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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;2 v+ V; {1 @4 @
k0 = 2*Pi/lamda;
4 i( K! g! u. b0 O+ \2 U
n1 = 1.4677;(*纤芯折射率*)5 _; K( k, z4 t+ @% ?
n2 = 1.4628;(*包层折射率*)
7 r+ r) T0 o d1 _. ]5 [
n3 = 0.469 + 9.32*I;(*银折射率*)3 o# v/ ~- K& F; e
a1 = 4.1 10^-6;(*纤芯半径*); j6 t G# `( ? _7 J8 M
a2 = 62.5 10^-6;(*包层半径*): k$ Q\" S+ O2 h6 H/ ^7 d; p
d = 40 10^-9;(*金属厚度*)
8 n9 [6 G: C# Z
a3 = a2 + d;
5 x! C! @& O% a
mu = Pi*4 10^-7;(*真空磁导率*)) H\" s, b( l5 v: \) q6 A- X) @
epsi0 = 8.85 10^-12;(*介电常数*)% z) a5 I) R8 X: w8 C2 |/ K
' x& ~9 q& |, t& e) G4 Y& X3 C* b
n4 = 1.330;
5 R+ R1 |8 I) D8 r U5 P
\" q; x3 z; @/ s3 W4 b, ]* Y( m
neffcl = neffclre + neffclim*I;0 `8 Q. S' X! _3 U5 @/ ^3 ^
, V0 E\" Y, k' Q2 W0 r! @
betacl = k0*neffcl; z6 _! a' }/ e1 W( R/ ?
omega = 2*Pi*299792458/lamda;
\" r# @1 O8 a, ]7 m\" e! d3 [
$ s! o5 g3 W! T% e7 q( x) R
epsi1 = n1^2*epsi0;5 f5 Z! a. w! Y& M( b0 C
epsi2 = n2^2*epsi0;: P8 ~) ~5 Q/ N4 C& }
epsi3 = n3^2*epsi0;4 a: M/ {0 o3 h8 a
epsi4 = n4^2*epsi0;
0 m! }7 p1 A, Q/ Z {3 a& S
; ]3 Z% L, D% h# j/ c3 e
u1 = k0*Sqrt[neffcl^2 - n1^2];
+ K. a4 S\" x\" s5 A9 M
u2 = k0*Sqrt[neffcl^2 - n2^2];\" h6 v! b* ]' H4 O4 X
u3 = k0*Sqrt[neffcl^2 - n3^2];
! H0 m! |3 S. i( g\" b$ B
w4 = k0*Sqrt[neffcl^2 - n4^2];
3 G4 I7 t0 E# r( ~, F
# b, q2 x+ H/ E ?2 N% F( U
Iua111 = BesselI[1, u1*a1];, G# T( d& Q8 \4 R% n6 x! P% E
Iua121 = BesselI[1, u2*a1];% w; ` e1 ^2 x$ D1 S\" b; S
Iua122 = BesselI[1, u2*a2];
; f( ]4 @; \* V( A, b9 I
Iua132 = BesselI[1, u3*a2];$ W+ i: x x# X2 G
Iua133 = BesselI[1, u3*a3];+ e8 p% J$ b; c' p
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;# V' [) \7 ^8 h% G' @6 Q! E$ @
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;. T0 m1 }) {; T2 w1 e% \, [+ Y% a
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
$ B2 h) S; B( b6 q+ G3 D
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;7 b, h$ z/ o\" [6 Y, q3 a
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
/ N$ w% L, M8 }' w: A# H- _
3 O1 `! c1 a- W/ o; H' t
Kua121 = BesselK [1, u2*a1];
- d( m% T& G0 U0 B9 u y* I
Kua122 = BesselK [1, u2*a2];
* w- O7 t, X\" }: h J: j
Kua132 = BesselK [1, u3*a2];
' \4 r; S' c& b4 W. ?3 ~: n
Kua133 = BesselK [1, u3*a3];; L8 W5 @( W' }7 ~3 k# t\" S
Kwa143 = BesselK [1, w4*a3];* t$ L6 v4 _; e) |
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;7 Q8 i/ ?; w0 l\" u\" [7 V
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
' N& e( l/ z+ N3 ^* R( J
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;( n& D, t( W4 D/ \+ |! n2 n
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
$ y& A9 Q9 ]5 @
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;4 L2 F! Y7 [- _5 ]
8 d$ e+ Z5 t2 l6 t\" }2 @
H1 = (betacl*Kwa143*$ g: s: T) L3 E& P
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*$ k6 g# K- `3 w3 M\" @
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
6 w& _/ O' N$ \9 p, n% P
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132* ] `2 Q& Q H
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*( a+ }$ j, s& b8 V\" N
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
# R7 j: U6 D& j/ \' M6 V( J
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*8 C( L( U4 K8 a
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; r' |( F- ~* j/ C' D2 N. D
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& S) O! y5 n& q+ v9 H+ O
: A v2 S6 E; r% \& F5 c
H2 = (betacl*Kwa143*' f) P8 R# A/ ~
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
$ r9 F* ^\" y* b8 I& l' v
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
% |& d( D' P8 `8 o( \3 [
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
: [* t. ~) t9 p1 H4 G7 r: g( A
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*/ ]1 h& q\" p# A0 ^$ V
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*6 ^) [\" g# `. C' Y, E8 b4 D) Q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
* z2 S\" P7 O. ?' G$ A4 n( P2 _
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
& o; j! ?! S+ R$ L8 z& _0 x
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
* R; |3 O- O4 S
' [# U6 V\" K\" A1 a' q
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*: q3 u( X$ a4 O! c
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*% d, s/ `& k+ j1 W
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*5 M$ s/ j# U7 W. |, U& t
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*3 o# z: ]3 }: A2 }- z Y! E
Kua122 - * ~6 p/ \! Y5 N& l
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ! D2 ?\" A) O0 q4 O% T% R; Z
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 0 a0 [* X7 G: v* V$ W3 H
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 6 _# b; l9 O. \) d4 R% o* _
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
; \' s& f5 W3 H1 D5 b
3 t/ {$ W }- y- p
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*- f ?9 ]' I1 K0 i* ~\" T( \( K* ^
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*4 V; m8 K Z3 ^9 W
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*& A c8 w' y% M* O\" L7 Q
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
* U$ f( B9 @/ S
Iua122 - $ U) _' u( F! H7 G
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ; m2 D8 Y K. O\" a( ~# I: Q
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
, D3 Z1 J- t) c) }) Y3 m# H
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ' ?' ?1 H, _& w8 U0 d2 ~% B
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
) X' S' T/ c6 l7 u( I0 @5 S& j; y
7 q. r6 N, X9 p
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
$ A) ^; ^8 n/ T z% E
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132** a# L\" E7 i9 U* B\" V
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
. ~; d8 }% k; A$ Z% V
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
2 { @' r2 J. a( s) Z! Y
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ! l9 ] I9 I& c* C+ k0 I+ i7 N
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - % Z) g( w7 P- L, x1 g7 W
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 5 d9 J; X\" k4 Y8 {) m' s
w4^2/u3^2*Kwa143*IIua133);
; q4 F/ R1 @7 u3 e2 I2 t& z9 Y$ }6 [
9 m( K\" t2 d9 l; _$ Y+ g' c ^. i
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*0 O9 k6 x- m' S. ?
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
! {1 N\" q; v/ J! O$ }/ B
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
% E% a: ^3 M% O) E+ Y% {3 w; ?\" P
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
4 ^/ A6 K }, p3 I7 R
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
2 k- J- b6 I9 H, i\" C
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
+ p9 e2 F' V5 p
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
- O. _7 ~/ K; z7 h& d7 t
w4^2/u3^2*Kwa143*IIua133);
& l# @; {7 m\" V# n3 v
: e( _: v* c5 e* B5 t3 l5 d! l
M3 = (betacl*Kwa143*
3 @/ K' b0 F3 w5 ]) \9 `
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
& G+ J; d$ `* t: K& [& L& L7 E4 N; Z
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
3 A* J2 m7 L& t; o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
. I) V: ]1 A3 \! M
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*1 V# V$ I' z( X7 r6 `
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
& q3 i) o5 l8 `
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*# j& m! V! F1 G, g. x6 I% k& V
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
6 O3 M8 n8 O5 n+ r
w4^2/u3^2*Kwa143*IIua133);4 R1 J+ Q- a5 u, y
0 V2 m# e% ]& w+ [) g T7 ~' X# P
M4 = (betacl*Kwa143*8 u6 j. W. N' P$ W\" D, _
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - % j% k2 E6 x& Y+ X/ A0 j
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143* U5 s) k\" G; H' z. I
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
2 D: I+ D1 ^ e2 w1 }
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
3 T4 s6 x% u8 ?0 A$ N
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
# y( _: Q1 Q! S0 N6 w8 F
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
p4 T7 A' f; f1 e
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
# O% d5 U L1 K* D
w4^2/u3^2*Kwa143*IIua133);
I; z7 \+ X8 p3 b\" p6 h* a; n
2 x: s2 J/ |6 v+ h% B
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111; D- m* }0 j\" Y# |
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
4 g! k+ I( g' u2 I
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
$ X\" n+ e. N d( T8 o2 n2 R\" G
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;3 L' w, G5 z7 e7 c! Y* Q; d6 ~
\" M7 w( o1 @; @. E( V1 C
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
& V: {7 W7 D; U2 r
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;+ D, N! i( c; R7 |) M+ x& `6 m
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;6 C2 Z8 @5 z8 C N& s
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
6 i' t4 r9 l, ]+ V( M: d7 r2 u
& ?: }: V' w\" x$ F* M. T8 j
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 3 D* X* k/ Y! v3 ]5 k/ L
V1*M4);- D+ z8 x& s( Y* b c2 M
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 0 B) i\" {9 z( ] o. x/ K. |0 i
V2*M2);
1 I( F, i5 U! a( j* ?/ W
2 U* G3 O, T5 H, P( B% g( L* }
x = xicl1 - xicl2;' o' e+ o* K0 }
x1 = Re[x];
% i& C5 H+ u& h' v
x2 = Im[x];, d. l( ~( z2 d+ k: ?
! s' M( B7 ~ T, Z0 F! E& H) _
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];5 Q# P; |; C8 }- B9 O
]' t- Q\" t0 u1 Q# [8 o8 r# V/ C
$ S' F3 L* D! O4 E\" T6 V

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