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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;
& X h7 G* W }0 [& Z
k0 = 2*Pi/lamda;
' |4 L# ^/ V' P7 `' B
n1 = 1.4677;(*纤芯折射率*)8 J k! G, O* K2 |* z
n2 = 1.4628;(*包层折射率*)
6 |. f' b4 G) q I
n3 = 0.469 + 9.32*I;(*银折射率*)& b7 `) Y9 V$ [
a1 = 4.1 10^-6;(*纤芯半径*)9 i6 Y' `: X: l# @
a2 = 62.5 10^-6;(*包层半径*), J4 z N+ c( v/ A
d = 40 10^-9;(*金属厚度*)8 w. O. h4 K6 c! B5 ^1 C9 k
a3 = a2 + d;\" B+ M4 i* N8 @, \
mu = Pi*4 10^-7;(*真空磁导率*)1 J- R% B\" P2 c0 c) a- @
epsi0 = 8.85 10^-12;(*介电常数*)6 P6 D \9 J$ ~5 ?
& P3 v! q3 W I. ^1 M( J* S2 }
n4 = 1.330;
5 {. U9 A5 T A c2 d
; E& e2 o! [ B) y% m4 i
neffcl = neffclre + neffclim*I;
- ]/ c. y q, h\" N
+ l3 G5 L/ R$ n7 H1 S4 g# Q/ A
betacl = k0*neffcl;1 Q* x/ h: \5 z! w
omega = 2*Pi*299792458/lamda;
% j: J( E/ O1 W\" i, T
! o: V$ n7 o5 {
epsi1 = n1^2*epsi0; A0 T9 ?' C/ W$ D\" {
epsi2 = n2^2*epsi0;, i0 o6 x4 Q3 _) p
epsi3 = n3^2*epsi0;: U( u( U. z7 r( J7 `
epsi4 = n4^2*epsi0;$ I2 ]& S; M5 I- B
- I4 m. p4 w5 G. F* C1 U7 D0 q2 x& |6 k
u1 = k0*Sqrt[neffcl^2 - n1^2];/ }: e' m\" v' J, T
u2 = k0*Sqrt[neffcl^2 - n2^2];
3 C$ B3 B3 j6 R& W. F
u3 = k0*Sqrt[neffcl^2 - n3^2];% c, t) R7 y\" H6 L
w4 = k0*Sqrt[neffcl^2 - n4^2];! A) R7 ^1 d4 q
; G( E3 f7 g. }& e
Iua111 = BesselI[1, u1*a1];# W' `6 z+ c% R! Z* F1 t
Iua121 = BesselI[1, u2*a1];
7 E: L7 A/ L9 W$ _\" E- S7 d* F
Iua122 = BesselI[1, u2*a2];
Iua132 = BesselI[1, u3*a2];
% p* ?7 x/ `1 y1 E' H
Iua133 = BesselI[1, u3*a3];
7 S# \2 V$ `$ p$ g\" R
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
' B* v) R, |- |
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;- C$ I$ f- i1 B6 c& _4 i
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;\" F( w. H9 t9 \9 M. y. I\" @
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;- ~5 \' f. ?3 r
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
# V6 R; k% w- V
5 X0 U3 ^, {% Q+ V2 J
Kua121 = BesselK [1, u2*a1];
: ^5 p+ O- v3 ]4 y4 f# Q1 C
Kua122 = BesselK [1, u2*a2];! u\" L$ a8 U( G5 b: a, a; B, y
Kua132 = BesselK [1, u3*a2];: \0 S% V4 d* o }
Kua133 = BesselK [1, u3*a3];& s! b- ?7 S d4 M$ _9 q8 L
Kwa143 = BesselK [1, w4*a3];
7 u% u2 y\" G6 G$ a0 K0 s
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
2 R1 |% u4 g6 \; \
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
* |( n3 u) F/ W- Y' K
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;4 z+ a( j0 }* e5 ^; q\" @
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
# y, x' X) S: O$ O, o, O% A
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;7 Y+ ]; M: K; v5 x0 J
0 m4 i6 P: t, u) d9 T% i3 r
H1 = (betacl*Kwa143*
* F/ k& l# ~0 l) [4 P
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
) w: f3 a! H% |: I
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*' _\" j8 ]* o% z5 V s: {* @
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
8 D' Q9 g0 `+ k. B3 ~, y. Y# u
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*( c' C3 p$ o5 |& N2 c8 J
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*# e/ Y% a# b. |\" ? ]
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
# S- N$ e/ p n: O' l: r! _
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*! r& m; H. D$ ~5 U
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);5 e8 K\" E' M# ]- f2 z1 z3 c! e
! ^ D. W6 [ o8 }8 W3 Y
H2 = (betacl*Kwa143*, Q' R9 W; ^' [& Y\" b6 W& B
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
3 B g! Y$ L1 x& |7 E/ X' M. ^
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
& J; u\" K\" b9 q* |6 R0 h
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*% v; Q9 r/ t( j: A( e
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*1 S! _3 n7 G\" b& i+ i; {. W
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
) b0 ^9 v5 U) I2 g\" p- R; H6 }1 F
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl** g7 ?\" o! e\" m
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
/ C, N, T. R! p9 a4 S9 g1 U\" a
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);, }* f; P# N6 s4 N
6 h8 E: Q: c3 v9 b' w
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*, R$ j3 A: y7 E3 u5 Z- L
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl** V, b% g3 _' k. }' _
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143* Z9 B0 B4 p( ?1 X$ s
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
3 R8 n# p8 w\" s\" p% D0 W5 d/ }
Kua122 - * X! E% I% A( [2 e5 m: E- _( o
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
8 R0 k, N+ |0 J7 W3 V/ Z9 B\" S. y
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - , g. u* `+ _3 `* ]# b) d- _ Y
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ! N- J+ E7 Y- W5 |8 V# Z8 N3 \) p
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 {) d* b$ X' M$ O$ s. `' ?6 y
6 M( i+ M7 ?& R, m4 V8 `
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*7 n4 B8 }1 B1 `( K* [# k) f
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
& W2 J7 b. q ?. B& m2 @: C4 n
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
6 c9 ^% G( J8 q$ }2 a: Q
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*1 q. k. u! R2 a7 V' m- J8 e
Iua122 - 9 i- t% T2 i0 f/ ~
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - c( D& C: \) m4 p
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
* U# Q9 H: w3 o: x
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
- y$ K) U* p% K3 ^* K; x1 [& c
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);: R+ ]# M, T. D& R
/ K0 _ A( z+ O# k, R
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
0 u. b7 q7 H- {
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*. F4 M: G\" P- O5 j. ?
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*, x5 a3 z- p- x: B; t# X9 I' H3 Y
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -5 _9 e. D, A\" f7 c3 ~- _3 u
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - . a3 c' w\" `+ y+ C* L2 R2 P
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - & v4 [3 K, V- b. `4 }
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ) R- H; m) `3 l9 E F% E
w4^2/u3^2*Kwa143*IIua133);0 p2 n4 a1 p; d) m5 X
. Z9 q& L$ x) T; f/ k8 N- S) H
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*! Y9 y, [: U9 x2 }
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
( p5 {) ?$ N6 D% q- c: u
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
1 W( C8 b3 l0 P& y$ s' V+ U
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -, `: p/ Z V4 ]
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
9 P' g0 i6 g% i4 H
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 7 o- I& }; @* a9 ~. Y# k' V! W
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 7 v; s- Q' @# ~- ^' W7 o4 f
w4^2/u3^2*Kwa143*IIua133);
1 N9 _2 A6 w; h- q2 }
9 x& y) a6 E8 k
M3 = (betacl*Kwa143*% }% w! W! c$ R
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
5 `: ~0 T8 R\" Z\" R& H. @
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*+ q i. ]% H0 `( B9 W0 R' m
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - K2 f C/ t, K' u; W% U) ^
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*8 @1 W$ m( F* N% @! a3 u\" s! x
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - & b( f, t\" W7 s e
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
\" I# \$ l! H+ ]% P
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
' X+ d/ h\" B% t; I+ _4 m
w4^2/u3^2*Kwa143*IIua133);0 a! Q* J; R0 Q, b& f2 r
0 B, `\" t\" |4 t& U0 R\" z# v
M4 = (betacl*Kwa143*. O- X+ z& E2 r( R) A, D
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 9 z/ T; S1 J B+ U0 t
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*' |' L\" N! E0 } H) }8 d7 l
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
7 y2 ]' u# N+ c
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*1 l9 c3 e W8 m! G4 X( b* N) n
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
+ n) n% d7 H\" @, C
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
& j9 E( k( N# M, J
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 3 x: q! G; \5 N/ E; h0 t
w4^2/u3^2*Kwa143*IIua133);
i5 c% m+ c5 S* [1 _# b' ~
8 F' D: X* e+ j: [/ g. Z. s9 p) O
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
! q, T. Q0 c. Y; n. {, N, T1 V; n, R$ i
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
2 B+ ]3 O2 ]7 h% y0 h* U0 s
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
$ h\" E- b+ d( c5 {. l. p) E\" S' c
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
9 N5 |! y% ~. S: j
8 S* [1 c x3 t0 B\" \2 @, c
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;2 ~0 m8 D, o/ b0 h
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
, o2 V' D3 G/ F/ p% `
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;! F# a4 ]6 S0 _7 y) _( F
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
+ v1 {& U( W$ Y/ I+ F! r
4 w7 o w% P' B( f% r
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
\" }3 x6 r8 z2 v( |% M& Z
V1*M4);; x$ O# q( _# w* E( t
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 3 N8 W1 @ y2 X3 D2 U- t* [/ S9 a6 K
V2*M2);
# V9 B4 v2 a Q: ~
# @2 z& |( I3 D# N
x = xicl1 - xicl2;
; _6 A) ] R b( s* x( E
x1 = Re[x];
( i, v% R\" w\" c3 s
x2 = Im[x];) M) ~6 U4 W: K, k& i# F* Q5 S
) i' Y( i% }1 V9 C: d
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
5 s+ H; o3 N. U( |. V' d- T\" M0 S! \
]
# @$ I- ~) K! @' [8 F$ W
1 W9 j5 Y3 A% f1 ?2 L4 x# d

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