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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;
. K/ \% I9 j: f3 V
k0 = 2*Pi/lamda;% n9 ~7 s/ w9 d6 y; G3 e( T
n1 = 1.4677;(*纤芯折射率*)
\" ^ b( T/ d+ ~& }( ~9 R
n2 = 1.4628;(*包层折射率*)6 e+ d6 ? z' c: B9 D i
n3 = 0.469 + 9.32*I;(*银折射率*)& o0 a: T$ U/ t3 z, w3 p8 S/ [
a1 = 4.1 10^-6;(*纤芯半径*)
2 V1 b9 J5 {8 p* p* s5 u) a. {6 h, _
a2 = 62.5 10^-6;(*包层半径*)
; i: K+ V- k# U9 s _! m
d = 40 10^-9;(*金属厚度*)$ E2 p( n( f- M C8 G
a3 = a2 + d;. q, R8 @) N% Z6 ?% f8 m5 l
mu = Pi*4 10^-7;(*真空磁导率*)
+ ^9 ^8 e+ M3 W7 s' C f. G: T
epsi0 = 8.85 10^-12;(*介电常数*)$ v% R\" q\" E9 ]3 t& b3 P
! t# q: n' ?3 S# ~7 l- H1 c' W
n4 = 1.330;( e) h3 a& w9 q: d } I
( ` S; D; W; s1 m
neffcl = neffclre + neffclim*I;- ~8 }- P) N6 ~. v7 W
, V$ |4 A9 Z, n$ e5 o7 G* K& g( e\" R
betacl = k0*neffcl; F$ b4 f2 \+ N; ^9 \
omega = 2*Pi*299792458/lamda;6 e$ e\" R$ H, |& C! N7 @2 ]0 c
- \9 K6 q2 `$ W- l& z8 s; G2 A
epsi1 = n1^2*epsi0;* G* G# B$ T/ ^. \% \
epsi2 = n2^2*epsi0;
; I% z- _- m. p B& }$ w
epsi3 = n3^2*epsi0;
* ^' M- M8 Y\" g3 b* h: A4 q
epsi4 = n4^2*epsi0;+ m4 n\" X% [\" X1 s8 `
8 K0 g4 r/ x7 \4 J7 A X1 \
u1 = k0*Sqrt[neffcl^2 - n1^2];
- p; c7 d7 T; E2 m, R+ z# ?\" {
u2 = k0*Sqrt[neffcl^2 - n2^2];
% _\" s6 t\" l: t4 b
u3 = k0*Sqrt[neffcl^2 - n3^2];
: A) T# r$ G# q* L1 z% a\" @
w4 = k0*Sqrt[neffcl^2 - n4^2];3 L1 P: Q) D' M: u) L0 w6 W: e. n8 M
$ c\" |8 E0 h2 C7 H; H
Iua111 = BesselI[1, u1*a1];- a8 F' y2 l N r1 h
Iua121 = BesselI[1, u2*a1];% A# G. I* }. H
Iua122 = BesselI[1, u2*a2];
$ l# {; q4 C, e2 d& I4 [/ b) M4 Y
Iua132 = BesselI[1, u3*a2];
( v6 }4 ^& f% ?; s& g
Iua133 = BesselI[1, u3*a3];
5 r! C9 @7 z( h2 ^+ J\" {
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
1 e1 {2 B, O; R. f. P4 T' U; F
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
, ?9 F# Z7 M; ]7 w5 r9 {2 U
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;9 t; a& C, f' ^6 B
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;9 r. l, b. k4 }# o+ `. z( u' ^8 [. U4 p- y
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;2 h% z! k\" Y+ B
: n; ]) B/ U* C\" [5 e
Kua121 = BesselK [1, u2*a1];
1 M9 b# o0 ?+ o1 s
Kua122 = BesselK [1, u2*a2];
1 d2 d# x0 _& @! m) ?1 t: E, i5 b
Kua132 = BesselK [1, u3*a2];9 ^ m' W' S. }3 b) C8 o
Kua133 = BesselK [1, u3*a3];: w. y7 W* a! i3 O9 b
Kwa143 = BesselK [1, w4*a3];
- m1 W8 y7 | n- z% o- ^* l
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
. [2 C0 P/ u: |9 h, R
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
1 }% V9 J; _* n5 o: G
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;) B3 a' A) R# Y( f' R, U
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
. P* B% V7 P( F1 P3 q0 C+ M9 g% h
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;( P! u2 }; ]; f: i- }
# b) A! X0 @3 a. K
H1 = (betacl*Kwa143*5 `$ _$ [% N: O1 v6 R$ Y
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*& ?) [, p+ o- x
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*: N4 \, N9 R- W# J6 Z3 f* V
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
+ Y H7 V, g) \3 i
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
\" M% R3 j9 @# F& t c6 p
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
2 L$ n8 x9 e% u\" E- v$ @* \ D+ @! A
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
6 \+ x( U7 S' y' |; A% o5 d
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
) F1 G3 q3 b! Z; |( Z
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);9 Q7 x3 N- Q% q: a; I' g3 y
0 d& F6 }! K0 c7 G/ S
H2 = (betacl*Kwa143*% X, [' _$ y9 G% K
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132* y6 p7 j( r7 |1 i2 N& x( K3 {
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*: }6 C2 O! C% J$ w% o, \- A$ J s
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
4 l, T/ B1 \$ T3 q
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*9 ?7 [9 x' ]3 p' y9 {
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* D$ I! T, E; b7 N8 L* \& W
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
$ F4 ? t( T/ p% _* o/ L$ H
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
- I) a, [ k1 C\" c+ p8 \- p
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);/ d* r; T. _& e/ L
9 E& G q, p8 l7 e1 J
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*% [& p3 r9 }5 o; }5 O
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
7 W8 @* x\" Q) W: |4 Z' L- A
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
7 k2 d5 j' ?! f# E. [
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*5 L3 V1 P; |: ?: h7 X
Kua122 -
. ~3 q7 G' X& S
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
9 |# e# A1 J8 O
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
9 c) n4 C B2 h' }7 w' u* k. E) _
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 5 F! t. M+ U/ ` S: U) k$ p
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 M. m, ]% x, k' m$ A
$ m) v+ R3 W1 P6 h6 _ W; E
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*( l4 v0 r: f, Y4 B
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
9 w8 u1 V4 B: Y( R\" M2 {
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*/ P; m3 u3 A( s$ P9 @1 N' b0 K- I
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
7 H6 s/ i V$ U# ^
Iua122 - & m' k j, \0 |3 R, b
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
! V7 l: w1 u6 a T
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
6 U/ |$ b# C h D
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
0 ~+ T. j! V6 G
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
* q\" X6 }$ x0 a1 J0 C; w9 l- \
/ b5 O, ^, J9 B4 F! o8 Z
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl** t% H. _; r; N/ M- Q; I
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*9 N0 @7 e Y* k# q8 h
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*+ H2 E3 H+ E Z( A. z3 M- e
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
% Y4 l9 a% L6 Z( V: T3 K$ `5 x
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - * c7 G `2 }& B/ s\" O& V
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
: f( @& l8 T\" E, U# Z
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - * E5 U' E2 z. R\" a& G! j
w4^2/u3^2*Kwa143*IIua133);
7 j% K$ d9 f% i
$ T: ]; T, M6 O' v
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*( y3 [9 k Q\" a1 X0 y: _4 y
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*' I& t; `5 |6 M! S\" L$ j9 i
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
\" Y( V2 N+ t7 t8 \( @( p
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
M; |: V6 `+ U8 ~' n# h9 o6 y4 \
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
. z3 |* k' I3 Y6 t
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
$ o R% c3 \4 }* F3 q3 a2 B- s
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
9 e6 _ i8 `; @7 h+ K5 K
w4^2/u3^2*Kwa143*IIua133);
# ?! m7 D) b$ ]; y4 M
2 H& D2 t2 x\" Q\" A6 i* J\" @6 H
M3 = (betacl*Kwa143*' _1 m3 a4 y2 c& P7 c0 i) V
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - b6 t5 Y; V3 _8 _
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*6 S! f/ H3 P1 _& [
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - + f' _- z* e- n+ C9 E; r
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*9 L2 ]/ F: }/ N% P5 g* z- F& r
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 5 I. \5 X4 Q Z. p6 q/ W( V3 E
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*: R4 T4 ]+ W. y) W\" Z- r' r) @
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 8 s, W, E. p3 H! I. ?. w7 Q
w4^2/u3^2*Kwa143*IIua133);# u) @( N& b5 G x) y! M, {7 d
\" l/ A2 O' H; V6 y0 E
M4 = (betacl*Kwa143*
3 M( S$ ]# L+ E* c$ ]
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
# v& m# n% T6 K# [: V1 m\" i
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
u3 D$ b: ?* ~' a
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
! I% E! m2 T4 f* r
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*- |8 F4 M& x K K/ S* E
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - # t \3 L/ S2 D, S+ i( i+ r, F
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*1 _* c0 B! Y# S3 o( Q
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 5 s( f9 M9 x3 g
w4^2/u3^2*Kwa143*IIua133);$ b5 F# }, {/ J1 \6 B4 B
8 E; g+ e\" y6 G/ m0 J& w% d
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
1 ^4 h! t* f: j4 r\" a( K
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;% M( U% q5 h% Z
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
, @3 M0 _' H0 m. s/ `
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;8 C8 R' O+ S1 t# M
, \0 `2 R: }9 {- H5 K# z
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
# x' W( i8 Q* x0 l
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
- B1 N. Z; {2 r
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;; j6 ], f* R; _: O4 f
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
- e9 k3 \2 M$ k* B/ [: I# H$ Y
) ?/ ?. q0 z( K1 G6 _& m
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
3 l/ s6 T/ t6 A& _% R5 U6 i+ z
V1*M4);: S/ i; f! S5 A6 B. z7 V, t2 C
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
2 X3 y! ?- b4 A
V2*M2);3 x/ Q) T' A# ^) v& e
e, E' |' |\" Q& ~1 Z9 k
x = xicl1 - xicl2;7 o ?/ H# b, p2 u6 r7 F
x1 = Re[x];2 I* j/ N- e$ d' _+ {. T# \
x2 = Im[x];0 V% U3 H! i8 W& U0 l% S( S& t4 \
\" h, P7 O# q6 m8 u) W m6 G0 W& g
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];, l1 [+ S' U; J
]
) v\" B* E4 d0 L+ _: [/ X
2 ]! p A C4 V7 \9 Q) V; 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