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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;
- F1 K( k! q1 \1 Q, s
k0 = 2*Pi/lamda;
, K, Q8 M' v: }/ o/ `
n1 = 1.4677;(*纤芯折射率*)
! d\" e) \+ i. g g/ n& J |\" w
n2 = 1.4628;(*包层折射率*)
2 b9 V2 R9 Z/ Z0 o
n3 = 0.469 + 9.32*I;(*银折射率*)8 f' d\" Y* _( z9 ?1 n
a1 = 4.1 10^-6;(*纤芯半径*)1 z# d! a9 U7 {4 v4 s
a2 = 62.5 10^-6;(*包层半径*). u. k7 f& Q' ~; y2 k( `8 P
d = 40 10^-9;(*金属厚度*)
, S; y0 _8 F- C; a0 ` q; A
a3 = a2 + d;& X- b6 W( |1 t\" d
mu = Pi*4 10^-7;(*真空磁导率*)
& d$ g% b0 b- P% q
epsi0 = 8.85 10^-12;(*介电常数*)\" Q/ T# s! S% V& R y( F
4 b9 W( y4 d7 a# j# G
n4 = 1.330;
8 v, ]/ J' ?$ e, n6 O. N! z3 _
, Z: E+ I! x7 e7 i8 g
neffcl = neffclre + neffclim*I;
$ A, H' J- o% S1 F
# t( _ \# v! i' Q
betacl = k0*neffcl;4 w5 O8 [& I! M; Q
omega = 2*Pi*299792458/lamda;5 l9 m H9 u3 c+ ^& [: K
$ \$ p- ^; _! s# F: P/ g- p2 v
epsi1 = n1^2*epsi0;0 A1 g L, h6 z8 f0 h' [
epsi2 = n2^2*epsi0;, v2 B; p0 T' w
epsi3 = n3^2*epsi0;
' c3 B; C6 p% P# `
epsi4 = n4^2*epsi0;% E9 K! R6 s* j. B5 i' q
8 @ Z6 u* H- @$ a+ |0 _
u1 = k0*Sqrt[neffcl^2 - n1^2];
, X( V' i, _/ O, K; {0 x( y; ~
u2 = k0*Sqrt[neffcl^2 - n2^2];
' O( P2 Q5 y2 H+ q; U( ^5 O! a
u3 = k0*Sqrt[neffcl^2 - n3^2];
2 S/ I# I9 N0 b, ^% d+ g2 _
w4 = k0*Sqrt[neffcl^2 - n4^2];
5 r9 v, {' O; j0 z
6 D; s1 Q M2 E, Y& ]. a4 j, l6 r
Iua111 = BesselI[1, u1*a1];% i [ f! C% S! C) f0 T) n$ [6 }
Iua121 = BesselI[1, u2*a1];: z/ B, d: \9 V+ {8 X
Iua122 = BesselI[1, u2*a2];; k' G$ n0 O* Z\" q+ v
Iua132 = BesselI[1, u3*a2];! F. G6 l8 }) n: X& H
Iua133 = BesselI[1, u3*a3];
4 s+ ]$ n# O; }' [1 c2 s+ X1 @
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
: J' i7 _. h. f4 b
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
4 g' I. j- f6 Q0 o* m
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
: a9 m1 U# T* l' B9 B1 X- p P
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
2 Q7 X3 ` N- _; b- E% y
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;7 ?; ]: R7 y) T$ O: ^: w
) C! w# U0 {+ e1 ~7 t8 c
Kua121 = BesselK [1, u2*a1];
( T- `9 I& S3 j& p: _0 d3 j
Kua122 = BesselK [1, u2*a2];% f: O' {9 O, ^4 D: A8 D8 C# Q
Kua132 = BesselK [1, u3*a2];
9 @2 ]- w; I4 x0 m( A
Kua133 = BesselK [1, u3*a3];\" v- S6 v0 F: j0 h. _# A
Kwa143 = BesselK [1, w4*a3];
/ O) D+ Z( p- B, @* w5 ?. C
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
- r, n p8 M8 H; b* g6 k
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
% a) V) I2 [3 l- K+ ]\" T( F' `
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;' z4 w* Z! h; b\" @ u# B* ^1 }
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
( f9 t\" r M3 Z6 [# }
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
; A' d) ^% y' P
0 I. e6 F3 E4 n0 F. o7 ~. S0 q
H1 = (betacl*Kwa143*( S& y+ s% P' R: T) {+ ^\" m\" X
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*7 w2 Q. O6 S8 M9 l3 ]- U
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
7 X+ ^4 p. T% Z. Q5 [4 U
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
/ d _+ |, y- w3 M: ~. N* `4 P7 @
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*' p) V2 n9 A* c
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
2 a- M- f8 i8 T- Q' ? h
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
! }, o! b3 J$ o2 U5 t4 ?4 o\" V
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
7 R% d0 }0 C: f t& D
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 z5 p+ P* t$ V7 |0 p3 G
6 C) n8 F& [6 T/ a6 ^9 J3 J
H2 = (betacl*Kwa143*
r/ s9 h- B5 L' u3 u. d5 z
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
[! q$ I% ^/ G. X: U' g
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
$ m+ E0 {4 K4 T6 u! `0 w1 L4 J
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*- n+ y7 \- ^5 m. m2 [
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*4 V2 Y$ S7 n( h; G- Y$ [
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
# @8 U8 U! G# C. Y- G4 Q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
' y( Q& @4 A1 ^) f$ g$ v% \) {/ Y\" N
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; z1 u5 S B+ I9 f4 C& ~
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);) D( Z) A$ f: x% C\" v
) }\" g9 Y5 K) p1 c9 i) M% R' R
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*- ]6 P5 I2 K! a, F9 `: X
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
9 E F& v: R# Q4 n2 X; S5 C
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*: P% V9 ]& f$ g9 L7 j
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
/ n: L: O% b, Z\" Q# `6 J
Kua122 - 9 @' _7 v\" |$ F5 d
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
2 z; o7 z$ _- w* X3 v! L
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
8 D\" d\" Y3 T, {: ^
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
% g$ J6 R7 @* C3 M) J
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);\" k' m: e; j: c6 P$ I
% z( j% A# G5 I( T4 H2 W
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*9 F, o K; g# f3 @! p
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
, r5 P+ k. G3 y9 s( u4 p7 w
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*: k: R- q8 d# B
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
1 D3 ^7 g0 C% h# w; ~% ?6 t+ g+ W
Iua122 - w, c9 \ g! H) s. L
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - % W$ z/ Q- i q. ^
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - . T. n' ^! r- J, S1 e, i* P7 q) O
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
/ R# u7 \; z; b/ u' k7 I
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
& f3 f C; N% n8 h% Z\" a- {
/ h- O$ U3 q6 U7 p: r- e' u; e
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*+ G! r. r4 s0 n\" J
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*2 I4 r2 F0 H9 M, g% O+ Y/ [$ O0 {
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*$ k# o W\" A$ H( C
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -* W: M\" }\" H# W\" M5 n$ |
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ' E\" K' Z, K/ e- A
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - % [( y9 j* {; y0 d1 I, @
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - . l b( `' a& T, e/ e0 |
w4^2/u3^2*Kwa143*IIua133);9 [- \/ Q\" O5 b3 O
* _! p4 T\" U2 c! w. g- F
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
, a% F- r# S\" p* F, P1 V/ p
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*3 u7 G5 I& _& J0 k: q% q# B
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*. B% J\" G9 e) W7 J* X) S
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
9 k) a6 }- ~9 u2 P( d0 v
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 3 d5 r* }) U. C8 n
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
8 Q, N' @4 V/ }+ X* \- {3 @
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % B+ h' S/ U- V* v: T, }$ N' D& ]
w4^2/u3^2*Kwa143*IIua133);2 z& g$ C' Z/ \/ a! W0 n, [3 ~
- L1 |% h4 ^5 B4 \8 |
M3 = (betacl*Kwa143*6 {! L4 W( f\" h
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 3 ^+ G6 t, H( u1 M d4 r
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
9 ^ D: j6 k/ [& M6 m
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - $ i( W# ]9 @7 X4 r, f8 x
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
; P7 x3 f8 W9 ~0 r. M$ G
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 3 W8 @3 G Y R/ [ y, @' h
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
1 ~$ e; z8 l% C1 g; l; ^
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - c. V' T$ k: c+ a _- F8 D3 _, y% a
w4^2/u3^2*Kwa143*IIua133);
5 m2 x: ?& H; c
3 D7 ~; U# z1 O* _) H
M4 = (betacl*Kwa143*+ b* D0 ?9 G# u4 K' h, X\" T: i
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 8 D( U, N* Y* }! `\" Y. E% W
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*# Z9 r4 ^4 m6 d- ~' n0 U9 x
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - ?2 E7 d+ O4 `% I& @. R
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*3 l% [% M! y( |3 a
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 8 v- x3 Q% Q( [- X9 o& j* F+ c
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*9 k, f, G5 z! p3 p% E7 W
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
) {\" q) [2 Z3 p9 {! j, O
w4^2/u3^2*Kwa143*IIua133);8 h9 J0 c. M6 M3 S; q
$ o, C) `5 p G( Q
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
- U( G+ c. G. s: A* k
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;1 X4 R% U+ e* S3 F: W' e
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;8 g1 d) Z. l% h6 w
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;6 V% j% x5 E3 o\" z3 S. D, h9 @6 l
W1 X8 @7 r' S+ j+ z
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;. m\" s* C; C3 a$ Y' I) b
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
: D6 ^0 O& ]+ d% S) I, `. A; r+ C
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
& Z' }, s% @- d9 @' G1 x
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;$ i8 y+ q) {5 L
- \: Y' y' y2 `! u( J
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
[( ]! Q* i& U7 A
V1*M4);- }9 j; I9 @9 l( D1 i
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 4 z% d& g# v* q
V2*M2);( y) n0 S# F |) ?3 y! w' j; ~
) m# u3 F9 r, U# @: g0 R
x = xicl1 - xicl2;9 J- W. a3 m6 H' ~# z
x1 = Re[x];
7 p4 k& M5 H1 Y. r' A$ _
x2 = Im[x];
' N' T0 Z1 s! A; g9 {/ m- ]5 @
! y4 e+ i\" S, I1 [' v
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
, m j3 ?\" d9 k, l
]
, w/ j v& I1 \; S1 S/ G7 O
' G0 R1 |/ p3 `9 j( 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