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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;
, w8 ~8 V- C* _6 P$ v
k0 = 2*Pi/lamda;
( o1 l+ A! u, B\" e M7 _
n1 = 1.4677;(*纤芯折射率*). G% T0 h( C7 x6 H# w& i P5 |
n2 = 1.4628;(*包层折射率*)
4 |, n$ I/ J5 @8 z: G) N2 m
n3 = 0.469 + 9.32*I;(*银折射率*)
$ |+ V1 b% Z& w( G3 m6 K
a1 = 4.1 10^-6;(*纤芯半径*)
- F! J2 V; ?: Y, n7 q# K! C* i
a2 = 62.5 10^-6;(*包层半径*)\" D2 S7 C\" q& V- D
d = 40 10^-9;(*金属厚度*): I1 v' _' F7 a3 I3 ^
a3 = a2 + d;9 q) w# J; w: f1 I. o7 L! u% ]
mu = Pi*4 10^-7;(*真空磁导率*)
5 t# \4 q% ~2 m7 n- _7 `\" K
epsi0 = 8.85 10^-12;(*介电常数*)
) ~6 U a( i) O) _+ k- N
9 I# E% [6 O8 q
n4 = 1.330;
4 i. _+ u3 n! \/ E
1 U. I( q2 L% @2 D0 _; @- A0 P( f\" k
neffcl = neffclre + neffclim*I;$ i4 Z9 T2 |2 I# z+ s! f. X
: E7 ~1 O# o/ t\" A4 y
betacl = k0*neffcl;
% P0 r% M6 l( D7 H6 e/ y' M
omega = 2*Pi*299792458/lamda;
' O/ c B+ l5 W
6 y2 ?* E( ^) E8 e7 ~
epsi1 = n1^2*epsi0;, A* F\" {5 P% e8 Z2 ^
epsi2 = n2^2*epsi0;
\" L% \) @7 k {6 Q\" o: F- G8 {
epsi3 = n3^2*epsi0;3 A5 ~ k& W: [! ?
epsi4 = n4^2*epsi0;
0 ~$ e\" V1 t/ i# {7 F. v. t
) w% H; ?, C% c: h ~! @
u1 = k0*Sqrt[neffcl^2 - n1^2];
3 C, l- G, N+ j. `# H( X
u2 = k0*Sqrt[neffcl^2 - n2^2];/ G/ C% r$ Z7 [8 e7 Y
u3 = k0*Sqrt[neffcl^2 - n3^2];( u, ~, L I* R: n& p
w4 = k0*Sqrt[neffcl^2 - n4^2];' m( p5 z, L+ u& z X% v( f6 m
+ W; O+ G5 s3 u' r& y( I
Iua111 = BesselI[1, u1*a1];
4 w9 j6 \2 S\" b; S$ h
Iua121 = BesselI[1, u2*a1];
& m5 w* P9 @! W) \
Iua122 = BesselI[1, u2*a2];( {( u) Y% i9 `# ]
Iua132 = BesselI[1, u3*a2];
) z% Y6 }7 Y6 N4 v\" A; T) Y
Iua133 = BesselI[1, u3*a3];\" G+ A* X. H2 m! \: F
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;5 d4 {, J0 E; R
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
# M2 K\" `& k0 H+ Z( c6 `5 d
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
s) a* z/ c9 |9 t+ z
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;) k: g8 c: H: M) C
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;( \5 a8 Q0 M4 w) {0 R! R
' A# R f* p8 _* z4 q$ \) Y
Kua121 = BesselK [1, u2*a1];# u* P2 t! Y1 q, N6 V7 N ?+ C& y\" S
Kua122 = BesselK [1, u2*a2];- J |. C$ \) b/ P
Kua132 = BesselK [1, u3*a2];
+ P: i2 h( h _% ?\" v# g9 e
Kua133 = BesselK [1, u3*a3];
T! c, T\" o2 _6 h\" m
Kwa143 = BesselK [1, w4*a3];
, o- ^' G6 l0 Y8 o: }6 i8 O
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
& x9 L5 v; r5 K* v0 Y$ X
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;3 v$ W: ` P6 E& Z
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
/ M& _- x. @4 b, Y# [
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
3 F# D' o+ @0 D- _$ K
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;7 j& Q1 h. p3 S% }. X8 p$ T
5 V: q! {- ]+ t5 ]0 ]5 U$ w
H1 = (betacl*Kwa143*
3 e' e6 A) Z0 s' [) h/ w
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
: {) ^ e\" Q\" }7 H$ u
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
3 Z# p4 {# s% U2 O0 ~
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*# _# |! `, J% h4 v6 N3 W- b' K% _
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*' ^7 v% ]: I. I, x1 Z, ?7 H
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
1 [' i o$ R% ~# n4 b3 q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
. o. g\" Q* u: @2 E- r2 f' B
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; J7 u: p4 {3 U q1 n. [* W0 ~- ^' |
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
1 m& q9 c/ J6 y+ g: t& z
3 \0 B' T$ m1 r0 i
H2 = (betacl*Kwa143*
7 h* p# d$ P @
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
& j\" d+ `\" ]# V# {\" {& S1 T
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*# |& }, W g7 P2 J, e' r
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
! K) g2 N- @, q8 w. X5 ^4 m. m1 n
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*+ h( t/ q+ g% |) I! F9 ~
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
: S' J\" v& ?8 R: [
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*! Z7 C4 E+ }# Q\" Z
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; J3 C, P; B# |$ `0 B4 U
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);, I& C: \9 A% ^/ \
2 s$ u- a1 `3 C% ?1 ~$ X# k+ Y
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
' M# ?1 S- J' H9 s/ Y% ]1 J
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*6 [( H* N; X: z# F& Y$ v0 U7 S* [1 B8 ?
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
a, p0 P s0 d+ h1 f3 f
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
, M5 k) Q2 \1 }3 e; D, n7 W) P3 o
Kua122 - ' z- ]5 V$ Q2 R& K1 R q: O
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
- A6 M3 `4 U0 k\" f& _4 d% O
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
& Q8 U8 g7 ` D- `
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - $ b7 D0 q( `2 i) O) y
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);2 W# f: V. X$ ]) _. I* H$ W, m: w
, K |' L) u$ l* ~/ c
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
- q! ^: W) |7 b\" Z3 ]1 v2 w' ~2 j
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
5 H2 U' w/ }# o6 s: B/ P( T\" V
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 P3 o9 b: Z; T0 F
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
# G2 b! c+ w7 M) X7 t! n
Iua122 -
5 y( @# h! p9 y1 z
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
- {: Z+ |% R! N' o: p1 ]
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
+ S; V' \9 N1 ]6 x
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 8 {9 w+ P\" s+ \. K+ n' e9 B% X7 N
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);% x& Z5 E: b) a0 E( ^
) I\" A) A1 u2 w q2 h8 [: Q
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*) H9 C, j) p7 @9 P5 ?: C
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*7 Z5 V/ w8 P0 p0 C4 T; x
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*9 g\" l; Z- d e
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
7 d! k, z3 v8 K, U
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
8 j0 q( d0 b) j8 p! P
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
+ |1 v2 k8 V% j) K; R, B/ r
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
w4^2/u3^2*Kwa143*IIua133);' D6 |/ h5 ?9 U3 M4 U' y
1 u) z8 D\" Y3 m2 {* X5 s7 [# u
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*. S& e' p) F) V g# L
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*: n5 Q, t) U1 y
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
P1 A( g8 D, J. _1 d
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
& |; |. t# D+ i8 J
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
/ c' q5 W2 f! L7 j7 G7 m$ A
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
3 v. S. o' e0 T+ E7 O# S8 ]8 C
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - : t) g\" w% Y0 d; s
w4^2/u3^2*Kwa143*IIua133);4 w3 a: ]. X: D: h5 w( J\" F5 `
1 j- _& Q) S @. b* [9 S: T8 M+ f. v
M3 = (betacl*Kwa143*
) L) [4 Q9 P! a: ~+ Y- y* q% Z
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
3 P3 {0 t: n$ s/ B
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*- G# ?' b* o8 c4 ?4 d* P* v+ z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
1 o3 f F9 c3 r( a& L
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132** X# s4 B: `( \+ L3 \/ J\" f. b
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
2 L: E0 W4 h5 C- O- P5 s
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*1 x' }0 Y; [8 u) ]
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 6 M+ I ^& S# h( E( T0 s
w4^2/u3^2*Kwa143*IIua133);
, k0 e. O\" `8 b/ V
; ?7 B' L9 j& x6 d( d
M4 = (betacl*Kwa143*! ~! w! z% M' b5 c3 f/ x/ c
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - ' s7 e: |, n; G. g* E4 K0 F
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
/ F% a: z; W3 C8 w- g0 I7 ~* B
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
8 f# S( C( [% k! U5 |) \
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*7 ]4 [1 ~7 I9 ?
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
4 D2 k/ C5 [' N
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*. V3 d1 m0 e0 D3 P
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - ) q9 h2 d0 J2 B8 ?+ s( i
w4^2/u3^2*Kwa143*IIua133);4 C/ b7 O. P( o
% N3 Z: A& ^0 G/ a' h* a
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;4 G9 Q- b+ N9 l4 d, c5 k$ U
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
0 i1 z2 ?7 E- d/ n X8 b
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
/ L0 k8 o' A$ e\" R' y N8 ]. C
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
$ K9 V, a8 q7 s, {4 z' ^. G, m6 a) q
4 A& `' a6 _8 `, C: L$ B
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
% J0 i& I0 e2 u4 L) a
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
$ Z/ [# U5 R6 F2 K- R* X7 O8 g
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;\" G4 R: \, W- H3 g
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;. Z% Z+ A- `$ R\" m* `
) E' s$ Y6 ~# Q\" `5 h( \
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + ) i4 U$ J; P/ l/ S6 m9 h8 ^
V1*M4);* @- o6 P9 v9 X2 R3 e- c
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
# H3 ~9 ~4 @5 E9 ` H0 G. D
V2*M2);% U\" ]& w: Q* m$ @' b$ l. k' S% W
. x. ?- s6 s( g1 ?. ~
x = xicl1 - xicl2;
; B/ @- k' T R2 ~& K/ O
x1 = Re[x];( _ G5 D$ ?% c' g1 {4 k& C; S
x2 = Im[x];
# K7 j4 o) _# _9 u4 ]: E
5 F$ W4 z% _/ j
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
5 p5 r+ p5 s/ A\" Y
]' H# e# e( E! C# k
! h, v/ z\" A8 J+ E( v

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