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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;2 ~4 ^8 n/ v+ l& g
k0 = 2*Pi/lamda;
6 U7 [, D& R. [7 U s5 Y6 H
n1 = 1.4677;(*纤芯折射率*)4 d0 u5 R: A6 a( _( Q
n2 = 1.4628;(*包层折射率*)/ j6 S4 a5 [$ e2 K3 E4 [! I! S
n3 = 0.469 + 9.32*I;(*银折射率*)! E7 i; |+ D- i
a1 = 4.1 10^-6;(*纤芯半径*)
V- v( G7 r, Q( o7 ^4 X! X: V
a2 = 62.5 10^-6;(*包层半径*)
! @/ T\" l) Y9 P
d = 40 10^-9;(*金属厚度*): H$ u. f! W1 }) `0 T2 F
a3 = a2 + d;5 d! a/ v& g; I9 @6 ~0 Q
mu = Pi*4 10^-7;(*真空磁导率*)
% R$ S+ L3 B; }$ a3 ~
epsi0 = 8.85 10^-12;(*介电常数*)
* V' G. `; b1 c\" c
. ]/ k; `5 M1 }* a4 a
n4 = 1.330;
, L6 J3 g$ t: u, D
$ s' P$ `+ x* T' z/ J7 f8 u) l
neffcl = neffclre + neffclim*I;$ A2 h+ ?8 z3 Y
- e3 s0 t& e& f4 v
betacl = k0*neffcl;1 R1 Y, d' b& b- L2 |1 G# ?
omega = 2*Pi*299792458/lamda;
, w' q3 Y$ X, r( Y6 d* k
7 q8 A2 h& ?) ^7 y6 e+ n! o* [( s, p
epsi1 = n1^2*epsi0;
1 Z: N. d; q4 B7 T: w
epsi2 = n2^2*epsi0;
5 C0 h1 I/ a3 h2 e: ?1 K
epsi3 = n3^2*epsi0;
. A# q0 {$ {, ]
epsi4 = n4^2*epsi0;# A\" N3 y- s3 P9 p
2 S7 ^, ~# U l- \& ~) U
u1 = k0*Sqrt[neffcl^2 - n1^2];
+ q% J% f u. U4 _( U
u2 = k0*Sqrt[neffcl^2 - n2^2];
' Z* a: z; p2 _9 r, |8 E
u3 = k0*Sqrt[neffcl^2 - n3^2];
5 J/ Q% G7 k4 b, L\" h. U* P9 f
w4 = k0*Sqrt[neffcl^2 - n4^2];
- \. l' {& p2 o/ l
& E/ z9 N8 Y/ ~6 D- b\" B
Iua111 = BesselI[1, u1*a1];* f4 J7 ^! m0 Q$ z/ d3 G. C
Iua121 = BesselI[1, u2*a1];
% t+ w, O) B5 q) @4 E J
Iua122 = BesselI[1, u2*a2];
1 u' j5 x( D, c3 Q
Iua132 = BesselI[1, u3*a2];
; K* e9 }3 J V! {' D7 U( O1 i: [
Iua133 = BesselI[1, u3*a3];
1 x6 ?* ]! Y/ p' l. X( G
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;4 m- s) i# y3 n& q$ F
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;- p8 F9 W2 H: H' W6 B
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;# t. T d! N% f; k# ~3 T
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
/ ~' A( {$ s$ j7 M
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;* w: f. H* k I
. ?% ]* K9 y: U5 r1 y2 E5 w/ r' ~
Kua121 = BesselK [1, u2*a1];5 _' v5 F( L/ q1 d; e1 L1 Q; w6 q4 o
Kua122 = BesselK [1, u2*a2];$ n% n\" {+ i v1 U5 _1 U- `7 E% U
Kua132 = BesselK [1, u3*a2];
6 d0 A' w1 U1 M5 F/ J# B
Kua133 = BesselK [1, u3*a3];6 }5 x x. n) i5 R: P
Kwa143 = BesselK [1, w4*a3];
3 L+ o/ S+ Q) s! o; v. M+ u
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
% v* p& c+ f$ n: |4 h- c7 N$ s
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;! J& e, f, D1 S$ ]8 f* c; t\" Y
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
b7 T( o5 X8 i
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
; H1 p G4 ~% T: ^% Y2 x' W
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
* M L( b* X6 R. M
. {; c( j$ w+ r5 [7 g1 J3 Z
H1 = (betacl*Kwa143*% w4 u- E' q8 f\" O8 n
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*2 c! ?5 C, p2 t4 ^3 i8 R
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
0 L# Q. Q) m1 J
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
, E/ n$ { J1 _2 z+ G0 W& u
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*4 R3 g\" {- O# M; `3 c$ p
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
# Z. n. H) ?: r2 t
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl* \1 ^! B0 S7 C A/ @
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143** e* v' J+ _+ s1 N& Y Z* e. B
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);+ \+ P( w3 A2 `2 j( P/ F3 N, \
\" o\" a0 d, o; E5 n: ?1 @7 D8 k3 f7 y
H2 = (betacl*Kwa143*
6 i# K3 z+ L0 ~! x3 j; K
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
! D) W0 w0 s+ `
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
' g/ H/ q5 j, F) F5 Q0 {8 ?
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*$ S% T+ j, Y& O7 d) U
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
+ [- V: ]+ N8 g2 U
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
/ D7 q\" h8 A7 y* Q$ T
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*2 a2 S% c: ^4 l P- @+ m
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
; K {$ @7 i% [2 {4 t
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);2 z; J7 ]' J- o+ R. `% F! ~; Z
D4 N\" v2 V, r8 D: l& C
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
- n8 t# B+ a' T6 G3 S! \& a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
( O. q) ]% r2 Y5 i8 Y
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*3 M9 r6 l4 ]8 y( Y! {7 X; Z
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
) q% N7 o* q7 n% p- H4 B\" f
Kua122 -
a: j. c& \( N- f) v6 g$ Z
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - . S\" }8 U\" y$ Y5 |
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - % N( b2 K: V5 @: K
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
0 Y' Q1 ?# |# v( ?
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
2 L! h$ c$ r( P. F
1 M8 ], e) I, a9 n3 V
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl** Q2 u/ B7 e\" N4 X\" V\" [
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*: ]8 f: |: @: t, n) U0 m! q# T. t
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*1 f, v. P\" G/ ?
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*! |& w3 y4 ^7 R& b A# s\" ^+ K
Iua122 -
\" N\" _2 z/ ^6 z! N% _% M& |
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - : Q0 Y' V3 O* Q: s( d, i
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
, A! D% q4 e# b2 a1 m d\" \
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
! x7 ^5 P* a$ G\" K2 j
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
6 k- g' Q9 b5 \( ^$ I
- o( I* c\" R5 l2 H0 V; @( J
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*; w _1 {\" _3 K
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*; Z/ S/ `: M$ t/ I# g r, E
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*3 p6 d8 C1 s ]' B9 {# H# m
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -7 e3 a9 c4 L) ^. Q2 z, b8 L- ~
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ; C; s\" K) \- ?% b8 R/ s1 o
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - / e; k! C# Q. f/ w# `! l
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
1 K8 Y, x& Q7 u4 l# P. u2 a0 G
w4^2/u3^2*Kwa143*IIua133);
7 g* K; X- R x
, e' a& ?* Q: R7 F t\" A
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*\" l- G* x7 d3 ^2 S8 g
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
% o/ J, _0 Z\" q: C% m
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
' x! Z/ ~+ O0 R2 F# ^ [
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
' ~$ L3 T- o$ @: f) A1 }& x
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 3 \% w\" h( S' ?7 e4 M/ k0 A+ Q% {
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - - a! ~, I. j8 r i7 ~* F2 y
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
+ g; f& J m0 |1 k6 O. b4 d
w4^2/u3^2*Kwa143*IIua133);
- _2 o9 d+ \ m
3 w9 _2 y7 {5 f/ `+ s
M3 = (betacl*Kwa143*
1 A5 z2 U% Q# H n2 T! b
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
* s* Z M9 L) G9 V! [' E7 I$ y
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*% P3 c, X. V4 P8 e. }\" y+ @
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 9 d; l. C9 v, ?2 M
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
# f\" v$ `: q3 u$ v! g
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
3 m8 n: [. S: G/ ]
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*+ u& Q7 \9 C) p\" d1 T- G
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 2 @( A% K p% h4 d
w4^2/u3^2*Kwa143*IIua133);
- I( H3 A( O* E
* [% T% j. }& t% e3 p% Y
M4 = (betacl*Kwa143*
0 X) ?% C: N, r+ L: t! G/ ] A\" d
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - ! ~# Z: L- h' ]7 K
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*) F9 k7 @2 L c: J) N, ]8 N: G0 n! R
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
7 q: L; w0 n _' m5 ?
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*6 A' ^* _! p4 M7 ~$ |, u! r
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
! ]0 J# f$ k% |% e
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
+ b4 k2 R9 J }$ ` n, a
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 7 Z( n' b; z+ ?3 q
w4^2/u3^2*Kwa143*IIua133);
9 N6 Z* L1 T$ M L1 t
c/ }; ^' {: l9 V) ^
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;\" i/ [' r: G! V6 T) f5 w
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
5 ]& c4 L& Q+ r* h) y- X6 l; b
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
2 X& E* P5 T) _: |7 ]. `
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
: l; ^4 F- \+ p' k, t. |
\" N( T9 k9 L* y. _6 W! w' a
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
9 s\" N% Q% m1 q5 L+ p9 P2 J
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
3 C: H9 o' b% I& ~, {1 a% |
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;9 ^( _( p/ ]$ ~9 s2 X! `( n5 m
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
! e/ U, w/ f% @; r! M4 z9 g
\" v: d K1 b$ r0 [\" Z: M9 T: M
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + * K& N! B- V6 L# K* k( W1 M
V1*M4);( P* ^, ~9 X8 A$ @0 {
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
. N\" s1 W! t# c3 g @8 r4 t
V2*M2);
! G( d2 m5 Z6 x) W8 C( {
0 R9 _/ W6 h9 y+ p7 D- R( P
x = xicl1 - xicl2;7 h% ]. j8 V. l1 t* T# ^
x1 = Re[x];; T/ [7 \& H$ n0 P6 D; d+ |. s( ?
x2 = Im[x];
$ Z0 w1 w) p$ S
- P8 A$ A\" m. Z' w7 \3 X
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
# Z! o7 a! n3 f3 w
]
' `, o$ R+ R3 t1 s$ s+ V' y
2 V' Z5 V/ a5 ]

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