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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;8 H) ~3 W# g. ^\" I, U
k0 = 2*Pi/lamda;/ d) c' c3 F: M
n1 = 1.4677;(*纤芯折射率*)
! m) E* P% ~# f
n2 = 1.4628;(*包层折射率*)
$ \6 q( i4 v\" v) @; c1 c
n3 = 0.469 + 9.32*I;(*银折射率*)) q, e; [1 P3 f2 Y3 U
a1 = 4.1 10^-6;(*纤芯半径*)+ F! ^( J- I5 W/ }0 @# Q$ g1 w' T
a2 = 62.5 10^-6;(*包层半径*)3 y1 f- k) o8 u, ?
d = 40 10^-9;(*金属厚度*). H# G, q8 X2 [! B8 y
a3 = a2 + d;* p* a( b0 [ k
mu = Pi*4 10^-7;(*真空磁导率*)
+ \% t! z) M2 A5 Q& z
epsi0 = 8.85 10^-12;(*介电常数*)
+ Z3 `6 M( e\" v/ d* T' d- ]
( F1 l6 j/ {0 ?8 U
n4 = 1.330; Y, C% s% d5 j( ]+ O0 _: j
- \7 x9 ^/ h2 Z$ `. w7 [+ r7 {9 H
neffcl = neffclre + neffclim*I;
1 o0 x1 r( V) j3 A7 {9 }! ]3 a
: D6 A/ P4 }+ ]1 o' F' \. ]( L
betacl = k0*neffcl;
5 N! h( }8 u' C
omega = 2*Pi*299792458/lamda;
! x* k: K) v S2 l8 T) j0 c
6 M4 [9 Q: w0 F8 W
epsi1 = n1^2*epsi0;
. j5 R& v# @% @$ V
epsi2 = n2^2*epsi0;2 l( A+ L& I) w. F7 N
epsi3 = n3^2*epsi0;
4 H& _# y6 A0 W$ F) m, M: L
epsi4 = n4^2*epsi0;
8 U! h7 ~$ o& g% |- m
! v+ @; [6 [) s
u1 = k0*Sqrt[neffcl^2 - n1^2];
. {\" l( W$ P6 ~) x$ ?% u: n
u2 = k0*Sqrt[neffcl^2 - n2^2];
. o# l. p& w1 l: i
u3 = k0*Sqrt[neffcl^2 - n3^2];
3 a# i1 F\" a1 z2 l5 A% l: ]8 r
w4 = k0*Sqrt[neffcl^2 - n4^2];
8 a8 ]\" K* n0 e0 h% m
: S' c- }! e8 \( x
Iua111 = BesselI[1, u1*a1];' C4 \\" ?! w$ k4 ~8 q; o
Iua121 = BesselI[1, u2*a1];+ a. p q: T% c; T0 _+ d
Iua122 = BesselI[1, u2*a2];
' H8 ~8 z8 C# |, y5 f5 [/ Z0 B E
Iua132 = BesselI[1, u3*a2];+ S8 G! D5 ?7 f5 u- p! X
Iua133 = BesselI[1, u3*a3];! h# @/ @# P3 L\" W
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
/ K5 V- [$ j7 ~\" d: g
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;+ _! N) x s) \
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;. d0 Q. Q3 Z( q- z\" n# \. Y( P
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;8 x, C! T% L0 l X Q# I
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
( ]+ Q2 O7 `! w' x2 Y; h5 d\" N E* Y
\" T4 {* T M9 S) q* M$ J3 L
Kua121 = BesselK [1, u2*a1];
* {, E' s+ @1 V9 ^2 ~
Kua122 = BesselK [1, u2*a2];
# s9 k. e& O; c3 z
Kua132 = BesselK [1, u3*a2];6 t# t, X\" A! S7 D- F( H: j* P
Kua133 = BesselK [1, u3*a3];
& j% L- d1 a) E/ k% f
Kwa143 = BesselK [1, w4*a3];/ K\" R/ ?1 \8 m7 F2 d5 |% [
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
+ | n1 f) U7 g$ w# D) w- [1 e\" D# N
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
\" X2 {; H7 m% f' q
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;, }* i+ g+ S5 J4 r9 s; R0 k
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
6 H0 k2 C, }5 e X
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
+ n* a i5 n7 E% v: D& _
! N; r. W1 V0 w2 B6 o\" W( M
H1 = (betacl*Kwa143*
; R9 Q$ E& A# J; b\" @
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*6 X9 [0 H! H\" [+ m
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*) R. Q7 K9 l1 F* n
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
( r( C3 M! U6 @' U. N
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*! A9 _, g7 W) }: T1 k. ]
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
+ ]- ~, \, e5 U6 E
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl** n2 j6 F+ f$ x' |5 s: [* V8 |
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
3 E2 e6 Z; D, X/ m# \
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 q9 }! M7 Z2 b+ a
}) x( E6 t& f& O+ T+ f h% B$ F- I
H2 = (betacl*Kwa143*. O* M2 ?1 Z. o# b\" i4 `- ]
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
0 X& I. W) f, R. k* H
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*+ ~( P9 T% u7 f& A
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
8 x2 v5 O) p5 \6 f+ |# S, o, ]
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
8 l, w; e0 h: O7 @7 _% Z! J3 m1 G
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*! k( p B3 g; ^6 @! w. J
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*! {9 x0 X( A3 q8 L3 L% R2 ~
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
) o2 ^# C% b: ?' ~' y
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);0 ^4 m( ~/ {. c: s0 g\" w+ `
' V. Y ~6 s# S5 d6 g
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*5 V5 x* B& J9 s/ W( G8 f8 q' X
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*6 T7 f' x0 H- \
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 L- V' z7 i& v& \
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132** X$ s$ n. G( R\" b
Kua122 -
& j' B& k1 s* [ q\" _( ^9 [
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 3 o% ]0 _4 j3 d) `
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - $ ]8 O0 o7 @0 n/ A9 o% i
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ' e& T% n( _! Q# v1 m
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
5 K3 w& Q\" @- }! G
+ L. q1 @. X1 t; |( O& t0 H6 R
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
$ }* W& f- m* [0 ^, d' p) U\" _
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*6 p& @5 N# q f' ~2 ~/ C
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
' r9 d- K9 {* z2 x
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 O) _# }4 |; v/ a8 C* Q9 o( C
Iua122 -
* A- ]1 c6 u R7 n: w) M
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - , x6 ]( S* F9 o6 y5 J8 U) b
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - % ~5 k0 M/ V) D8 ?6 f7 [. }' G8 G
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 7 L7 N q; i! r; C5 s4 w9 h( I
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);2 G2 P% E! j3 l& S* T0 |
A! t' \5 }# \9 R1 U
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
1 |9 Q. W2 l4 H2 b
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*' Z$ B0 h4 ^7 i$ ^7 g g( n* e
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*; h6 F* y8 a\" r* v; n
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -9 g& ?+ L& @9 T& g9 `
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - . E- @. J2 C5 [
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - / X' |+ [9 K) ]$ t+ B. z- e
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
0 M- t) K3 D( K6 f\" v5 P\" J0 R8 D
w4^2/u3^2*Kwa143*IIua133);
; @1 I P( c( Q! P, m! Y \$ I
4 ~5 {3 I! Z: ~2 i1 }5 R3 D+ C
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl* r2 w/ m: H' _& p
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
! B: ^/ Y( O* K
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*( _4 u/ T% m6 _3 k( Y6 l
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -/ A. g+ ^; x% p/ x& ?
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 0 q/ q. w3 e' J$ N; i6 G
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 5 C! O U9 c r$ j* v) A
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
1 C# E8 F: M b. u' _$ _: W
w4^2/u3^2*Kwa143*IIua133);& D: [3 @ D) R( g
7 ?; n0 M( V/ B/ |
M3 = (betacl*Kwa143*\" D- ?5 u! _* @ C6 z5 I
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
8 ^( |) T% K- x% ?; Y# C
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
' o5 ^: q6 Q0 O) S% W* {3 i; G& M
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 9 k+ C! ~6 y' {* u Y+ q9 w) l
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*) _) M1 \. C! W7 S# s
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
0 I: |7 J. O+ z; b- m
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*5 g: b% n: Z6 }5 l
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 0 z! p& Q6 a, F
w4^2/u3^2*Kwa143*IIua133);
& ]9 b3 x5 l8 O1 _
+ d9 U( `/ f8 F. f7 h
M4 = (betacl*Kwa143*
* \( q8 b: p* E8 A
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - # ?) G8 {; R# B0 ^\" X1 @
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
5 }7 y- C( v* F# {9 w8 U5 o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - . t: ]+ j3 ^% h$ E4 p
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
6 O& Q# g) F7 {( p+ K1 |
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - - w a' t\" q5 P8 T5 }0 M, T
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*8 u( P* ?) S) p) m L$ N9 d% v) T9 ^
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
\" o' A$ H5 ^( b\" a1 R& X& u\" `* E6 R
w4^2/u3^2*Kwa143*IIua133);+ N4 |7 w4 s6 d
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
$ B- A. i7 `: R$ Y, J) I\" ]
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
; U2 m- |# W; h& n
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;6 n) D# v% e- Q. s/ K5 H. u- K, m
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
% p! ^# t, d$ x\" J; W4 k, R. \
- w\" {\" o& d- \\" |$ _* D
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
; ]/ R4 j8 U4 P& m/ w+ X P, k' s
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;- Z% Y! y, N7 K* ~9 D6 N! T6 c
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
1 l( \: }; j+ r: K2 W) H% B9 [! P
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
# E1 ^& R1 `: J4 N
( `9 |# A: E- U\" }
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + ! F Z5 D; t# Z$ ^# b4 c- Y5 [4 T
V1*M4);
1 F/ p# X- f: B/ P# j) y# l
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
! U5 A/ |' n& n\" F, Y
V2*M2);
9 O+ A P* {# j- t/ c5 f
2 i& O) B1 L# Z
x = xicl1 - xicl2;- x6 F+ m0 T0 N5 n+ M1 F
x1 = Re[x];& z/ M9 x* w$ L: {+ j
x2 = Im[x];
& [& f7 y- `% E: ?/ A
* Z8 f) {% C9 O* L4 @0 q' [
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];0 j& X9 R! b* |# E
]$ L9 n( V* S: q
# J6 n; h, G* H# }0 }, j

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