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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;+ g, T. x+ l7 H0 e( z
k0 = 2*Pi/lamda;4 A8 J E( j( s( M! ~' M4 k- e5 U
n1 = 1.4677;(*纤芯折射率*)$ d; W) F6 i9 `3 Q\" W, k3 E
n2 = 1.4628;(*包层折射率*)
# n* g- I' V8 ~- r3 N% `5 T* Q
n3 = 0.469 + 9.32*I;(*银折射率*)2 \+ E\" N3 B( a& r0 Q# Q
a1 = 4.1 10^-6;(*纤芯半径*)# e3 b0 |1 `6 u; V
a2 = 62.5 10^-6;(*包层半径*)% A( x9 x$ g% w+ U8 k3 D* i
d = 40 10^-9;(*金属厚度*)
* }9 j& Z6 V5 S& o. R
a3 = a2 + d;/ T. t\" H8 t7 O, O\" \
mu = Pi*4 10^-7;(*真空磁导率*)& n9 x4 b/ \1 R& H/ A, r
epsi0 = 8.85 10^-12;(*介电常数*)
& R1 p2 J& d; q1 D9 {( T8 t
% N0 G, U4 {& C
n4 = 1.330;
$ L, X4 C3 l6 V* ^4 L& a
7 m/ u% O' ], \' K
neffcl = neffclre + neffclim*I;
1 |1 d4 T\" F1 i
' d. G2 U: r- H9 S; n! m
betacl = k0*neffcl;
+ V) S) _8 |1 N
omega = 2*Pi*299792458/lamda;
3 k, I ]* S: c8 \: t, S
\" G2 d! T2 Q. S% D T, e, W! e
epsi1 = n1^2*epsi0;
+ i0 P! |$ @* U% x0 E/ L, w
epsi2 = n2^2*epsi0;
& L$ |7 J# N0 m9 J5 A9 |
epsi3 = n3^2*epsi0;. k$ U. H8 Y5 ]' T' V* V- l
epsi4 = n4^2*epsi0;( h8 K, v: d5 O* X
: Z3 t+ Z6 ] m3 K/ H
u1 = k0*Sqrt[neffcl^2 - n1^2]; V0 O6 o W/ B9 O4 b
u2 = k0*Sqrt[neffcl^2 - n2^2];
\" E' P: g+ Q- O- w \\" f$ T2 M- N
u3 = k0*Sqrt[neffcl^2 - n3^2];# f+ t' F$ q- b+ a s* D8 f3 _' \3 L\" J
w4 = k0*Sqrt[neffcl^2 - n4^2];9 a- w\" z- Q0 C0 [3 s
7 a1 r T+ p% X3 k9 U8 x, j
Iua111 = BesselI[1, u1*a1];
6 E5 C! }* j P
Iua121 = BesselI[1, u2*a1];
; }- H. ^- |9 A\" g/ K1 b
Iua122 = BesselI[1, u2*a2];/ @& m3 R! _; b! S9 w) G& T
Iua132 = BesselI[1, u3*a2];( {2 ]1 _\" I6 e: ~4 l3 H' e
Iua133 = BesselI[1, u3*a3];( `8 x: Q5 e. K+ Z3 a- Y
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
( ^7 E9 H9 C\" c$ r V9 H+ k
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
& R) I& p3 Y9 z! }0 K3 M2 k: s
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;0 m% K\" W: K5 C
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;( Q: ~. N( d' v. m) r5 ^
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
( p: x7 g+ i+ B* V
$ R/ ^- ?\" t+ t5 [2 e1 @
Kua121 = BesselK [1, u2*a1];
4 O( a% G) Z$ T. U\" P
Kua122 = BesselK [1, u2*a2];' f( V5 k+ o& u2 O* v8 l4 r, b% L
Kua132 = BesselK [1, u3*a2];
# P( N# S9 _0 t- z* m4 L ~, Z
Kua133 = BesselK [1, u3*a3];
( i1 [# y9 ]* }# T& Y9 Z
Kwa143 = BesselK [1, w4*a3];/ G. S% a5 C) [: W6 o
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
# O/ X5 r4 X1 Z0 n\" |4 c
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
1 \5 r4 Y4 l6 N. g; C
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;3 E' x u5 t\" Y5 U9 u4 |
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;1 y4 i+ \' U2 p7 K; O: W
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;7 [2 }) I, C/ {' V& Z V
: R7 G' j! @4 ~2 S2 W
H1 = (betacl*Kwa143*
6 y& b8 z/ v7 a: e6 u6 F
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
! [ H) m/ Q2 R- f
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*+ ], e1 i\" P5 _2 E, E h5 V
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
, P4 s: D+ B8 `9 ?( D
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
- d1 Z Z7 a3 w
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*( z, z) k7 N7 S) H
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl** q6 D' p* ? c$ j
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*6 Y7 l8 Z3 [$ I+ i; G# s4 m
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
2 ^2 W0 A2 t/ I J& [) d
\" m1 s9 n$ p' ~' S# j0 P$ D3 w
H2 = (betacl*Kwa143*8 U) t; _: N6 [
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
, y& `: n, l\" T2 L! U: I
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
Y; k2 e- r+ Y, _( g( z6 H- u
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
8 H9 h3 I5 ]6 P |9 f
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*5 Y2 O! q& m& p A
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
3 R$ E% U: U* U9 X; h+ j
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*1 N5 s$ \& u: s
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
$ ]\" A* f1 A2 ?. C
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
* Z9 r: t/ {2 Q
) e* ~% U3 H# o5 _* y
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*/ m8 d! P: q u, t/ ^
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
3 z, I, r$ `2 Q2 n! l& D
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143* K, j3 U: U+ f- `) n8 b$ q
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*- J. D! I# q$ A- ?8 h, w2 L4 l8 r
Kua122 - ' {+ i* j( h# R4 H \! M. m7 _7 X
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
/ q* p2 t7 w9 r\" i8 }* H
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - $ J# q& v5 c\" ]& G! V
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
+ S$ E& r: c+ Z% M2 A: D. X% v
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);: {' F8 b3 m% M) K\" c
1 l7 ]8 I# f8 i
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
7 n% q+ B! ~0 x6 ^; F2 V8 t+ K
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
, N5 t& @& n- Z9 _8 i t
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*. m% R4 H5 C# L1 d
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132** V% [4 T1 [* ]9 B& _- V
Iua122 - / F% ?. L' J# Z2 D9 _+ U* p& Q
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 2 ^. E( s3 \% u\" s$ }% _% I
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - - X, h3 n ^* F5 l
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
: _$ @0 B% I- }6 B' t* n0 ]\" m3 e+ ^
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
1 P; G0 ?1 q4 O/ F i5 g% E7 c
! x0 z1 p/ M+ q8 r* `
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*' M4 h2 j\" E7 A6 {
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*( S2 g5 Y/ w) H# o- M- ~; A/ C
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
7 j2 r$ N\" @! z/ l
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -+ A' M/ `% {& ]* _& R
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
/ V6 v4 U( [2 z
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - , [* G' ~$ N\" ?, h* p
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
6 x, h# \3 R' M1 }+ K
w4^2/u3^2*Kwa143*IIua133);7 ?4 _) {% f5 J- w- G
- _) \2 F# c& N) t& u
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
2 u2 i0 u7 q8 w/ |* f( V( s
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*0 v, k. L( ^+ r* ]3 P\" z7 E- E1 S
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
9 U5 }1 ?( \. Z5 n; u y. @
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -8 s1 x8 p5 T4 B, D
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 2 N/ C8 `* t/ T$ i5 x
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
3 N/ N/ R( D' H* t0 x
w4^2/u3^2*Kwa143*IIua133);2 f7 ]: }9 c* |. k* g; ~
. Z7 ~* r0 x* ~' d5 F2 X\" F
M3 = (betacl*Kwa143*& O' S# D# l. C\" ~. z6 f9 W
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
' w4 n8 i/ V8 G( l+ H# d
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*) X* {# G: B6 D* D. v7 A! R
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
3 b/ z0 W# d2 _' N
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*/ e+ H2 C5 m6 [ l& a: b1 E
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 3 h& m+ f R4 X9 }
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*% X \# X1 K: [/ U0 c' p7 M
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
4 S( }8 ?. C0 r0 G$ P7 W
w4^2/u3^2*Kwa143*IIua133);/ a; a+ @7 N' |1 W
! X5 q* t* b# O
M4 = (betacl*Kwa143*
; u$ I$ f\" s- ]9 l: v1 V
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
# W( L' P7 k& y. r
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
7 A8 d7 l. f0 i2 m9 m s# g' i
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - ' J- M, g5 k, d\" q% Q5 z$ S
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
- `& O0 Q3 t: J7 I
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
0 F- I A1 p% R
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*; A, P) a7 L' B
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - & e( @2 {' _' ~1 x( H! e. ]' q
w4^2/u3^2*Kwa143*IIua133);) T8 L- y+ y( `' T1 L! q
$ C7 R6 {/ i+ u0 }$ E5 m _! x9 [& r
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
( m5 q6 _/ V, N
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;' e) P: N+ f) Y; @, }
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
# {8 t( H6 Y) r9 u\" ^( f h
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
2 V% \$ O$ K; A5 C; |
0 ]9 k! d: T2 c5 \: z; D
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
+ c$ E7 X, ~: _5 c' @
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
! h% a+ m, ?2 Y! F$ f! u
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
\" q7 e- _2 e- [/ h9 n( ~9 N
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
' c& R [ }6 r- `4 Z2 s
0 v1 C4 l2 v! m/ I4 _
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
* w; }. u: g+ O& c; w
V1*M4);
( D) F* w( E' r) ?; k
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
+ b0 q0 v( D& l# n C' s1 X h
V2*M2);( h$ |9 n! ~- y2 C# v7 v
% [7 X4 d7 [' u) X
x = xicl1 - xicl2;
0 _4 P& z8 S' `7 s3 l
x1 = Re[x]; J! l0 L- d s
x2 = Im[x];6 q( c& g2 L4 J8 Q
9 _5 l! U+ b8 e, i7 ^
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
% W8 j! g\" m\" {+ s' D
]
( X# l: E; E8 m7 Z- z% Y( O/ \
: H' S! y, Y0 w) t5 k1 z5 S

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