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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;5 _& ?9 A: i' p& ]2 x3 [
k0 = 2*Pi/lamda;
+ b8 \% ^1 e( i4 _
n1 = 1.4677;(*纤芯折射率*)% x6 g+ A* [# z- m6 b0 w* d
n2 = 1.4628;(*包层折射率*)
$ D\" ~* J$ L7 g. f
n3 = 0.469 + 9.32*I;(*银折射率*)
R. o6 ~: F3 ]9 P/ I- n
a1 = 4.1 10^-6;(*纤芯半径*) A, m5 z) Z. J9 c1 y9 Y5 p. Q0 Y
a2 = 62.5 10^-6;(*包层半径*)
4 G5 m+ d4 W9 f7 Z j; }8 K% d
d = 40 10^-9;(*金属厚度*)$ ?2 V5 r- o# o- F5 `
a3 = a2 + d;
, J! x7 [5 L' `' W$ Q\" Y
mu = Pi*4 10^-7;(*真空磁导率*)8 G3 Q- U! O. A6 x3 j
epsi0 = 8.85 10^-12;(*介电常数*)5 a5 A$ i3 @6 O3 y: m
9 ^& u+ k$ S8 L$ w9 I5 x* W' w) Q
n4 = 1.330;
! L% w @( U+ g5 K1 F2 ?+ g4 J& `
( U\" M6 _3 T9 V. g' Q
neffcl = neffclre + neffclim*I;- k0 b9 s5 W/ \1 s) L
8 o( R5 s( C$ U, u+ V6 s' y9 n
betacl = k0*neffcl;% U% L% P5 d5 U* T7 d
omega = 2*Pi*299792458/lamda;/ O& A5 r/ m3 U2 H! o# ]
! Z. a: \5 j, z0 V. o/ ?# m
epsi1 = n1^2*epsi0;
. l9 `8 Y* n5 s ?' U% y# I: i
epsi2 = n2^2*epsi0;
$ d6 D/ e* d4 X4 Q8 A
epsi3 = n3^2*epsi0;
\" j6 y' d( B1 S. A' b' N
epsi4 = n4^2*epsi0;6 `% U+ s7 b$ m1 U- S% W2 s
% t5 U- _9 F- w8 K' H G0 F
u1 = k0*Sqrt[neffcl^2 - n1^2];0 N' s- g1 H2 c/ g) }) X
u2 = k0*Sqrt[neffcl^2 - n2^2];& c) Y8 J! C, B( G
u3 = k0*Sqrt[neffcl^2 - n3^2];) }* M$ B5 o- |, L
w4 = k0*Sqrt[neffcl^2 - n4^2];
\" K! Z+ o, K) D( P- l6 t( z
c$ b\" A\" N2 P+ ]+ ?1 O$ g, I+ R
Iua111 = BesselI[1, u1*a1];. r. o3 ]+ m, {5 j; b8 b) g% u
Iua121 = BesselI[1, u2*a1];) b$ }: h) T2 J2 k* F
Iua122 = BesselI[1, u2*a2];% o+ }+ g# [ w, }% K
Iua132 = BesselI[1, u3*a2];6 X4 ~7 |6 E! L4 U: t; m
Iua133 = BesselI[1, u3*a3];' l: T' m# \7 G. B
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
1 y. l Z- w' A9 P% ?1 u
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;8 N1 G2 n\" I3 S+ J5 l7 s& W
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;. D; M* D, x. U$ ]! N* e3 R: A7 Z) F. t' ]
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
7 B: U! ^+ M; a* W- a
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;# S' ^) J( _% S5 h
. G# c- n* U. W+ _5 K3 A
Kua121 = BesselK [1, u2*a1];# L. o4 [ u' @0 a0 ?\" _: a2 F
Kua122 = BesselK [1, u2*a2];: J N0 N _2 o! O
Kua132 = BesselK [1, u3*a2];$ ?! H% A; o- G% u8 d: O1 E6 H- s
Kua133 = BesselK [1, u3*a3];8 ^8 J$ F8 Z7 }\" x\" E5 k8 r4 I
Kwa143 = BesselK [1, w4*a3];& I& `, ~( d8 d( W1 w& i4 ]1 C7 H
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;+ J/ P0 J; Z, M0 A2 d5 M! m& h
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
) |4 g: D) z; Q6 V! z' ^# A
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
. q! Y/ [1 `9 P
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
/ e7 R. q9 G: |9 K+ c+ n4 B- m* p
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;* K0 c6 T$ Z8 c+ v+ O5 L
$ X5 n$ C. i5 l
H1 = (betacl*Kwa143*
\" D( a; m7 }3 R) C w/ a
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
\" x7 P% d+ y, a) O
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*: D9 N. S! N6 }4 P5 y( t
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*) v3 I+ Q5 O3 P6 p
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*8 c: ~0 W+ e+ u, l* j
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*4 p1 B/ ~9 N/ s, v7 T1 J- I( t; j
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*+ U3 l2 T) b6 g! I1 [1 Y: Z
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
$ m\" U/ M; ~! S( x
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
8 g% ]+ ~8 Q\" L, Z
\" z# E( H/ d9 r D7 n
H2 = (betacl*Kwa143*
% y+ @( _1 E8 H% S1 e; x1 m0 d2 j, H
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
9 U, a! V# x% j8 ?# ^0 [
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
* I5 o& w7 s9 N# O3 F
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*/ n0 o\" @! `& R4 f
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
8 w6 ~7 ^8 q- b9 I& W8 G' ^
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*\" `( L# z9 q6 i
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*# i Z# }, g: x5 f z\" g/ H
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
1 ~2 k4 w, L9 _1 d
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
2 |0 r, X% J) Q4 y1 V
2 y* F8 D$ `3 w8 O6 A\" K. a
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
7 B6 V! t3 e+ M; J: b; s- f, x0 w; a5 j
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*! b6 r( {0 e) b# J% I% Y
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
2 j+ }. y' E' ~/ e
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*. _, Y$ a* K9 N/ D5 m0 i: f
Kua122 -
( F' z3 H' O, a6 `& Y
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - * m: g( p _. N/ c; n
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
/ A* c\" A& W- o1 f3 S4 v8 N
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - \" X+ z( q( _$ r& j9 c. I9 R t
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
: V3 H1 ^3 C* D! X
0 \5 K( T0 K6 @. F& G: f
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
; H3 C6 T+ S/ _ L9 H* }# G
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
. O4 C- o0 Q4 t: G
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*, u( d! I& w4 k
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
1 t2 \) C3 ^/ g0 k
Iua122 -
7 ]$ }3 w0 e) s5 _( e
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
9 Q\" Q! @) E5 Z& ?
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
* X9 m0 Y\" L5 I% N8 T
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - . @4 A8 ?: T* J6 y: S# A
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);# s( V2 [) |9 G( M5 x: {( R
6 Q7 b# c$ \5 w\" \! I6 J
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*% q8 x* `1 O. j\" M+ {( l6 p
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
- ~4 K1 b0 M; v' k
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*3 t; k7 ]+ b5 {' A
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
2 J2 ~& w\" d: Y( [) L' s* ~
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 2 {! P: M0 Q# q( ^5 U
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
\" p6 m( v1 ]\" v3 }
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
# a4 y0 i\" X\" H8 |
w4^2/u3^2*Kwa143*IIua133);' t7 K: i$ V% I& ~3 |3 M4 \0 l
8 c: `6 A1 q! y' l& C8 a
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
- l8 ?# y0 r/ E
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
& |( I0 J* F0 |: M# }8 V) r0 N) b
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*+ T; V# v) j9 Q3 o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -7 \6 f3 [2 N; m+ G0 l0 |2 c9 ?: f
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
8 @. t( _ d\" `( s3 P5 B! Z+ I
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - \" ]! Q+ v, a' C/ B3 W% _1 c
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
& [8 x5 L' D* f0 ~
w4^2/u3^2*Kwa143*IIua133);% g! m8 {7 Y+ P
/ i7 u6 Z: N\" U) }& H' C
M3 = (betacl*Kwa143*/ [# Q+ ]* l. I' X\" p5 B6 B: P& K
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 0 Q1 p- X% `7 G: `' U8 `
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
o( m' Q$ ], l1 F: r7 R2 v
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - - J1 v4 K% h5 q& b\" n) x) I/ _: L9 X
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132* r N) P. ^) r\" i
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 2 K Y& V7 R( G) N, y S
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
+ h/ Y0 |9 v d
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
e\" F) k, B/ U, B z2 _
w4^2/u3^2*Kwa143*IIua133);% f; p\" n* G\" P1 R7 i
) z4 K\" o- I5 E' C# ^4 y% N* h
M4 = (betacl*Kwa143*8 [7 L\" e% l( P
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - - [\" L1 w. y0 @) N' d, s1 t
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*/ ~0 X7 P0 A2 H
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - ' `( Q1 s& K/ o: \ d
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132* \. N6 c g& P9 [ @- `6 G
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
% C( _( f: @- J, D% [. i- {1 ?
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
7 k6 d0 a \5 ?) n4 }
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - # f( D* l! q% x2 e- [7 Y* |6 T
w4^2/u3^2*Kwa143*IIua133);% V( e6 ` \ E: W4 S\" c1 b
# x\" M, X r* Z
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
1 M0 p! v0 D' C0 z% N2 e
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
8 K/ I+ P- i1 C- h$ C' @0 h$ R
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
1 T+ e& o- e# G( j3 G
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;0 ^8 c0 P) ?$ N0 y1 N8 n
/ S, m: Q; k7 J' Q) R, ]
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
7 {- a, v/ V2 b1 \! y# J3 ~9 h2 Q5 j
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;7 O# W0 `. o# {. |: v
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;4 m5 M' s2 f* y! ~' e5 J4 \
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
2 ?' f/ j5 G, g5 w* f6 S# c: ~
# H* \* R, c5 C5 U
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
' r) U\" F0 q6 V- ]# G7 ]. ?/ r* W
V1*M4);
& S8 o1 t0 S$ e, h
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 2 `4 P \0 V* A3 }4 q- T
V2*M2);
U! U t! S) a; d. N
, y1 H2 b( u- m$ z2 d
x = xicl1 - xicl2;
) q' e, I0 }9 U( _
x1 = Re[x];4 I9 V2 l3 `5 y: s2 W, r$ J' F7 b
x2 = Im[x];: J7 [, g9 j2 H. ^. A, o( p: ~# C4 W( E
! \\" L\" n9 ^( P( M9 p% Q
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
2 b; b0 ]- @; `$ Q
]
\" s& x) l( ^) C. ]+ G9 f
' X: R7 y8 [3 w6 j6 k\" z( w

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