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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;
# z, J' Q$ |) u* X; h K. x, D0 G
k0 = 2*Pi/lamda;/ Z) |' Q6 R, T0 |1 q! y
n1 = 1.4677;(*纤芯折射率*)
0 `2 O5 J# Y' D- p0 @9 u
n2 = 1.4628;(*包层折射率*)
' p) A- q+ h5 O: F6 @/ u9 J. ~+ u
n3 = 0.469 + 9.32*I;(*银折射率*)6 I) u\" B8 \( {6 m3 f, s I, z$ o
a1 = 4.1 10^-6;(*纤芯半径*)% a' w' Y9 U% W1 }- F; N
a2 = 62.5 10^-6;(*包层半径*)
- ~& Q1 |9 Q; N' X* y1 c5 r
d = 40 10^-9;(*金属厚度*)/ }1 _- x9 g& Q
a3 = a2 + d;
1 c/ u K5 S& w- v
mu = Pi*4 10^-7;(*真空磁导率*)
3 [1 q* u\" [) X% x5 {
epsi0 = 8.85 10^-12;(*介电常数*)
3 G; h. F# e% W! O6 v; f
3 ]/ A0 k; w0 ?$ g0 C0 ]- V5 Y
n4 = 1.330;
9 [* {& i& j1 N3 a. @
5 A& j/ ^) |. v/ Z, e5 v A3 q
neffcl = neffclre + neffclim*I;
; v\" V. }) n6 Q2 V2 |( y
) u& X9 J8 o1 [' P+ }; C
betacl = k0*neffcl;! a8 a: V% s$ E* G/ F
omega = 2*Pi*299792458/lamda;# Z! s5 U! N+ c, A2 h% z
! G3 K' p/ g: Z9 s0 v& c2 z% c, t$ s
epsi1 = n1^2*epsi0;; i+ F$ l! b4 h: G0 N n% g
epsi2 = n2^2*epsi0;
: H J9 N+ L) b
epsi3 = n3^2*epsi0;9 |9 N# G8 s/ U+ J; E4 U
epsi4 = n4^2*epsi0;
3 L% K# x7 M2 ]8 ]8 ~/ {
k, j% x0 A) [/ ?8 W' |- w& q
u1 = k0*Sqrt[neffcl^2 - n1^2];6 }7 x3 B L' e/ q
u2 = k0*Sqrt[neffcl^2 - n2^2];
0 }, x& c2 H- k. h3 D) D, o
u3 = k0*Sqrt[neffcl^2 - n3^2];
2 N# d8 y) n, r1 w5 r! r8 W% _
w4 = k0*Sqrt[neffcl^2 - n4^2];( ?5 g$ ?/ f: D% T# G- H% n+ R; f& S
) o) N9 B8 d* Q; b7 o! F
Iua111 = BesselI[1, u1*a1];
/ g9 @0 e& S. ^0 w6 p( J8 k
Iua121 = BesselI[1, u2*a1];
P6 S* C9 r3 ^. Y* G\" m/ ?, G! @
Iua122 = BesselI[1, u2*a2];
8 @/ Y# D$ `5 o7 I9 d% o
Iua132 = BesselI[1, u3*a2];2 M2 U9 ]+ y2 Y, j% L8 X% w
Iua133 = BesselI[1, u3*a3];
& p: @* u& ^; D. B1 v& \& U
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;3 n+ d& H- I* J, m0 z) o
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
7 N3 t/ D* u8 g7 m7 U# H
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;& D( u& o7 Y4 K
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
, K0 G( `1 ]1 u8 b
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;) t, |$ K# u. T
8 q% Q+ `$ R3 i J2 M
Kua121 = BesselK [1, u2*a1];
9 v7 E& h\" g; m: G- K* e
Kua122 = BesselK [1, u2*a2];9 W) ]7 O4 M/ H/ o
Kua132 = BesselK [1, u3*a2];) o% q' E/ P- h
Kua133 = BesselK [1, u3*a3];
( _/ x3 I, {/ v n
Kwa143 = BesselK [1, w4*a3];
, u- |, |\" p/ H$ S* _6 o# @3 u
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;% S' U6 ]. G; L
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;3 {% g: j# W8 U& m* x( }: H' o3 B0 M
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;' e0 Q+ a* y# G\" S& m5 J
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
0 j, p- k- y G/ w# p0 ^
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;9 s- ~+ e0 ~, k# Q, M2 ]1 _
0 j0 c |( s! K8 t8 k4 y) e
H1 = (betacl*Kwa143*
* H+ J9 p- b: q% j
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
3 L( t8 d) ?1 x& g8 F& I
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*/ t9 `+ e% n+ |\" [% \
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*& V V6 H0 j& }
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
6 Z y3 T. m. R9 q8 X4 o; W
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
- _2 x( {) c9 I5 b/ U8 q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
* ]8 p8 y0 R# F# j- Q: ^4 W
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*/ l( a, |) `, F6 q
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
) j! ?5 O3 Y' f
3 O. e. t/ |' P' u, H& o5 r% d) V
H2 = (betacl*Kwa143*: |* d& O! @: x. j1 H0 B
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132* [0 {$ C. X1 z% Y
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*/ C9 v# w% ~$ L0 s
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*; ?$ w+ s8 G. [7 y
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
4 g6 ]6 q) M2 M I, Y\" L2 i
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
: o4 x: B2 | q7 i8 U
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
; m: J+ T. ?: a+ f. K6 g
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
' H3 X; U9 s\" D3 f7 v3 Z
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);% L, q2 ?' U+ H1 C
* ~# s' B, L( ]* e6 x- V
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
+ b$ b/ x3 s6 s3 f
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*( Z; T/ w1 \7 R, `* Z* f
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
. g5 n7 T# X1 q
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
. n& ?1 U9 U7 S\" S
Kua122 - $ S6 Z: m1 S1 u9 d! [\" F0 v, T1 `
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ' U0 y- ?# G7 a: c/ f# s5 o
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - H( f* r( H5 `' O; u- r
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
# n$ {6 n* t) j, F+ K& O
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
p. j% n% ?' L5 F
7 U/ E4 M) p9 e7 z6 x! c, H( Y
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
( ^! d- Q0 H4 M9 h6 D) j
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*. s8 ]# q! n ?- W1 A4 m3 L
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*# |' c1 x$ b* L% y
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*1 {) ?! n% L; I$ c: T! R0 b% @0 A
Iua122 -
1 Q& W3 R, @' _. q- h, D6 Y
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - . b* h3 ~: F/ b8 U6 j$ F, L, A
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - % V% }$ g& V* T
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - H2 F# q) A& u\" w' [
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);* m. C! C5 {0 s8 h6 B7 L1 I, {
+ q3 G) V: [6 {$ {# W7 e
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
\" e* l! l1 a, G\" i+ r8 M$ t
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132** v\" j* l% M- C; W: W9 O
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*8 [) m5 N5 ^7 F2 Y
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
* ~2 H8 [ o% [8 b3 B# b1 N! e$ U6 [
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - , |* u9 D/ D; r! }4 o
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
. Y4 G2 s c4 Q5 B, B! x4 j
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ) ?- N\" [0 i\" }' f4 }9 {3 A8 h
w4^2/u3^2*Kwa143*IIua133);2 L5 D7 N' H) S, T1 e& l
8 R/ w; x: i& }. K0 N3 ]
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*4 Y' _2 v9 _3 S1 a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
5 o0 v+ F9 i) \* v, ?9 {+ C
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
2 Y, d\" s! G4 X3 K8 U
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
% j8 z* S4 l\" l( A: p9 s
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
* @) |* H\" Y) {
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 1 v! a+ G3 M$ ~1 @
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
c: ~ }2 l/ p9 T# W& j7 U6 c8 j
w4^2/u3^2*Kwa143*IIua133);
! f# V8 G' L9 x# h& K, a
3 Q$ I; n K8 U% X+ I5 ~, r/ K
M3 = (betacl*Kwa143*1 w6 l8 o! k2 s. i
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - # N' n9 G3 o* q5 o
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*0 _0 ]. x9 u5 c2 j' F5 F
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
& T( ~' c. a% c) n8 [
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*+ D7 j4 N. `/ c' \8 O3 `
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ! Q/ d: N6 b$ ^5 U& Q2 l
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*# ], N9 J9 q h0 C
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - ) A, X8 a5 p! C: d; M$ o0 s+ H
w4^2/u3^2*Kwa143*IIua133);. D+ ?2 E ^8 ]
- P8 {\" d- T) v# l; P9 ]
M4 = (betacl*Kwa143*
\" j, S' W/ f8 D' h
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
8 U# I# U! ? b7 `$ D3 c* m
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*0 Y7 l& k- y! r# _* a
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - ! t! [: S1 j* `- @; S
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*) {! @' Z5 O0 G t* _( }! y: E
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 4 M, `9 z\" X6 P- C
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*' {8 L, W- G! R* `+ F
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
' g/ U! X% m' |' b' _+ [, R9 H. W
w4^2/u3^2*Kwa143*IIua133);
2 I# |5 p2 z4 R. p\" [
( r: j; Y$ h* C; q, s
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
' s- P3 G3 N% U' E# u
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
8 X* p6 {\" c8 ~* F3 d% \# b
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
* K' ^3 T* `6 h1 a8 f! h
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
; f\" ?, ?& x2 j1 G# |
# E9 g$ O& F( [* y9 g9 C2 T
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;# F* `: C6 S& O+ B+ R1 K# w+ \
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
( s e' N+ A# w. }. i
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;& j0 Q8 U9 |6 h( @( u1 U: y) A
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1; E, T: [& d\" \# w
7 b+ I0 i& v. ^$ R9 c
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
: e$ Q6 i! y! A- I
V1*M4);
( V: R5 U6 `' o) P
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + - Y( S& r, b3 m+ }4 U
V2*M2);
4 y, y\" U6 K( y- ]\" Z) L
, H* @\" M+ s9 u- Q( v7 I' a
x = xicl1 - xicl2;- U. I$ V# T# S h
x1 = Re[x];: V2 ~3 J4 n% O! W
x2 = Im[x];+ J4 _0 X9 n8 E0 z9 h
$ e7 r: U: I/ ^- V7 X. H
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];# \7 D2 p8 }5 C9 A, z/ h
]4 T2 N% F9 {\" X/ s2 X8 t
0 [# r* t6 r* Q) K$ k

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