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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;
, |5 l9 Q+ s: j: z: S
k0 = 2*Pi/lamda;
n1 = 1.4677;(*纤芯折射率*)
- f8 S5 p1 g, h( [/ Q; f8 C- y
n2 = 1.4628;(*包层折射率*)
' F) r& o3 R' F# a
n3 = 0.469 + 9.32*I;(*银折射率*). Q3 v5 G, A- ^2 }/ W+ b
a1 = 4.1 10^-6;(*纤芯半径*)
7 |0 o, H( ^- Q\" Z- V6 m2 C' }( J; h
a2 = 62.5 10^-6;(*包层半径*)% L( `7 h3 B. y( E; W U( ^/ `3 ]
d = 40 10^-9;(*金属厚度*)) O! J( P( o7 c7 D
a3 = a2 + d;- e# l\" k( ^) F\" P
mu = Pi*4 10^-7;(*真空磁导率*)/ y/ D5 C\" }\" b v) }3 M
epsi0 = 8.85 10^-12;(*介电常数*)
) [8 Y' H\" j3 U2 m! _
: ~% j5 L* d$ s5 g9 r/ G+ \
n4 = 1.330;) h C$ Z' s; g) P& k& u2 e; [
( s' b, k7 h/ o& Z5 k
neffcl = neffclre + neffclim*I;
% {7 ~5 A( p& T
betacl = k0*neffcl;9 ^/ ]) q5 t8 H. |3 E- D; I
omega = 2*Pi*299792458/lamda;
. ?8 u: R8 ?' R\" q7 y* r0 u7 a. D
9 ?; h; ~: w% w
epsi1 = n1^2*epsi0;1 G' S: |% E/ X/ `8 n
epsi2 = n2^2*epsi0;
( j% F- O0 ], o* T
epsi3 = n3^2*epsi0;4 T. W( @2 Z! Z8 Q6 @\" k- c
epsi4 = n4^2*epsi0;! \4 g t) [7 e% I) [6 m
8 m6 o9 a3 Z! D: h
u1 = k0*Sqrt[neffcl^2 - n1^2];
: Y* D0 c9 c6 V$ M% A% f
u2 = k0*Sqrt[neffcl^2 - n2^2];: V9 [! N- d0 j
u3 = k0*Sqrt[neffcl^2 - n3^2];
\9 K( C7 }. S+ p0 G! _
w4 = k0*Sqrt[neffcl^2 - n4^2];
4 T8 @% g; }8 L0 e
0 Y$ {! J' W: G, Y2 [
Iua111 = BesselI[1, u1*a1];
Q. C\" n\" W& h6 `: _, P
Iua121 = BesselI[1, u2*a1];6 _& w, e/ ?: y) |
Iua122 = BesselI[1, u2*a2];1 P! E5 S7 r; i0 z
Iua132 = BesselI[1, u3*a2];
' G+ R5 d' s! D3 l2 m7 v% C- u
Iua133 = BesselI[1, u3*a3];
l( h6 }' g' J6 b\" V, d2 A
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
4 `! P+ h& V4 W
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
# ~, A! S3 j9 P0 ]. }
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;. X\" J! c5 Z8 Y
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;, d. f' p/ W) S, ~9 q
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
; d0 I: o6 i0 j- Q% |
& r+ h' `; {2 r+ n3 U* ~
Kua121 = BesselK [1, u2*a1];
- N% A. i% E/ D9 r; X. |
Kua122 = BesselK [1, u2*a2];7 a* G; _/ z+ b\" R5 R4 K f! i
Kua132 = BesselK [1, u3*a2];6 u* {, E2 l2 H0 c. n5 }
Kua133 = BesselK [1, u3*a3];
0 z# J1 `% `\" G4 B' }
Kwa143 = BesselK [1, w4*a3]; u1 f7 p5 b- R8 g& S
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
2 d. ~& s\" }* _+ i' f
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
& J, S; p& T, d h: P! M: C
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
+ ~ P; g7 G! r9 r% @
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
2 N$ w. N# J! N* N$ \\" f
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
0 h$ ^% g$ `% ]! k) i! r8 _, q* P
4 g$ d2 _* P; Q5 C- }& `0 p5 f
H1 = (betacl*Kwa143*7 ^1 z5 k. j5 J9 U0 p
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*/ _+ Z( `& Q/ {\" G4 W
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
3 y( v* p; Y7 [8 E2 g$ y1 A
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
$ u# g( Q' m0 ]& P
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*9 v, _! G+ b: _. k7 C' `* |
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*+ j2 _4 Z& z7 X! d$ c
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*7 D6 H! l% e/ w: ?
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*9 b( Y- ^0 v$ q) A1 r
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
3 r4 ]# g- ]* F* }' Z+ N- P$ Z
, n5 f; }* M* g5 `/ ^
H2 = (betacl*Kwa143*
& z9 y- j( |) n! h
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
7 G9 t$ o6 e* P! g8 Z
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
0 W. y; ?) s7 k9 C8 X\" i# Y% t\" x
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*: b- Q: i( V6 k5 c( K; c/ P
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*\" E& e# p0 Z/ M7 ^) X0 c; z3 A
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*& y) j5 {: H' H, c4 M+ ?2 H7 r
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' [. _6 z6 `0 r9 s2 N
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*$ z7 n5 y D\" c# ^) N2 Z5 @% ?4 `% N
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
. x0 @' q% {) E% ~) M\" b t+ u
' u, t# I; H0 S
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
0 ?& ~3 x; S6 T+ h
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
\" u$ M\" _; i4 L( Y/ _% Q
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*3 e0 N) E3 `8 k8 _9 G
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*! g\" W2 r2 C% q9 ^
Kua122 - + @/ Z' @4 l* S\" g; E/ A$ D- x6 t
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
5 D$ z; Y$ [ a& S9 L! b+ z
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
) g( u4 H2 b+ m% E) ]
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
7 s% _, l1 ?\" g4 u8 J4 S
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);6 s( f9 z, R+ R# g. ~5 e
4 V' e\" Y) w' B* I4 E
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*. Z9 m! V( g* C
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*) h! k7 e) `) A2 |2 S, B$ y
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*% v* K, E\" r9 ^+ q7 p
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132* \ j: x3 D4 S( \
Iua122 -
5 q9 c$ @8 ^% c& z
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 7 j6 z( G6 Z0 X) T. g3 M
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 8 U/ ~: f7 W2 z, s d
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % D) L$ p- r' _
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);0 V/ Y4 u\" h; u, w' ]# R7 K
) R, R+ D% _% E0 V% q3 x
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
+ c$ Z$ B: \: S. D
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*, t6 b; y# u; k$ e! e9 A
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*, [- E0 d% F8 V5 K; j% B6 x
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -# c ~$ C* m8 s
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
2 F. x4 o0 W; I, a5 T& W$ w( ~
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
/ t8 A9 a- y* R$ w) K3 T
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - / [3 ~2 M1 {' i
w4^2/u3^2*Kwa143*IIua133);+ M e+ ]+ j+ ]) r' E9 t1 n
3 k& o9 k6 Z& H1 |% l' A
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*4 h4 d2 E ^0 l# E G9 a3 A% \
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
, W% W; y( {* k3 ^0 m; {
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
; W2 T K. f' E: q$ d1 v
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
( x4 [\" K, m# G5 c; f
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
; O/ b( Q' M( {; P
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
! u- l* h$ [0 Y; D
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
) ^2 c( i* u s( o6 i
w4^2/u3^2*Kwa143*IIua133);! `; ^8 J! F, S1 {1 y8 y
\" r1 U7 U* O\" v0 y3 F: a& b2 D# C
M3 = (betacl*Kwa143*
0 J/ H1 L8 ^# a1 t
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - $ Y( x8 N* F1 N0 p+ K\" X\" x
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
$ J5 S1 Q% j0 t) r& r. q) O
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 6 X2 [( {# Y( |7 Y8 I- Y
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
7 G9 |% J' v O' P% P( a
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
; }' C* J4 ?& L6 c\" e, n) x
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*% k3 i, t, r5 \% [- r9 i) {
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - ; c\" n% a* Y! o0 L9 ?
w4^2/u3^2*Kwa143*IIua133);
0 [7 n+ Z6 I! }+ l\" K$ c
g4 }: u/ p6 k2 c1 C4 n$ a4 D; O
M4 = (betacl*Kwa143*7 _- H, A1 \% k) L. Y+ d: G
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 4 D' i: b; s7 }7 Z% v$ L/ ~ a
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
2 @$ O$ F0 K( @
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
$ ]8 l* \/ @4 x! W/ a/ t$ {
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
7 @2 j2 _6 O\" `( A
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
) d3 ~: M y% L. o\" ^ _
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
X& N/ X0 W+ A
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
2 i: {3 ?7 V; w
w4^2/u3^2*Kwa143*IIua133);
* ~0 S4 p1 Z1 D E
\" R5 c+ r5 G1 e: c
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
~! ~9 y- I# w9 ~# X
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
\" I) S2 V- [, |& ?: t: }& }% K: ~* f
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
# ^) K9 \8 |6 y1 V+ y( v3 e
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
8 {& d6 y# F* A* o$ i
/ I1 |6 J. q\" `+ L
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
/ e( B* z! y* m) X+ s
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
; h7 {8 }6 y J5 p' Y
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
. ~, I- R4 j, C- d9 D0 p
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
^! t3 B! O' p U& e
( Y: ?. r\" P2 [
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
9 Q4 h8 ^' }+ T
V1*M4);
# I4 z2 s0 o, Z: s. d
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
0 Y3 F ?6 G8 R: B
V2*M2);& ]0 K# o. r7 a. n
, k3 m' G4 j. T6 [
x = xicl1 - xicl2;4 l9 J/ E- \+ r* f' Z\" z9 M; a6 F
x1 = Re[x];
: [- g( [) {4 F+ }( k6 H
x2 = Im[x];
8 |9 ^+ H D9 W6 s& W* A
0 B0 J: q: }6 d/ \: O2 P# Y
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
/ Z9 a7 T7 e- x* O/ q4 N* {/ u
]: R, I1 T3 y6 T6 m% ^2 K$ \
1 j2 n' {7 [\" b4 x

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