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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;# w/ e6 j. A5 X8 \9 d0 j% ]5 q
k0 = 2*Pi/lamda;% @; {& o0 d* s4 k! U0 ], }% l5 t7 |5 V
n1 = 1.4677;(*纤芯折射率*)3 L! u( B% h4 Y, Q* f0 L9 p
n2 = 1.4628;(*包层折射率*)3 |\" E+ f6 H/ X3 g4 Z; ?
n3 = 0.469 + 9.32*I;(*银折射率*)1 x/ T+ ^6 D- K4 A0 b
a1 = 4.1 10^-6;(*纤芯半径*)* k4 T7 G# A3 o: R2 T3 L+ M' q# ?
a2 = 62.5 10^-6;(*包层半径*)
# f+ Z/ |5 t/ D\" T! X
d = 40 10^-9;(*金属厚度*)
; n# k) [+ K) E& J2 F2 Q4 y
a3 = a2 + d;6 p2 N) ]1 v\" K7 z9 |( ?\" T
mu = Pi*4 10^-7;(*真空磁导率*)3 j8 u! d: ~4 @8 p' o4 G- J
epsi0 = 8.85 10^-12;(*介电常数*)9 d$ ^% u: w' y- y
# e# K+ |\" V) w @8 C# H
n4 = 1.330;
' T$ J# o% Y. c) G) B$ ]; e5 y
/ ]# _% g: M: U7 J
neffcl = neffclre + neffclim*I;
1 n* b# J: S0 o
n7 u\" u, Y# `# w. M3 d! C+ v
betacl = k0*neffcl;
' }# Y- X* Z% ]$ h
omega = 2*Pi*299792458/lamda;
- S4 ]2 z6 s! u5 q
+ J( i- u* H; a\" a' n _3 r# F; `- N
epsi1 = n1^2*epsi0;
; W. f! Q. h. M1 v
epsi2 = n2^2*epsi0;2 ^, _* R3 b/ F% g
epsi3 = n3^2*epsi0;
- N' l\" b. v* P+ Y) U0 g. W
epsi4 = n4^2*epsi0;
6 b. b2 A: j7 G% |) w; N& e
1 v6 C2 X) ~+ a\" M
u1 = k0*Sqrt[neffcl^2 - n1^2];; t5 E6 u0 W- h8 [# r' `$ z
u2 = k0*Sqrt[neffcl^2 - n2^2];& b. c2 d. ]6 `
u3 = k0*Sqrt[neffcl^2 - n3^2];' X! c2 g* m' u2 E8 r6 t) W1 A
w4 = k0*Sqrt[neffcl^2 - n4^2];
9 g( \. q\" X1 t( J7 ?) @- P
3 E& n4 H1 t$ K( Y6 n; z
Iua111 = BesselI[1, u1*a1];
4 h5 J9 r' k0 Y\" j
Iua121 = BesselI[1, u2*a1];
4 O4 B% O* I1 [, O
Iua122 = BesselI[1, u2*a2];5 L0 I! N7 z, S
Iua132 = BesselI[1, u3*a2];
/ \3 l4 k- ?8 ]: S
Iua133 = BesselI[1, u3*a3];
# t' G9 \\" O+ W+ a\" J
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;% D; g/ K: L4 l0 L u
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
7 q7 j* s: B2 @( b2 J
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
. l# L- @) \# d9 `3 y% [' x. V
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;. W a* S\" G2 }\" ` V, J( R4 o) o% k
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;& A8 r$ h! W* J, w- O
\" S\" L. Y: U\" Q0 K
Kua121 = BesselK [1, u2*a1];; q) M\" X' D3 i7 O
Kua122 = BesselK [1, u2*a2];
+ x; @/ }! L0 r
Kua132 = BesselK [1, u3*a2];1 [; k; G1 c( K, G5 e& b
Kua133 = BesselK [1, u3*a3];
% ~* j# O) j: ~
Kwa143 = BesselK [1, w4*a3];
& P4 P2 l/ Q6 ~- E5 ~! Y
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
. p# D: a5 P8 @4 b* o
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
5 L! t r; _$ E) X% Z* F3 B
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
* O1 _* z7 u/ _; f
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;\" e; J2 ~3 ~0 f3 b
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;: `8 h/ x+ y( s
6 u2 L* u1 Y& a8 J$ l9 Z
H1 = (betacl*Kwa143*& O, ?/ a! v* t, a7 {, E
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
\" G/ D: [- n7 F2 v% r. U! i
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*7 w* U3 x0 E, K' e. F B
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*$ \9 ^! }, k* x7 Y2 _. b7 l# V4 e/ c
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*2 _5 z8 U k( W7 k B
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*3 B* m. F% G) z: ?. C0 V+ K$ f
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
- w7 P% F( Z+ g) A/ z! x, K
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*6 |9 H! \6 k' ]% O3 m4 T) m
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);4 s5 j6 f% k1 r( Y* @8 N- O
r4 @6 t; _4 A
H2 = (betacl*Kwa143*# i7 ~6 ]! Z! ~+ H4 F0 g
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
$ R( B0 w* j0 _! q, ]' k
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*6 E. R9 ?5 |9 P) x* M$ H# w; _
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
8 B# G( u( I* A( z/ J
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132* ~) Z+ D% k, g5 ^2 s# Q
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* `# P) Q% x% w; C/ P& X( n9 ]6 t
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*3 A. H s' d5 U8 ^
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
f- E% A% |7 g6 m5 c! v\" M/ q c
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);3 }6 y! p3 D1 m, Q
/ N3 ^* x5 y; \$ u' f8 l/ K
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*. w8 _2 Q+ Z) B/ y
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
4 p/ d\" ?* R- ~4 n @% U3 ?
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
! g p. J, W7 ?) W6 i
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*4 ^8 z/ ^) T, ? q: w* Y% R
Kua122 - + B\" W! D9 I4 O1 {3 b9 T
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - + {: F F1 w' a. D
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
) T. V+ R5 \- g# }4 E' q
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - * o7 a: q7 D+ F6 H+ ^
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);0 j' L: T, X/ R1 {8 M# e
4 T/ D8 g; }8 y& o$ N% }
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
7 } h% k( @1 @. M8 s
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*# q3 C5 _0 d* m4 o9 e
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
7 V9 k, |$ l) ?1 i/ \& N\" U( \
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*' e( d! ^\" ~) u/ G3 T
Iua122 -
0 G; G* L0 {( n/ a
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 7 J; f% c; n$ U- C+ X. z0 X/ l
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 2 D5 v/ j7 w& d# g8 E$ c( p
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ) i# U1 h1 ]) ~) w I) S
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 X! ~; D, j8 t; N f. f/ V$ I
9 Z- b9 k+ W8 A$ s) p0 \
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*: J9 d9 `. ]3 ]# u# T
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
! ?1 s2 p$ q6 f' L. I
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
N& G/ F, X' X4 Q$ @2 G
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
0 ^8 o( ?$ a% X: K\" u' _0 }4 c6 M
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ; g; @) S* e- {9 _
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ( p& n3 w2 `, X
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - ( {* }5 f2 e7 f$ ~) |, e+ f
w4^2/u3^2*Kwa143*IIua133);
( D6 v! [* @# r8 \7 h1 n\" u
1 @; x3 Z* z+ V\" Z) W+ W! n
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl** c2 }, s6 b' z8 B i\" @
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*+ d9 {7 t; ]! H( L# j' [6 b
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*' |4 t; g# p, i$ b1 u: x
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -- b+ O- X8 ^\" |0 r
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
3 C. H- q! u) U- x- P. a, G1 D\" }
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
$ r8 ~# {) m( }
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ( g2 c% y& Q) o7 }' ~4 {
w4^2/u3^2*Kwa143*IIua133);8 S\" i; x- U- k5 v8 `
`, `) e. o$ s& h, u \) } }. v
M3 = (betacl*Kwa143*
6 L% @! Y& @1 l
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
\" q3 {/ \. D* s- g/ v
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*! x& d: U2 d8 [; h# w
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
5 _) y2 e' M\" i, y; @* \\" x2 e
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
/ ]: o. J' S) A
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
' `2 b# o+ s6 _9 ]0 P- S% u
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*& m% ^: [% X! c- e7 t
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
2 j& U6 b/ c6 j
w4^2/u3^2*Kwa143*IIua133);8 {0 g( t! D4 Z\" f; X
5 ?4 J3 m' P; q6 H+ z4 F% u
M4 = (betacl*Kwa143*. }+ ?8 C2 D# M5 C9 @2 t5 P
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 0 R }! B* k: v' i5 I+ \
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*7 R% w; u# P1 D7 }\" ]
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - ; A) _/ b8 r( ~
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
( {+ j4 p: p! T% a6 w
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 5 }$ d. e& [3 @
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*& S& d( J% B* `
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
% Z- I: v4 g! r
w4^2/u3^2*Kwa143*IIua133);
% e5 E: p5 ?. l9 j1 x. X# k- ]
, p6 o: F4 g! ^% }+ P2 L% l
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
& u0 n/ t4 M) ]/ \
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;* \: r* G/ B3 S+ g; r' S+ w
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;/ B6 v% |7 G3 @\" P# }
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
. j5 x# x' q( i G
+ W& j, h7 R4 i! s; U4 T
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
4 z8 S8 ?3 ?2 G1 G- \+ z
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
( C5 J, P' I+ Y\" u) n2 d
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
% {; E0 q5 E& R1 h Y
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
0 @* `; ?9 d/ b; J% A
& B4 K3 i5 v3 f9 w4 }% y, P
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
( {* M5 p- p* c2 Z6 u$ i
V1*M4);
2 z% F3 q1 D3 E6 T4 S' @9 }4 y' S
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
& I; y% i1 c0 P2 [* q4 C
V2*M2);
- D9 F! f' m2 f$ W1 ~
6 r3 }+ ?6 |+ ]4 r) R6 r: C! _5 B
x = xicl1 - xicl2;; x2 K% Q$ A; N( n
x1 = Re[x];# L8 |8 A\" ~+ H- S& O i/ Y v
x2 = Im[x];6 j6 u9 K\" H\" W
E' j9 [% K) h. ?1 U
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
8 f' R! L) \- z, l
]
1 ~# G+ E/ Y8 e4 X% y: E
& a& N, K9 p7 e2 M0 H5 `8 P; X

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