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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;
& D\" K/ n& g$ m. C9 Y\" ~
k0 = 2*Pi/lamda;/ Y* _8 R$ s' o2 w- i. h
n1 = 1.4677;(*纤芯折射率*)
8 S: w3 N# n8 u5 w: d; I1 i
n2 = 1.4628;(*包层折射率*)
: @! y# M8 D0 ]
n3 = 0.469 + 9.32*I;(*银折射率*)\" N$ H. l, c) M. v4 P
a1 = 4.1 10^-6;(*纤芯半径*)
; C: m+ U8 y1 o& E
a2 = 62.5 10^-6;(*包层半径*)
; s. @* Q4 M0 O4 b( K2 M
d = 40 10^-9;(*金属厚度*)
- ?' p; L9 D: ?& d+ Z
a3 = a2 + d;$ J9 S1 V# ?5 J' d: x
mu = Pi*4 10^-7;(*真空磁导率*). U2 A- ~) a' D0 B9 j; J6 K
epsi0 = 8.85 10^-12;(*介电常数*)
1 W4 p U0 q( g\" [
+ ?; [; U5 Z8 \2 a2 \& G/ i
n4 = 1.330;
4 v4 q8 ?. l+ ~9 }, V
0 [1 k: W a6 X\" Y9 c3 V
neffcl = neffclre + neffclim*I;
0 {% v\" M+ C7 A
' J+ E9 I3 d N\" e8 M
betacl = k0*neffcl;
) X$ \7 u A+ e( Z
omega = 2*Pi*299792458/lamda;
+ H+ g9 T: r* u' ]: j: f9 i
' U! c& T( ]9 K. T7 M$ E
epsi1 = n1^2*epsi0;
1 v! t% ~' ?1 K/ V2 p' }
epsi2 = n2^2*epsi0;& {- ^# g2 L& F5 }1 H& W. @) X( o
epsi3 = n3^2*epsi0;
+ s; [3 C) a# E\" V, `3 h
epsi4 = n4^2*epsi0;
' `0 k! Q5 Z/ L8 A% h\" V1 M
, k: w& u# ?; n% ?\" W
u1 = k0*Sqrt[neffcl^2 - n1^2];
$ j3 q( V\" U+ I+ x
u2 = k0*Sqrt[neffcl^2 - n2^2];9 W: e! U% ]# X! N5 ]* v
u3 = k0*Sqrt[neffcl^2 - n3^2];
. X6 `% x9 v' u6 `/ M* Y
w4 = k0*Sqrt[neffcl^2 - n4^2];
, O/ }! ]- U8 a/ c5 l0 Z9 Q8 P2 Q
8 R\" X& e; F9 P2 ~ s
Iua111 = BesselI[1, u1*a1];\" ~! |$ A* [\" m) N2 t\" |5 Q
Iua121 = BesselI[1, u2*a1];# r4 T, r# S, i# v5 j* w
Iua122 = BesselI[1, u2*a2];\" _* p: V- [7 k. z8 f\" N
Iua132 = BesselI[1, u3*a2];
) `# A+ J4 r/ y
Iua133 = BesselI[1, u3*a3];& @) u7 e& z- _7 f, ^) G! m, @1 X
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;) S. k! Y9 o; j1 q7 Y, P
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;+ }) G+ a, [1 g$ Y
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
6 h% `# P Z2 ~
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
8 @6 x% q8 n& ] V9 v
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;/ W$ s# k. x8 S
! u% C( L4 Q# \7 K% @$ }& Z2 T1 @\" d
Kua121 = BesselK [1, u2*a1];/ D$ ^+ G2 X& J0 F
Kua122 = BesselK [1, u2*a2];
2 G, f) c\" H, T# R9 D1 B- F
Kua132 = BesselK [1, u3*a2];& s/ Z* R$ i5 N) B% D4 G/ e( t
Kua133 = BesselK [1, u3*a3];) ~7 [4 P& L\" `. G1 R# b7 s
Kwa143 = BesselK [1, w4*a3];
& }6 `- A/ \! ]. E+ g- a5 [
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
6 L _( P( A! ^ [
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;) [# [, T2 ]7 X' T- F
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
& J5 K' Q- I$ ~( T
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
! v& {2 R9 |$ P r3 Z
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;( j+ L- V1 I+ V% e/ v x
; b) q: W) g# z
H1 = (betacl*Kwa143*/ P\" t3 D/ h9 l\" d. ^$ g, {1 J\" w
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*( B4 O* }3 h. x/ u
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*5 d: K. u6 f6 K! O2 |
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*3 {5 a o. ^. N5 o
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
/ d' N6 L4 v; r: `
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
) t2 o: t\" J; T/ M
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
( D% K% r\" I1 m H9 b1 |
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*2 n- H$ T3 D- P+ a- a1 A3 v
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
% |\" ]! y- ]# X
) z& L7 y% _. p
H2 = (betacl*Kwa143*/ ^% ?4 |+ k$ r2 x% E
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
& o) T7 b; }# g1 w. S
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
5 K* V, _) c- D
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*. F' f5 h3 s1 w3 [4 M S! w
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
3 x5 ]% i: g% A& Z0 D
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*+ }% G\" _6 {6 ^5 j! c- U2 [, {\" E4 |) @
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*2 T6 }& W- @, e5 ~/ j1 C9 V
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
$ `& w4 I! O( [4 h$ M
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133); X/ ~) e, K+ }- r7 R
6 O) D! X/ e+ V1 N
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
/ D) E3 z5 J! y w# J
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*! o4 B& Q4 d* m4 y% S. Z2 [
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*+ `' _/ s P) }( V
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
) R6 F0 G4 }/ D\" i5 ?
Kua122 - $ n, N1 o. D\" H+ `7 V) M
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 3 o' y7 k3 z) n# H) f
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
: X( v% P% \. _) V! {2 p0 ~$ t4 h, r
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 0 J6 p/ L, v% M3 ?1 ~ r
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);\" m; b- ]1 V8 U* H- ?1 u0 @ @( _
) o# Y* R( c/ e3 I% P0 w+ p
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*, f\" L) G\" ]\" z: u3 U
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
$ n* |! V# t) R) q
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 q3 g' r) N$ X3 O L7 n
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132* k8 M2 I9 d0 \. i; u. c
Iua122 -
0 G- m# n1 Y) L$ Q
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
! C3 u' h: K\" R! U1 l$ e
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
6 k' e; ~9 \+ S2 @
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 9 b! F' L! t |, [9 B
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);1 y/ ?! ~0 b2 B1 z- U\" K* i c
`4 O# D\" N3 L8 N- C# [\" f/ i, Y
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
, P( K5 O0 t' @8 ^ p7 I: c& J
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*; |; M# Z- }) z* g# u' W& B
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
, ?$ y L7 W6 H% F5 o; ^
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
5 U( K\" E\" K- |; R/ r! p* R4 ` G
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
$ ?# d( n! ~+ ]. B
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
, m: `4 ]0 J: Q8 E; ~3 z+ i7 S
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ! }+ [3 j4 y5 i5 Y. o4 M3 ~
w4^2/u3^2*Kwa143*IIua133);( J' ^, J0 z8 t. x3 S2 G
- K4 a8 u: m7 v# F$ C
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*6 y! G, I( |+ L4 s1 t
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*% w# K2 @0 H' J h. y/ J
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*/ k% L( W6 W, @% P/ |
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
2 u3 ~* J- i3 J h
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 6 \8 E7 y% m9 z* j
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 3 U\" t# `% d o
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
' Y\" x* N& {* x5 c6 Q l+ b$ ?
w4^2/u3^2*Kwa143*IIua133);
_4 {& o( F5 Z
\" h1 V5 v1 r' c1 u) l( u4 T h
M3 = (betacl*Kwa143*+ V! w1 I+ Z1 W! K6 R
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 0 H ?) l1 W\" D. y
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*) l! q8 u/ `! C& B) p( F* U- J2 e
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - \" m8 c* A& k/ I) \, Z$ B
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
& \# N( G6 h m! l( Y
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
/ n% l8 O$ B* D. g\" m0 V/ A! U
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*) Q. [! h3 u5 {6 N& ^; V+ Y3 ~
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 4 n% H: V3 V3 \1 |4 @6 h4 c) S d
w4^2/u3^2*Kwa143*IIua133);5 n, {& ~- x* ]: d/ P
: T7 a; g3 H* V& e1 O. p& a: w- |
M4 = (betacl*Kwa143*
6 v) \5 ~: l) a+ n+ ], l
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
) y' C. J Y j! a1 V8 x
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
3 S' c' N) X2 ~0 X* J) r
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - - M* U. K2 E& H# Y
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*& n6 U\" c# b) v) s# ~: [, S
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - , b4 j$ Q( l7 E
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132* r+ [) K2 c2 l1 @* v3 z: Y4 @
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
* S- Y; u. R- W6 o
w4^2/u3^2*Kwa143*IIua133);
1 C8 j2 {- Q1 _% P& O
, Y; a) N& ^( z7 W. n+ @) G
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
+ F0 a3 h( n* q4 l4 V- x
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
0 ~+ t3 D' b' u3 G
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
! ] W- S, B% P\" O$ c
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
2 Q0 m8 B( K5 |7 S\" ^- a
2 v1 h: J0 m, K3 {% |* F9 n( ~
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
. {! m) B/ J. R, W# v
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
* {; ~: @1 A( l2 A1 K& y\" @& Z* v x
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
% V6 U8 ~8 u# ]8 i+ K) m
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;1 m. X1 _; z3 J: C* r
3 y A8 n/ B$ x, _0 I- P+ C
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
! ~; I1 G- H- }8 [
V1*M4);# q7 N9 \* J& ?0 @' o; x( | ~2 |' T+ k
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
, A, \2 d* m* l O% B
V2*M2);
) }4 D* O9 D, N\" ?) z
) ]3 e+ r1 y' Z2 x; x
x = xicl1 - xicl2; |. T/ g\" S$ q# j) Q9 I$ O& t# Z& o' x
x1 = Re[x];
: B- _+ I/ f1 Q! L5 z
x2 = Im[x];\" Y! |' ~% _1 W$ Z
' ?. G! e5 i$ N3 }$ e4 A, P
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];# V' r) _' C- ], ^8 n
]
- k$ ]: ~; N g( s. r1 U\" G
) c* ]0 {2 x/ c6 u, T& }$ r

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