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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;
4 [: K# Y1 s2 w
k0 = 2*Pi/lamda;
) K\" c; M\" |, C5 A4 A
n1 = 1.4677;(*纤芯折射率*)# B [9 Y# s+ y- K\" G
n2 = 1.4628;(*包层折射率*)( K1 T% _; x- w% P3 e# \$ _& b p
n3 = 0.469 + 9.32*I;(*银折射率*)
2 h9 ^$ ]% K2 f: @2 q+ \* }
a1 = 4.1 10^-6;(*纤芯半径*)+ r% S- v1 P# G2 I
a2 = 62.5 10^-6;(*包层半径*)
/ k, r8 c; b6 N, l, O! ]
d = 40 10^-9;(*金属厚度*)
7 | b |9 v$ I
a3 = a2 + d;( I3 N! {' Q: {& y$ _
mu = Pi*4 10^-7;(*真空磁导率*)3 T% u/ p2 g% Z3 M, c9 r& F2 J
epsi0 = 8.85 10^-12;(*介电常数*)
; W J2 V6 F5 k. c5 ?
0 S$ H2 J; V4 V2 a2 Z s- o: B: G/ X
n4 = 1.330;) C- S7 s+ Z% F, L! R* T
U; j% |! `& {/ f: g\" l; C
neffcl = neffclre + neffclim*I;
) U# l; m! } e1 e( U; H
0 n' p$ k* b4 h* D7 H% `: u. v4 K6 H
betacl = k0*neffcl;) Y+ \! O- f( ]
omega = 2*Pi*299792458/lamda;
& W6 {6 r$ v\" `7 z! j% B6 i
. r1 l5 _ _% `6 [\" E/ M1 Z% u6 u; x
epsi1 = n1^2*epsi0;
7 e; B! ?( s; d
epsi2 = n2^2*epsi0;& e7 u$ U* c6 T L
epsi3 = n3^2*epsi0;
' [/ Q: e\" s1 @- }0 {$ n S& p
epsi4 = n4^2*epsi0;
! y% k/ K+ @- v+ h* `7 ~
2 o' @2 Y* T& U\" S9 g
u1 = k0*Sqrt[neffcl^2 - n1^2];
) z% |5 v0 j! K/ V4 \! p# o
u2 = k0*Sqrt[neffcl^2 - n2^2];, e: Q3 s5 y; Q. ^
u3 = k0*Sqrt[neffcl^2 - n3^2];
/ b9 @, n4 N/ G- H\" K( v% _
w4 = k0*Sqrt[neffcl^2 - n4^2];
; Q\" J0 L: P/ T0 y3 i
% y' v7 s: h) Z+ ~. t
Iua111 = BesselI[1, u1*a1];9 {6 J; _, N5 B; |
Iua121 = BesselI[1, u2*a1];7 d8 O, t/ S& Y4 [$ L b
Iua122 = BesselI[1, u2*a2];8 j) G& m8 V\" `# E3 i. u
Iua132 = BesselI[1, u3*a2];
\" a9 @; q. L: H3 \) ~8 m4 p
Iua133 = BesselI[1, u3*a3];
, c7 A9 i* W# C- d# Q
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;) n9 a$ u3 X& t! B, T1 z$ @9 w3 e2 W
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
! J2 M% K+ D/ g) ?\" l! l/ c% h. ?
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;/ K9 M/ `. N. }% @9 x5 F. g' @
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;* T) w! i5 _2 u* D0 Y: T' [/ X& ^\" `( Y
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;7 @ W; A; z5 D/ h0 ~+ y% |
' y# Z( ^+ N5 _4 M
Kua121 = BesselK [1, u2*a1];
; K/ P: R1 U) n9 A1 |$ E3 |( D$ H
Kua122 = BesselK [1, u2*a2];
+ N. Y0 G( M7 f j) B
Kua132 = BesselK [1, u3*a2];
7 m ]; f- I+ r, T$ Q
Kua133 = BesselK [1, u3*a3];
2 l: T c+ {\" b7 `5 |
Kwa143 = BesselK [1, w4*a3];
T# ^6 Q8 j4 q9 i% M% B# Y5 T
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;# p7 @5 h. {8 ^0 K( H4 {6 H
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
* |8 i; t6 q9 v% @* n' t; W
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;0 w' E% i' L+ j% z& i: w, v5 R4 \3 H
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;2 F, ?0 B. D* ~5 T: N1 H5 @+ z# m) l
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;5 \! U1 ?\" \2 o/ w
: M1 [# X9 a- ~& ]! C C$ {
H1 = (betacl*Kwa143*! F& |9 Q8 `8 i! H8 h
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*, \\" I4 S* J, }/ P% [
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*+ w6 o G* ^9 [1 F3 W0 x
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*# ]$ |# Y/ L7 ]1 j, y\" f. K
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*& M# A6 z8 T+ C+ ]% e6 I\" t, e
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*4 a! \$ B- i8 I1 `8 @5 \& Z
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*2 N! U7 U9 m: f b2 m/ Q
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 [; c! g0 y3 Q- c$ h E8 q8 Z
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
5 M8 n\" n7 {6 _+ y6 O
3 ^& d0 h) B: m& I# L$ x2 Y
H2 = (betacl*Kwa143*% [; |, v. X( ^
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
: ^6 z, k2 p5 B\" w+ { ^* B4 v
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
; b) F2 j$ e: a' K- ]' N# E' ~* ]
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*/ K) u, g( _- `. l9 v
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132* d+ U. O\" y8 d3 ^9 j% f
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
- G9 U\" t N2 R( ~1 q5 x8 f3 p% E
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
5 M+ u& p/ |) W9 r J) T2 J
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*' F3 H% O7 v) z* _% e+ i
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 Z% z; G _\" p% ~! K e
- s o* D\" [& Z% n
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*- `+ ?# I$ s8 s' H
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*7 e8 K5 u2 x8 s! |; z: A4 a
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
- c5 O9 e7 U) q. d
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
5 W5 S5 M7 {* |
Kua122 -
! _\" B& d+ B, H) U
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - E6 ^3 k) _$ D+ ^
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 8 _* p7 R: o# N
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ( M; S5 A, J4 b0 V
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
! S+ d\" A( t& n9 w6 o/ m
$ d/ O* e$ x6 P! r
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*! Z7 D$ M) d) l$ u
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*$ q! [1 X\" r+ _# c\" C
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
) B, K& u3 ^- h7 f0 g
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
; r3 q& n: n& \
Iua122 -
( {$ K/ { b4 l1 b! n
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - : X, z, y D1 a- Q8 s; L
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - ; L- b$ A# @, X9 ^! y
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - / k& m3 O+ @2 F1 J0 v' D$ u8 W3 o2 L
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);4 H7 V' b+ ^$ K\" m# w: \! C9 {
9 ? G- E% m\" u4 o\" m
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*0 l( ]0 H5 e0 h\" R% H% r8 w# G
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*: `0 {# V+ X5 F
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*6 B* l, R( i( Z' f
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -/ X! S) `3 j9 m/ g
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - & ~\" \' g2 J+ V; v
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
. T. k. w$ V; W9 v! U* y
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 0 H) n( r, @\" F+ c4 H$ f. }- e
w4^2/u3^2*Kwa143*IIua133);; E' g. A) e' ~6 l# R
9 U5 {; W$ g$ B& z
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*' H( r3 @# ]' S1 a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*\" S: s, M& \, q* k' x% t( m
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*) y8 }/ H: T, S# i: T' d3 r0 y
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -+ }1 M+ O: h& H7 V
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 9 t3 I) y+ C* \0 Q( ]
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
, h5 u. d' q. [
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
8 X: n0 A2 u2 Z5 y( ?\" o; {* c
w4^2/u3^2*Kwa143*IIua133);
( M5 }, v# s, J
4 }* m( e; p' R
M3 = (betacl*Kwa143*0 a. G5 H1 l/ g1 @. T8 R9 e( Y
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
, d# I\" c, y) R- v0 u# Q
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
2 G- t5 u* K* k\" W5 i( ]% v
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - / U( b3 m\" Y0 W6 r6 Z: L D3 N4 x
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*. C\" p% s' [5 ]1 ~ |
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - . C& T6 b( o! H* G( R$ Y; L
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
& J/ Q# e; m- X O
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
4 e! R& w3 _! ]6 \/ i
w4^2/u3^2*Kwa143*IIua133);& V. }. c& ^\" N: C, r9 j1 X4 p0 m, U
' p2 K. v- d' Y/ R\" \- U4 m! R
M4 = (betacl*Kwa143*- i* e& R' y# y( X' g8 s( X. @/ }. P2 \
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - ' e; x* Z2 D1 O- R
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*\" {\" ~0 ?7 `- j, U1 _; S2 c+ R3 u
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
\" c1 P$ q. y G+ m' R) h2 Q5 ~' G
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*8 l& P\" o6 L4 a* x% D W8 G: r- u
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
4 ^) R( `* K. J
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*\" s4 D: G* v. ~
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
\" h p+ e2 U/ @2 y. q
w4^2/u3^2*Kwa143*IIua133);
3 w# L+ C# ~ Y$ q9 M5 [# F
$ g4 S: M, [9 Z! {$ B! L6 p
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
# z M/ |* W8 b/ v% C
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
g4 ]1 ]\" D7 X3 B+ Y$ y
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1; M6 e1 {# U+ P4 {
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
2 u' f+ A( F+ O/ Y! p
. i6 S8 [$ r' i
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
6 O. D# Q {- P4 P+ a& b6 c
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
1 K8 Q% o! S6 K3 I0 Q
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
( {- |4 K! L3 I$ `2 |+ _$ ?; F: k
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;) L/ o; P# P w$ n, A! f
3 ?8 w' V! K% M+ W3 T' q
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
) w1 Q) K3 }, b\" ~0 i& m
V1*M4);3 r: a% K2 K+ [
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 1 O\" b: Q0 r* d6 H5 O' f
V2*M2);
( }4 @7 {# ~% N; O8 ?* t; ~
' G5 N3 x8 o) B+ y/ _2 s
x = xicl1 - xicl2;0 L. J l1 s& m) v4 S R
x1 = Re[x];
2 B; s; X; A# f% t) i3 M; a* G* j% L
x2 = Im[x];- p) b6 y/ _/ i8 S* c% e/ t
y8 G\" A% \1 N+ i
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];1 e; c6 S# y1 M
]( R; d% W9 o% ^
! h* i\" c2 |) n) C6 C4 d

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