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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;. [7 K+ L; b* n& Z5 |! L
k0 = 2*Pi/lamda;8 W* x3 ]+ w2 o2 C4 x. {
n1 = 1.4677;(*纤芯折射率*)
5 A9 K3 H# x2 M9 v/ `4 R
n2 = 1.4628;(*包层折射率*)/ c9 B' W/ O& I* X* V
n3 = 0.469 + 9.32*I;(*银折射率*)
8 T& b, h# V* ]7 `
a1 = 4.1 10^-6;(*纤芯半径*)9 ~\" v4 n' N0 f4 [( N
a2 = 62.5 10^-6;(*包层半径*)* R0 f\" }2 a& O4 O+ f' S* Q. S5 o
d = 40 10^-9;(*金属厚度*)
1 B- a/ T9 T/ M/ x
a3 = a2 + d;
+ \0 a/ K' O) H- o8 G3 {
mu = Pi*4 10^-7;(*真空磁导率*), e0 H, y/ a$ {+ U! h6 d
epsi0 = 8.85 10^-12;(*介电常数*)+ X# t8 n; S6 a$ y5 c
# w, I6 q9 Z\" w% r
n4 = 1.330;8 P. L. u. X- B: [
' W% H' ]0 `' E/ S1 I0 f. O; c* l5 t
neffcl = neffclre + neffclim*I;
: O, m- D& F$ c) R9 Y
2 o0 z; ~\" l1 G# A' j# g& G
betacl = k0*neffcl;
% u; n\" T* }& g
omega = 2*Pi*299792458/lamda;2 S$ |& F4 F) }2 q! B+ D; [
% |/ x3 }' j _) v) ?! A e4 |
epsi1 = n1^2*epsi0;* j. H! {4 U7 D# f\" J% r) d
epsi2 = n2^2*epsi0;
2 @1 d\" ~\" b' s& A
epsi3 = n3^2*epsi0;! e+ ~6 c* g7 e' N\" I- I4 V1 J0 I
epsi4 = n4^2*epsi0;, y) x$ k- ]% T4 c8 {\" X
% ?3 Z\" U3 q, \; T% g
u1 = k0*Sqrt[neffcl^2 - n1^2];3 b6 ?% [+ S' Z4 \2 [+ o' G
u2 = k0*Sqrt[neffcl^2 - n2^2];
# E/ W- B! n1 {1 b
u3 = k0*Sqrt[neffcl^2 - n3^2];3 j0 S\" M% ^2 D
w4 = k0*Sqrt[neffcl^2 - n4^2];; ^) {) _& ~/ L. [* Q& {7 z
\" p# }' j4 t) r. u$ |/ V8 @% S `
Iua111 = BesselI[1, u1*a1];$ v2 r$ T& N! j8 y2 b* Z% B
Iua121 = BesselI[1, u2*a1];
8 c0 o0 C5 L; u; l7 i; `
Iua122 = BesselI[1, u2*a2];
9 A, Q M' B+ m
Iua132 = BesselI[1, u3*a2];
) d4 t! |, e- p0 L( E3 v6 R
Iua133 = BesselI[1, u3*a3];
1 _- g R\" b' X' `8 l1 V+ Z. }
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;7 o' F: e1 ~0 s! J. P2 U3 w
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
7 y* P5 w! e( ]4 \
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;$ T% U1 D2 m2 G G$ w) A [
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;. p- J) B3 G0 i) f# j5 J) E' K
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
% A: x/ F$ j; D4 h; c$ A5 K T; F
& _+ e% r3 E* K! p
Kua121 = BesselK [1, u2*a1];
/ U; p! @* {6 C8 K/ W6 }0 }& G
Kua122 = BesselK [1, u2*a2];
! U: ~2 n0 M: L\" ~; u h7 \4 s
Kua132 = BesselK [1, u3*a2];
' ]3 G, }) p8 _6 u- d: V
Kua133 = BesselK [1, u3*a3];/ }) X# r\" n9 p! r+ E
Kwa143 = BesselK [1, w4*a3];' B7 O4 E9 f9 o
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
* \. p% K$ C$ } @9 h+ S2 g
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;* m6 k, e( K3 q' _; ~% z
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
\" f6 E' J7 k9 a) z1 U5 `/ |
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;\" T2 U* E) d( i% A2 h( c) z
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
& P/ G' \; b: @) Y( K
8 Y2 }! P5 F9 i9 s% Y
H1 = (betacl*Kwa143*
1 H4 Q& Q. r1 q3 U
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
* t2 _. K2 R/ i+ q( m0 d/ ^
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
- G. v- O5 {0 M! J3 Q1 ]+ e
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
' ?9 G6 c' a5 R! {1 U T
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*/ m! U0 T: y4 B- u
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*3 K; `6 n- O U( i7 x( w2 J
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
3 y& J8 K. x3 e3 g3 _( o\" [
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
. }) K/ D\" [\" C2 W+ C
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
- {; ^+ \2 h7 p7 v6 R; }/ i
2 d7 S$ A: U1 r' b0 L; I
H2 = (betacl*Kwa143*0 v# O6 w1 V5 v5 P, h
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*( E1 v$ X* \2 W G4 }1 Q
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
7 `8 \( r6 F& N- V+ _3 ~1 b
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
5 b7 h$ [* X3 \# ]
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
% R6 c. R0 J# G3 c6 _7 O
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
' A. W5 l4 k2 h- |( [9 z7 g
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' c7 k\" h& k! W! C\" \5 S
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
( r6 {+ H# u+ w& {# p* ^* c
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 A0 s; L6 }: b2 _
& O& M5 b& x, D\" ?2 S! j
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl* n, `+ i* ]! a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*/ J ]: U I: O4 Q
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
1 P; ^% v3 j\" S: p3 H
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*2 l2 z4 k# X9 `' Q\" Q
Kua122 - 9 K6 T% k7 C/ w. J
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
8 O7 C: U C# s4 R% j3 t
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - : p. _# Q: b: j* i4 L! u( N2 d
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - * H/ S# ?7 A9 S% Y8 ^/ R% P% G
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
6 s! L) k% W+ T, C8 z s
O+ H$ ^0 q% L8 ^( J5 l& S9 Y
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
. T+ G- N% x7 V. j( y
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
' \# @2 \6 M2 {. ^, ^( m
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*( r4 }5 X0 n+ B\" ?( s! F
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*! k+ z5 @% N# V( A0 Y& @
Iua122 -
5 b\" I/ b# \( o6 f# L
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - % c1 P5 Q, D! L: l7 R
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
: X# ^7 P5 T. |
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ' X( F8 n! @0 t+ M* H
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 X4 M( }( b9 j
; o0 {* P/ m t
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
; N% g. o, i `/ R% ]4 U
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
, ]4 ~- {( r- ^5 C+ x
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
* x) M9 M; \1 Y0 s j
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -! F% ^! q4 E6 c$ e, I% A* C0 U
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ( E7 m! F5 u/ A+ t: A% t
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 5 ~+ u; t1 N; X
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
6 Z7 l! _/ G }1 m0 I8 R0 p3 G' ~
w4^2/u3^2*Kwa143*IIua133);$ P- i8 M0 c. w& X
' t# z8 s\" {+ }# _
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*4 _5 a- J0 b4 |1 [+ e+ F- G! b
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
; ^. p: X2 x3 _8 b \
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*: t( x% k# q$ O$ {2 c9 D3 }
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -6 W1 g. @1 h8 s ~# V+ }/ Y0 k
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
6 m3 k! b1 k9 b, H9 \8 D! ^6 @
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
% e9 U9 m6 W1 s' t9 } N/ J, _
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - \" ^- F& J/ N' P2 B1 A ^
w4^2/u3^2*Kwa143*IIua133);
' I' H4 f. y' I
4 C5 ?( T7 I- G& q+ ]9 [
M3 = (betacl*Kwa143*2 a& b4 ~: R- Q' \
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
+ Z+ b5 v. E. E. r6 b* L
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
( f- T& X8 N) u! V9 G0 o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - # }4 g9 \/ q/ k3 w3 |
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
$ h3 c2 o\" ^$ u1 _
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
6 q4 R L# A* h( e
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*$ H1 h$ l\" ~4 m/ E) K, x
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - $ L, O& f* C- m8 ]
w4^2/u3^2*Kwa143*IIua133);
& F8 N5 M Y3 r s\" a8 k
- m* `: ]$ t2 `6 N! K
M4 = (betacl*Kwa143*
$ V) s: Y' f5 d$ i
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
. l1 R! _6 D- |4 O& i; H
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
7 O/ V( n$ |' C6 r
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 9 r+ K0 C$ A8 [. R\" b8 ?. l# M
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
: b! w( ~0 i\" u5 \
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 7 K$ C+ Q( V, e3 E
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
: S# t: m5 y4 ^7 Y$ a* [- [/ I& q: Z
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 6 ]; c9 e$ S% k S$ N
w4^2/u3^2*Kwa143*IIua133);
( d5 k5 ]9 C5 K5 L' z3 W7 E* U
* B, _* n9 R4 I: j# s2 g
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;8 [4 m8 e7 B) Z5 Q* v4 L# A
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
+ F, i/ g8 k9 D7 V+ f1 J! P
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;; z0 [. E: [/ L+ T
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;& c+ N. ~9 u1 T0 R* [( D; @
& @8 v9 B( Z% q) n- q; [
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
- d* S7 H5 d9 u
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
2 q% a! W6 M7 L
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;; b7 {( g; G# t2 \& L# E
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;& e( S5 S% K: [4 N. K# U
* y [. `3 z+ {2 A* N5 i
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + % g( `# v6 a+ r9 p5 R- i3 O
V1*M4);% ~9 P# u\" h9 z* e\" t\" w& e. Z, g
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 8 e2 e5 z: G$ f\" U: i. U
V2*M2);
+ B- T& ~( i: }$ w/ z
, d/ @ x- \7 B1 C# [: @
x = xicl1 - xicl2;
+ @' D' j0 S( [ o- y
x1 = Re[x];% [4 t) @& ?8 M( o, Y
x2 = Im[x];
' T( u\" e/ c( G; T4 |5 H
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];2 h1 U, N/ Y( j& o: C
]4 H) V7 y% ~. \- Q
5 N1 L. M( t, `8 j. [* f

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