 = 8.85 10^-12;(*介电常数*)\" J! e8 Q- J; o
1 B: l2 Y# l7 k* h1 A! Q& I\" L
n4 = 1.330;# }+ Y1 b, U& O5 ?9 T
7 A# l# a- \) y9 o
neffcl = neffclre + neffclim*I;
' p0 |8 F+ g( z2 R
, i; r. z, D/ K' m: w
betacl = k0*neffcl;
\" T0 U1 @8 M1 p$ d
omega = 2*Pi*299792458/lamda;1 J& M, C- N2 E
- z) J! Q\" l- i+ Y; O
epsi1 = n1^2*epsi0;
# ]9 g9 a% u& S8 T* R
epsi2 = n2^2*epsi0;9 R2 t) U7 R' Y& B' J% i
epsi3 = n3^2*epsi0;
) r5 X/ @/ v0 [: _3 N
epsi4 = n4^2*epsi0;
6 m* ^9 @: o0 m# {: [- E$ b- D
u1 = k0*Sqrt[neffcl^2 - n1^2];
5 l2 R* m6 g6 W/ W
u2 = k0*Sqrt[neffcl^2 - n2^2];- W' f8 ]. ^: R) ]; w. u
u3 = k0*Sqrt[neffcl^2 - n3^2];
0 v/ D b, Z6 U0 D0 _+ u
w4 = k0*Sqrt[neffcl^2 - n4^2];
* w! A/ f* t3 T* R& P3 b' `
4 j8 z1 `; m) k3 u
Iua111 = BesselI[1, u1*a1]; J6 Q' C$ E1 P3 ^' h7 U
Iua121 = BesselI[1, u2*a1];$ B# ? u7 |3 H4 N
Iua122 = BesselI[1, u2*a2];& P; _* e5 Z$ \
Iua132 = BesselI[1, u3*a2];
* k/ Q' d! ?8 l8 c1 y. M
Iua133 = BesselI[1, u3*a3];
' j6 z, {( h/ {) W2 \
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
9 B# |& n& \+ I- `! O2 k
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
$ x3 k$ R9 \$ a) ^
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;# d2 l& F- t5 {! T& K! t8 P
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
0 F5 a/ j, G! v9 f0 Q
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;/ H' j8 c9 x2 i% X. U\" j0 k
' {$ Q# o! r6 T- B; B i
Kua121 = BesselK [1, u2*a1];. B# b: Q2 ]5 l\" R
Kua122 = BesselK [1, u2*a2];) S. }6 q6 W; ^1 m
Kua132 = BesselK [1, u3*a2];
+ R. y! h5 ?$ w9 ~: x
Kua133 = BesselK [1, u3*a3];
3 }# b( I+ n% ]& l5 N
Kwa143 = BesselK [1, w4*a3];% V6 s2 z' |3 f+ k6 X _2 [: r
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;! F4 A+ G& V; l4 M) V/ J
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;- w7 f Y2 j$ n3 Q- P' b
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
* k* d# e) d- U0 k
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2; {* \+ q1 |; M2 y* u' z& a6 R# p& M
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;* `9 h! i( ^* X: U4 Z: W* F+ ^7 I
+ q/ { K! Q2 X6 k5 c8 ^5 s
H1 = (betacl*Kwa143*- ~. F$ q# ]7 A- j+ ~
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132* F9 _6 f7 x/ l3 ?, ~
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
\" o\" L. U& D& m7 f2 h7 P+ i
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
7 J9 I+ e9 W! L( k
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
{* I% [$ V6 b, a; u: _
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
) C- I6 k& t\" ]5 Q2 \9 m- H
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*/ g$ n+ k, T; P
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
! ~% t+ y% E. @$ ~1 n* H
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
o. t: V, y, }8 B8 Z9 `. W
; B8 i- n8 P7 c- T; p3 b
H2 = (betacl*Kwa143*
8 t, z% A, g. N, q, v3 O' e
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*- q+ z/ @8 b4 _* x4 U
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*: u) i: r8 f7 ?5 Y3 l& _- b
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*8 Q1 F# v0 n* _1 ~
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132* }% }; e% G! D& g
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 n1 Q, ? ]. b2 A Y\" Z. x
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*\" s- {! s9 Z, E\" P
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, X: |) }8 C @, j! G( m
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);+ `% i8 |: f; ]& o\" b
: N5 W2 a, y) U; O! a
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*8 ], A T\" [8 _0 p9 I; K; \( ^
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*' d7 b\" }/ i/ P\" p% ]! H+ r
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 j* r0 p- z4 f$ v5 s$ U: R
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
4 G/ z\" R1 }8 h4 V
Kua122 -
( X2 L+ t/ R9 Z\" q
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
4 t4 \7 E8 l' f. l( Z$ k. g
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ( k4 G9 a6 C V
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 5 q8 \' p. b! W' t& F1 S+ W- i
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
( E% q* H; {- e' N. y
- L) H+ N6 L, Q& t) ~$ `
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
; p& @ M+ u4 H\" n! i
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*5 r5 K6 J. w, Y1 y, D2 m
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
t1 b- u/ z: e
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*! e, `* G' u# ]$ v
Iua122 -
$ [9 ?0 A$ {! d, G% X
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ( H9 H* T( W6 P) j
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
9 Q1 k2 b( |; C# [+ X
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
, j\" I+ D+ R\" a
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
# F& ^0 A' ~; T. Y' ~
1 j3 w1 R/ Z: x# W0 w
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*' w( A B# Y: R$ ]! X: O4 ^\" I
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
3 c- Z$ M\" J; I
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
8 U9 H1 Y/ Z! X% t/ f9 y2 R9 C
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -& i. k- t& b( w/ l- E
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
0 |; s) g/ {4 q\" Y& t0 `/ H% x
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
- I% O: K6 t# G9 |! P6 U
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
# ]- n M( y+ d1 g/ \
w4^2/u3^2*Kwa143*IIua133);
0 A5 j4 w8 k7 F+ q
! N( d; ~& e6 N& G* s
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
; I. S( t; I1 M% {8 r/ A+ |* n# ^4 a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
% X u1 E; H8 g
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
, I1 M# \: w7 V) r ^
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
: w$ f2 q\" _& U8 j0 Q! g3 u# |& c
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - , g B. e7 n& Z; L
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
+ m0 z/ c& V, o8 |0 b4 ^
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 0 o L& o3 q& N+ ]: [
w4^2/u3^2*Kwa143*IIua133);5 R2 l4 w6 \1 p
( f1 P' g! z1 B* \
M3 = (betacl*Kwa143*
/ H$ B# f u1 Z! t4 C/ d
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 9 d( d2 L\" e l
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
) M$ K/ y0 h y1 m4 S5 X
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - ! j, i\" ]' c5 I
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*3 p4 e% H1 A5 F& T6 b8 U* P3 @
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ! Z9 Y# ~3 k3 F6 K% G; I
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*\" T7 z0 z, Z+ P( [; q( K6 M0 y( p
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
7 B: H% ~/ b- ?: ^5 l S
w4^2/u3^2*Kwa143*IIua133);
/ h! I/ w1 R2 {/ r) r5 M' D. K
- m$ `% P% W% V! v& f5 _
M4 = (betacl*Kwa143*
- I- s8 N; [: }) t& E
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
; U0 @& {1 s& G* ]' V6 M
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - - Z8 b: n/ |+ R2 r7 S
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
/ Z) Y* ?; C; P9 M$ H* k6 Z
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 6 K0 I3 G S: R' P. y* G3 h! H3 c
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
: q0 B+ E X% g7 o* a
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
1 |. w& l+ }\" N
w4^2/u3^2*Kwa143*IIua133);6 W+ ~ y' M' r! t! e2 F7 ?7 ~
\" g$ T# a2 h6 r, f
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;% L7 _ ] t, T# ?, ?1 A
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
$ E& I# Q! r* Y, T. k, h
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
8 |( b# j8 H% x
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;2 L, F; E6 I1 k( ]7 o; h
8 |: ], T7 y2 C
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;: x+ Z3 b- D\" {5 n7 A W
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
( l- J* o9 _+ U# {& o
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
+ [+ |& c3 r0 ?7 B- t1 L
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
5 v' L8 g\" k7 p4 n; d S- R! n
( W5 q5 M8 n) ~! d* R# s
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
6 i) F- n5 a0 [4 b, l
V1*M4);\" I- m5 e1 f, d5 `
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 8 C% M: v4 D M7 u
V2*M2);$ o7 k: i p3 v8 O4 B1 C
3 E( c1 c( D' `/ K: H2 G- [5 L
x = xicl1 - xicl2;8 c/ |- O( Z( X4 e
x1 = Re[x];5 C. |% @! |* `' f# R
x2 = Im[x];: f7 `% P( C# G$ P! p) F4 R/ o$ |
9 R/ I( J+ W: K* w4 a
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
: r7 s' q\" ~- w% \) |: \
]; w/ M& D- G g R7 a% ~& a
2 s2 J/ E' e( X+ M, ]) `$ @

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