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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 |正序浏览

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lamda = 1.55 10^-6;* M7 `3 b+ H: I; Y
k0 = 2*Pi/lamda;
4 Z' V, V; s# @3 f! e\" e$ t5 |
n1 = 1.4677;(*纤芯折射率*)+ k4 j$ X4 W( Z* F) R
n2 = 1.4628;(*包层折射率*)
i) r V% O' o1 k5 q
n3 = 0.469 + 9.32*I;(*银折射率*)( O* ~6 u& [+ `3 ~6 t: P\" D( g/ l
a1 = 4.1 10^-6;(*纤芯半径*)
9 a& g- E' } `& L$ E z2 ^. B
a2 = 62.5 10^-6;(*包层半径*)- x; W) ^8 f5 a3 l- u
d = 40 10^-9;(*金属厚度*)
& o4 K# w5 Q, X1 A R7 g
a3 = a2 + d;: W. ?0 `6 t* y' {' n+ S
mu = Pi*4 10^-7;(*真空磁导率*)( s N7 O g7 G3 b, q# ]
epsi0 = 8.85 10^-12;(*介电常数*)# ]% B L( j! i* Z
' V; h! i! y0 c' V; w: B' b2 F
n4 = 1.330;
9 \* v( O, S7 f3 m
2 T+ i\" {$ W, Q9 t& B2 U% z
neffcl = neffclre + neffclim*I;/ I2 e F% u, r) ^: u+ c7 Y! h7 T
9 R- G5 f% c4 k4 o7 {2 w+ y
betacl = k0*neffcl;
6 ?/ r\" p( y. l) K$ z( w
omega = 2*Pi*299792458/lamda;
6 X1 J ]+ a! m2 ^
- f6 `6 H- p% B
epsi1 = n1^2*epsi0;
+ y Q. y$ p: D9 N3 Z
epsi2 = n2^2*epsi0;4 E' D7 J5 y* n4 J8 v N S
epsi3 = n3^2*epsi0;
* K5 i- Y& c5 q; d& R4 h$ U
epsi4 = n4^2*epsi0;
. }4 U; P: B L& Y$ t( G
% F\" \) ^% G9 x3 p% F8 E
u1 = k0*Sqrt[neffcl^2 - n1^2];
6 N. H/ ~; G8 o) ]- u
u2 = k0*Sqrt[neffcl^2 - n2^2];
- t5 A\" K% a% Z* k7 P- \
u3 = k0*Sqrt[neffcl^2 - n3^2];
. q; U( [6 p: R; R1 V% `
w4 = k0*Sqrt[neffcl^2 - n4^2];7 q6 A$ Z n# ]3 c\" B0 n h
' }9 R3 ^6 |& M
Iua111 = BesselI[1, u1*a1];
1 T6 k/ J1 s1 D( B- Z( }- x
Iua121 = BesselI[1, u2*a1];
Iua122 = BesselI[1, u2*a2];# X, r: Y: F* c\" t\" H8 [: b
Iua132 = BesselI[1, u3*a2];
( C4 Z4 _/ L\" i1 y( Q: [ N9 Q
Iua133 = BesselI[1, u3*a3];0 z {5 ]7 ]* J: V. q) y5 P\" c) Q3 f
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;/ F4 l8 E& U4 ^% m( K$ Y
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;5 X& k3 A d, n& F: k/ O' [- i
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;/ b/ B\" v# e$ s: G\" \
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
0 R3 O+ d$ w3 ]: a; S: ?, D B
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
4 F; L\" [6 f- `( U9 A7 b
8 }9 z9 j7 i% a2 u# e x n
Kua121 = BesselK [1, u2*a1];\" J7 s; L; ?$ d4 f9 U6 s
Kua122 = BesselK [1, u2*a2];8 s! W- V+ l D. _: N* ^
Kua132 = BesselK [1, u3*a2];8 |' }+ l* {) {7 j' K
Kua133 = BesselK [1, u3*a3];6 ?+ f1 S u& E# ~8 L- T
Kwa143 = BesselK [1, w4*a3];
8 ]- h# R8 H1 z/ C3 `8 t
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;. I- V5 G$ C\" g& V. K9 x5 M5 s: C
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
6 Z8 w/ t& h U5 U
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;* l1 i Y) G, U# @
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
! B8 K5 v# g$ p) h; p
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
% n2 |; s, M. _9 e
, @+ C p( d\" K) W6 u- B
H1 = (betacl*Kwa143*4 ~% Y5 R0 m$ ]3 Z# N; z I; c
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
: \+ ^! D9 f. k5 K
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*3 s B: {9 M) {. J& a, g0 k
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" Q* d i4 u5 }+ e' `# A* {
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
# e; u F1 m- e1 v6 S& |
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
/ W' b- Y- w7 T0 }8 h. z
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
4 g8 j+ A1 p3 S; h. r
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*& V- I7 h+ j- G# {% u+ v
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
, P/ o) y$ F2 F! p4 h
1 }0 y/ W& ]; a! v; F+ W4 d; @4 M
H2 = (betacl*Kwa143*% E1 B9 u& ~1 S0 g\" @
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
: L' Z) i\" T0 \) E
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
$ l( [/ M g, B9 }
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" N% b, v5 r0 V+ z
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
J/ v8 H: y7 V+ H0 D\" p. `# |
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
1 G' L0 i; g) ~\" I
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*$ L4 ^+ W4 b+ d& |- w0 X
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
9 C6 K\" L7 w+ x
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! Z- G. p. P) H6 J9 h+ W
! }$ q& C8 L, D2 t) y0 _* G$ A
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
- F9 c6 K* W) t
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*4 `4 q- ]: G; H/ A
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
! x- ^( H8 f' N% V, {1 I
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 T7 O7 _( q0 f2 ]( e3 a
Kua122 - : a) d7 Y4 {' M$ x& k/ x$ ^- {; r. X
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
z5 P# j; F3 S5 q% X# r1 l
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
# E [& s; }& m9 K* F# B, v
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - : B2 X2 I N0 F4 F2 I% W# L
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133); @. s6 R Q2 d# g j0 _$ Z# ?
4 _( K3 Y- q2 F5 g( ^
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
) H9 e. Z( e; H$ S
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
# @% h2 L! K5 ?. ^( q. J% {6 L( @ R
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*- Z+ l- c* p8 r5 ^) ?: _. c
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*7 A2 D, t: p. E2 u) e
Iua122 -
9 ?) Q* Z0 \: h7 K( ~
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - # _4 [/ I- _\" W6 s; u0 e
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - \" w\" ^' U# E8 w+ Y9 X
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
# ~6 r+ i8 o3 b- Y
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; A; d/ ^& s$ Y2 F% n
# n% ?+ N1 b& d6 h* Y\" Q S) q9 D( u
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
/ a$ E; [% G' p1 i+ T
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
- H$ p# b _* [\" w# @: G# X& O& i
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*\" P( }. k4 |% V( T& H; x# W9 Z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
) I' p& D- i) w4 j. M
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
8 {' | S. _. }- D0 E0 Z5 k8 G( J8 n
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
) J' b; n8 h) L
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - - z! L1 }2 W; d9 I* T
w4^2/u3^2*Kwa143*IIua133);
/ Z. Y# A! A. o- A\" V' ^# q$ x
\" W) k2 S; ~7 \; R# \
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
$ K1 e7 K( b1 S\" y$ G) l
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
! R- i* _; s$ N; D5 e8 C- j' P
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*- q* M$ o k\" Z\" r# W
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -4 K( r: A7 M2 o* ?% M' \
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
; J* X# l: F6 T; R/ ?
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
0 c; K( K7 k6 \9 M. B7 N s
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - \" H( h: F( W, G6 H% r, u
w4^2/u3^2*Kwa143*IIua133);\" r4 x9 z& ~; ^) ?9 |% u
+ X' j. l0 C\" u8 @\" s
M3 = (betacl*Kwa143* k! C' A/ A$ t9 \. `# r; h$ o
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
/ X% L' ]1 a ?: F; A- d: A
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
! K: M7 r1 V1 o( b& x8 o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
' z* B- U r0 M3 N* A/ m
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132** B( R; [5 O8 @ L6 E\" ~% j
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
}& ~, M- j I0 n3 ~- I. G
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132* K8 p8 B& N. ?7 g: Y
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
0 ]4 y3 [2 F+ H+ p6 V
w4^2/u3^2*Kwa143*IIua133);$ o( V! B; {9 {
; O8 V0 e U\" p& k& o
M4 = (betacl*Kwa143*5 Z* T% z9 ?% i. C
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
, L8 a- [; o0 C- \2 ^* n2 h
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*+ N P$ a( ~8 R6 E+ O9 N3 e3 E2 i& F
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - / j2 [9 `- a1 @- j3 O
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*) g7 c5 s9 p- S: q# T3 M. _\" h
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
2 N' A) r! q1 A m
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*$ E# g. N\" }; l6 |9 C7 M$ i
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
' C$ c, _* ], M9 O6 {0 ~' P
w4^2/u3^2*Kwa143*IIua133);
2 w- \2 Z, F( l5 h
9 @/ V- N0 o8 h9 c4 R$ a, c
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;; t$ v+ i# h; |- U/ i
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;6 K4 w7 ` W4 w Y! F
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;7 X K1 F9 u8 r
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;8 t9 [! r9 ?6 M; \/ [
) `% m5 X7 G9 n1 F+ P
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
, V& {' y$ h/ @; b* U. F L+ [
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111; E# y4 {8 N* w& j# ]
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
* _ D9 G- w2 z' J, ?1 F
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;/ m$ f. n; L+ N7 r$ X
5 `, g. p5 V) Y/ z4 ^\" |7 X
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
( @, z: q7 {+ _( K5 ]+ P
V1*M4);- y; I: K; K- p! ^
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
3 T- A' q( s0 @7 V3 M
V2*M2);$ `$ t2 a7 u! i
% }( A' ~\" g' s
x = xicl1 - xicl2;: p$ c l g# N3 @+ u
x1 = Re[x];) }# ~, ?, }1 C: h. p) J A% E3 t
x2 = Im[x];
6 E% y8 e$ n1 w. j# K- y) M
. x( }& ?* Q0 V
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];7 F1 O: f' z+ _% N; }- W+ h
]' ^) k\" B5 t9 J
( v\" V4 E3 W3 F& t

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