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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;- x* g4 B8 x: z
k0 = 2*Pi/lamda;$ }* ~5 s0 E\" t3 p# ]0 ~1 V6 Q, E
n1 = 1.4677;(*纤芯折射率*); Y, \0 A' H/ [& j5 c' E2 I7 @6 ~+ O
n2 = 1.4628;(*包层折射率*)
' d; g( u' ^' q, _
n3 = 0.469 + 9.32*I;(*银折射率*)5 p9 D% j& z; j' _
a1 = 4.1 10^-6;(*纤芯半径*)9 D# ]1 T3 y; D% R* B, C a
a2 = 62.5 10^-6;(*包层半径*)' X5 n& H; ~! D3 _/ A# C, b
d = 40 10^-9;(*金属厚度*)5 U3 H& P; p. v& u/ C$ a3 k! G# b
a3 = a2 + d;$ y: h h2 Y' f; C P5 N* @# R3 ~( ^# x
mu = Pi*4 10^-7;(*真空磁导率*)8 @% p, D/ ]+ E X9 u2 \9 m7 g& \
epsi0 = 8.85 10^-12;(*介电常数*)2 n7 a4 k\" A9 S( J\" i# t- c
! U; ^ r e/ z+ n! w5 Y% `; ]; f
n4 = 1.330;
5 x; F* j& M. z& A
# [$ X4 ?+ p |' ~! u7 a
neffcl = neffclre + neffclim*I;3 _: `( k2 r4 n
0 f, W. ^+ `0 d8 ]! M
betacl = k0*neffcl;
8 v) h B# T/ R s
omega = 2*Pi*299792458/lamda;
+ z5 m* @. b G. J
0 v3 H! c/ t+ I, J( F
epsi1 = n1^2*epsi0;8 h\" U' u5 I( }3 m( l3 \
epsi2 = n2^2*epsi0;& m9 n9 w9 H) q& G! k\" T% L
epsi3 = n3^2*epsi0;
. B4 q1 M. x. A1 y
epsi4 = n4^2*epsi0;
) d1 [6 J- T4 K. R% {
7 X/ X9 d# \% O1 M5 p* e% b. R
u1 = k0*Sqrt[neffcl^2 - n1^2];5 {, g; E# }4 i9 k
u2 = k0*Sqrt[neffcl^2 - n2^2];* ]; s) t! _- Q) A. r
u3 = k0*Sqrt[neffcl^2 - n3^2];
8 i\" r d- a$ g: T: {
w4 = k0*Sqrt[neffcl^2 - n4^2];* O( B$ j' ~* r/ X( b7 `( l5 y1 f
! d) P) q _4 t A8 f' {
Iua111 = BesselI[1, u1*a1];& ? Z# H, H/ A0 y' A: q& N
Iua121 = BesselI[1, u2*a1];
; z6 K# t4 l! {: p\" N0 N& \2 \
Iua122 = BesselI[1, u2*a2];
# d( u' Z6 S$ F0 L1 `6 @( }' A: g Z
Iua132 = BesselI[1, u3*a2]; T2 C. ^- y1 v3 r# R* D
Iua133 = BesselI[1, u3*a3];
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
3 A& e/ C' @8 p\" z' s; N
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;% }4 W\" k0 I6 s! @* N9 f
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;: z+ A# v7 y. j. ^* O0 r E
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
$ g4 n1 e0 ~9 U
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;0 z( J* s9 K9 N3 \/ w
( r5 ~' Z0 j F; ?: @
Kua121 = BesselK [1, u2*a1];) {& ?( e- s, P: G' U
Kua122 = BesselK [1, u2*a2];
. a3 Z Y( D- z: B2 f
Kua132 = BesselK [1, u3*a2];
; u U- ~ l, c! j# k) F( K4 D
Kua133 = BesselK [1, u3*a3];: l\" ~6 @' t* n! }& R! t7 G; k
Kwa143 = BesselK [1, w4*a3];
`+ ?1 D. A, s. r: U
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
6 V/ j' q/ u' x# ]: ~5 x0 X) t' `) E% O
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
% w\" f( `, C- h+ j% A
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
3 D( ?+ y& o* P( j\" @6 X
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
# J( M: G1 c# f6 z9 }3 X0 ]- W8 _
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;2 ~' v/ J( t' ?' `! C
7 ?7 k! P% H+ N9 [3 l9 Z
H1 = (betacl*Kwa143*
2 x( r' ~) C- A6 n4 u8 q
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
* l3 p& B/ k9 z$ M
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*; ?0 q$ ], g8 a% F
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*) a4 |' J9 p2 _& G2 c
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
2 b4 O! g4 L+ \' {. R! J, o
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*/ ]0 K% C$ e6 N
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
Y, C& r9 L1 v1 q8 x9 l
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*5 ]- g% g7 x4 l. z
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);: y# n; d; c- ~( w/ G
. j8 c ?/ {6 F5 B! j& d% Z
H2 = (betacl*Kwa143** _ G* n& C& X' N4 `
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
# U: V, A/ q2 u! J8 F
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*! r- C\" G4 O\" {* Y\" J! I
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
% t$ {/ H7 e8 ], z( C/ V
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
' ?3 K# i9 v8 }
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*8 F; K# p+ l$ I8 ^! N& j4 E+ e
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
: H) c) ~' R: y. i( {0 D
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
: ? `- N/ \5 y
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 A6 t$ l+ v/ b# j! Z. C4 n
L4 i `; Q4 a8 U
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
( c# N$ n; q$ f# U, z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*' |9 |: T& k; Q, g+ n1 p
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*$ `: z' r# V/ O: e
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
. u' q5 v6 o/ d: B3 _ L/ Q+ y& p
Kua122 - 2 Q- G3 J5 P) T$ e
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - b! c/ i3 l6 R3 i# ?, H) p0 W
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ! P1 R# E( h7 t0 B1 S
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
0 H& }% F' v! j, T2 m\" t
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
; S\" C# ]! F9 ]+ f
\" H2 _: b: J0 X( L3 S( M
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
* Q( O' m8 p' |' @3 g# o* Q; c
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
. D; G) @* ~- J) E- [* G
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*& S& [% [4 Y3 a3 z& i- O
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
, N; A/ ]. x3 y8 Z; A
Iua122 -
+ }9 R% T* n- N2 O
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
. i+ V/ y4 Q: d; g0 e\" K
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
a( s$ M* Q) e- `! e
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
\" }8 s- |$ p/ [8 i! \( r3 T
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);) [2 ?/ ~0 @% m- c& E2 B
% N% W3 l h; n, M0 Q. g' {
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*: q% e. K+ M5 `8 i. w
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
5 f- q( _+ Z\" P5 O$ [% ]
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
. f0 D2 g8 ?0 \7 o) i
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
2 H+ r) F7 P9 {* [6 k
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
\" x; Z8 L/ M8 p$ s1 H) f
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - : h s n$ o- y- P, E2 m h- g+ |% N
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
1 F5 s* r* f1 w
w4^2/u3^2*Kwa143*IIua133);
* Y/ z& Q, ^9 @1 Z0 E+ g) c
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
, E) t5 P& C8 m# ~! w
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
2 i- E. m' C, n
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
! j) E' q6 @/ b& @\" a0 N
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -% G+ s\" Z; g. x) I3 N) Y( e' n
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
5 i5 ~! u# M2 s2 N
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 6 j\" o' c- j0 y: Q1 p$ A
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - / o' t* ~2 w/ z
w4^2/u3^2*Kwa143*IIua133);& s- d+ P u9 A3 K
) l9 m, Q G/ H' N3 `) J' J$ s
M3 = (betacl*Kwa143*
D\" \- z) z ^$ ]2 A _3 F9 y
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
$ G- r' k' r W# E. F$ s% l
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
6 d, _ N\" ~0 n- {
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
\" C8 B7 Q) n8 U: P) x
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
% T1 }$ B% o6 P8 Y
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
, J# g+ w) v6 f
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
1 Y0 L1 J, k+ T( n: w; A
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
- Y4 l7 C+ A, \6 X/ y7 d% \
w4^2/u3^2*Kwa143*IIua133);* H\" m1 N\" W% ^/ g; |3 o% |
+ s7 U\" X0 F% b7 X
M4 = (betacl*Kwa143*
( i\" R' {* e1 b1 K3 ~+ c
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
% x2 C; V$ {\" u
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
6 `; R: X3 N- j\" Z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
+ k5 m. a' P* K! d( u
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
* ]9 b% R3 L' I) x
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
* n& ]8 E6 }, B+ I# I$ F; q
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
. y* P1 p4 V* R, D' M. [# l
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - , C; L5 F. N- e- q
w4^2/u3^2*Kwa143*IIua133);
+ M, { \/ {! U3 R; h
2 z/ u. W% u# ^, t3 o/ o
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
- O( D7 _6 c' V, m3 R* I2 T
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111; y$ Z+ w) s! P( A% U+ p3 A5 ]
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;/ K! v% W! `8 G\" Z: P0 V. i7 b
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;5 {- |$ t1 Y% ~% R! B
8 H8 Y% f- @\" n `
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
& k0 j1 D: r; M) f3 I! G1 k
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;; c7 F$ d4 I; q9 o; ~
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
; n- p; B8 S# h) `
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;+ V, j3 J$ `6 R; O9 F
; T' n O i: p' Q% E! W% l
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
$ |, z7 Z0 ?+ Z2 J- M( D$ d+ {
V1*M4);3 i0 K {, S' @1 O( N: d- w; k
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 7 H- \5 J' u0 r5 p/ A
V2*M2);6 J, q% n0 z* c
1 N8 Y0 M. ?( w0 n$ Z- e0 Y
x = xicl1 - xicl2;, i\" C6 z& N' e3 p0 f
x1 = Re[x];3 i: o0 Q9 x\" Q8 \& L5 X3 e
x2 = Im[x];& m3 V W% J9 R6 K
5 N0 T! A- ~4 R0 R5 Y\" g2 P6 i
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
9 e, x; ?- {! ]& D; D' z- l\" P
]% d, w; E: T6 b
+ m2 x. Q& ?\" 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