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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 M/ N: C2 o9 h# Y! v; I
k0 = 2*Pi/lamda;- t% Y2 W3 p3 d' @! ~
n1 = 1.4677;(*纤芯折射率*)' t% m$ Q: S) \; C/ M* V
n2 = 1.4628;(*包层折射率*)
3 `2 C0 C: D& ]7 j: e( S
n3 = 0.469 + 9.32*I;(*银折射率*). h; a; i3 E. a8 J\" `
a1 = 4.1 10^-6;(*纤芯半径*)
0 R y' v. S+ [4 W1 N
a2 = 62.5 10^-6;(*包层半径*)
1 ?3 R( t( i7 }; |
d = 40 10^-9;(*金属厚度*)- `; `2 l6 R V3 H
a3 = a2 + d;) f$ Y ], @! D\" B$ W
mu = Pi*4 10^-7;(*真空磁导率*)
$ H3 E$ t\" R X$ o }
epsi0 = 8.85 10^-12;(*介电常数*)! D5 _+ \% [, Q1 K% w2 W1 U. C
( ^% [6 m0 k+ `8 H* r2 Q& t
n4 = 1.330;
& s/ n6 z- E' t( ^+ X+ M
+ I0 c! N) f2 ?$ y. I
neffcl = neffclre + neffclim*I;
5 k9 l8 A9 ~4 T9 w
+ d+ a M% J) s3 I
betacl = k0*neffcl;4 l D1 U! l& Y, @9 h1 c
omega = 2*Pi*299792458/lamda;
1 p( x( Z; Y8 d) k8 ]
# f! F a/ P8 \7 o( \
epsi1 = n1^2*epsi0;
6 j( v+ B' K: V/ a* G
epsi2 = n2^2*epsi0;- l& t; P8 {. c\" e. c! E0 s
epsi3 = n3^2*epsi0;& e: I3 P: p* ~5 O' |; d1 L
epsi4 = n4^2*epsi0;
$ F' L8 G1 F; e* {- V* W, l
) a' G\" e# u6 ~3 D$ F/ A' v J8 R
u1 = k0*Sqrt[neffcl^2 - n1^2];
; u [0 c' |' t; \) f1 {
u2 = k0*Sqrt[neffcl^2 - n2^2];, t& H* A1 \ S# s
u3 = k0*Sqrt[neffcl^2 - n3^2];
* M, }6 P* P ~$ P) u+ y4 ^
w4 = k0*Sqrt[neffcl^2 - n4^2];
, _8 m% W. X9 \6 c; s5 l$ R
- k0 b' i' f# R9 ], |
Iua111 = BesselI[1, u1*a1];0 z5 O+ ~9 v8 I, u* |8 ]- r' o
Iua121 = BesselI[1, u2*a1];
: ~0 g7 j9 b9 e\" Z! Q8 {( D\" {; B8 m
Iua122 = BesselI[1, u2*a2];+ M8 w; F2 Q' V2 X$ g
Iua132 = BesselI[1, u3*a2];# ^# N+ C3 k* ?' q3 B) `
Iua133 = BesselI[1, u3*a3];& Z. R+ N) `5 X% K
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;# U- j' ]3 Q( @9 g
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
, m d) W( b6 m
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
0 l\" P; \. s* _9 J/ g$ V7 l
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;: d Y* v! ~5 O5 s
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
. n% f2 t\" U. R( t
: Q/ P( p9 y0 {4 d6 @2 P
Kua121 = BesselK [1, u2*a1];
' i' _8 x% v& |! m( e
Kua122 = BesselK [1, u2*a2];\" O7 o, |+ N9 ]4 J
Kua132 = BesselK [1, u3*a2];! O( f, L1 c. S) U& F& V+ t3 s8 y6 V
Kua133 = BesselK [1, u3*a3];. a! [7 _! G- a5 T9 P: K% H0 |
Kwa143 = BesselK [1, w4*a3];
) l8 d3 v3 @# ?! E6 A; @
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
' `4 p6 G\" X# ^4 P. [2 m
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
' `9 E\" f3 ?7 _1 x6 N. ?' @( k1 Q
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
$ F f( y, ?7 L9 v5 x% ^, ]
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
& P, o) e/ P& o9 n
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;' {) Y; D3 L/ G# d4 [
# o% [9 [ U3 T [8 N$ O+ T6 y
H1 = (betacl*Kwa143* n @$ k) c4 c% `8 w
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
( S6 A4 q6 W) E1 E1 A
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*; }\" Z( Z+ m# V5 Q/ J
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*% J9 e\" k. s9 G
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*\" a$ r% I4 z\" }\" k: @4 v) ]
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: f5 i+ e( Q, u' [
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
$ S( [6 F, [* O* T, y4 x' S
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*9 B ?0 n2 s f I4 |% o2 t0 c) U; T. w
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);1 h4 S; e; b' G/ Y: ]
0 w P+ v: ?# g4 Q( k) } Q9 G
H2 = (betacl*Kwa143*
* X# O! s! T9 J0 B7 J
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*4 a8 S% M; [! ?* M6 G' v
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
4 b8 |# |) |+ K
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
$ R8 c+ o1 | ^6 x3 c
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*- u% y- S. F0 |+ K5 I- b
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*$ }4 z4 d, n- g9 ~\" ?: N
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
9 Q8 ^; F, [1 Y8 V' Y. {8 [1 H
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 X4 q# c2 W# q* J3 s0 O
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);# X9 G- h1 Z( d p: [ ]
% L$ r- j3 d8 d' G
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*5 E! ?; J d4 j9 [
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
$ t9 K/ A% y6 f1 o8 d2 B# z2 @
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*# e: O8 U( m# C1 p6 p/ \' A
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*/ }: Y3 t' \7 A8 W2 B$ y
Kua122 -
( h. t0 s4 p, |# V+ x ]
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 8 C+ Z/ @, @$ O* |) Q* j: w
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - : }3 M# H5 l* j0 N
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - % h) H7 L7 l- O% |
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
* J2 Q' E, M) w$ }# p3 T0 d
/ c8 k7 Q+ T k' {) }2 K
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
- F7 {5 V2 t; O, ?2 P2 z\" k% z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*8 H4 j% ]/ G4 J
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
' {5 T0 I\" z, }* m1 i\" c
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*\" @ v& t# a) U7 \0 F/ e
Iua122 -
+ ~( A, C' C ]% \
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
; j0 F* M$ ~; R( B9 N
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - ; M! q& b4 R# k
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 0 p+ m9 m0 ?' ~, ]3 ^ R4 P
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
7 d1 `$ S6 p! |5 l7 U, y
( I7 d. j$ C2 a5 A; L i- T
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
1 h& c$ \9 y& K g2 P/ j
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*0 e- U( F0 R* g% R! ]4 ?( |6 a
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*, t) ?% c, e0 \$ Z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
. \1 q* d% u N
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
( k6 d3 J5 S9 q) n% a0 {
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ! `9 Y0 J* V; M# Z, z7 y* z% i% [! x
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
1 e! ]: [1 X4 \& w, f2 F Y
w4^2/u3^2*Kwa143*IIua133);
% U1 L+ m7 r# s4 v' W7 a- t0 [! W
, a* Q6 j9 Y: G( F\" X
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
* O6 g8 I4 }9 e0 I8 o
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
. {8 |7 ?/ j% ]\" b
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*5 F0 }\" e% _7 C$ _5 z% W1 M
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -7 }: m, q6 l9 f. ^- }& C) z2 h! l
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 0 |$ b$ { Q6 j0 X9 f$ s
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
- o h2 O- e: ?* q6 y6 @3 S9 q
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
8 q( U8 _ l, J2 j0 C
w4^2/u3^2*Kwa143*IIua133);\" L0 V\" A. y\" C\" c1 V+ s0 B# K\" N
' ~9 s& G8 U8 M
M3 = (betacl*Kwa143*
0 m3 S) {3 S3 M- a
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
/ M* q( B8 E0 A0 d% i
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*. m- h& V! o8 ~# ^; w5 p6 `8 [' L9 b
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
& i+ {* F4 l7 `/ h
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*5 K2 S u0 ?: C1 y, b
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
; y v6 i; N e5 X7 |0 n
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*8 A* ]; _ Q\" ? S* ~
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
) G S/ J$ K/ d, F
w4^2/u3^2*Kwa143*IIua133);* d& d5 @ A* j7 c, m& r' }
' Q& i2 `' c# N+ r9 e0 [1 K v
M4 = (betacl*Kwa143*# ^3 r5 W# E8 s- n
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 8 ?$ O* a [; Q% R) `
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
$ C. ]2 d4 i( D5 S
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
% C$ H\" e: ~6 Y7 ~' [6 ?2 u( W% L
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
0 o$ q4 P; o! [ Q# a- Y- y* {9 h; C
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
F7 a. f5 Y. m' Y' ?7 f
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*( P! E# A( V% d# F [
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
; O) v N L% P
w4^2/u3^2*Kwa143*IIua133);
: A+ F2 M+ F* Y% ]1 _, }6 a: v+ U
# ^6 \; z8 \ y$ O2 G. |& i0 g
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
6 M+ b3 c1 D$ v$ L$ g
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
3 K& G$ ~/ n! y
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;4 y4 e! i( t/ H
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;$ o `7 \- G# q( ~, v
% }, V+ S8 s i$ N
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
+ N0 M6 ?) ? t6 a) c, O3 b
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
8 \9 }- ^0 R, s/ [ M
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;% N5 B# J( w: f3 r& F0 ?7 h% }
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
; E+ N: ]. L! w( V1 l& l/ w g
) G8 h$ D: \+ e( V) V4 x' p1 m
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
! M5 U' l3 }3 S2 \3 Y7 F
V1*M4);5 O4 A0 Z- t7 R\" Y
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
: t0 `% c4 D9 g3 d7 M2 w5 a
V2*M2);
/ l# l2 s _! D; Z2 [/ D2 a( Z
! [+ x$ i& U; ?+ d
x = xicl1 - xicl2;
* r5 u. L\" z% w# J1 }( J$ V
x1 = Re[x];
# x* @- g M3 K
x2 = Im[x];
9 t$ q Q* G' R& h# D# ~
- f5 a5 X2 Q. Q9 ]
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];) t/ Q2 S' C\" f. t
]
) O' q$ l j& q
! }: n5 `4 |\" k

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