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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;9 S- k- q: B1 ^1 R) [
k0 = 2*Pi/lamda;
8 i/ h$ W' |- [: }9 ~# L4 t( L
n1 = 1.4677;(*纤芯折射率*)
- p2 v0 V ?4 T2 ?+ U! U+ j* |
n2 = 1.4628;(*包层折射率*)
9 O# ]( u/ @1 D9 a, i0 c8 t
n3 = 0.469 + 9.32*I;(*银折射率*)
1 @\" \: X- r; o# S5 V- \$ x' s
a1 = 4.1 10^-6;(*纤芯半径*)
6 f: ~/ T9 y\" j: Y1 s3 b! Q
a2 = 62.5 10^-6;(*包层半径*) o0 d. _3 s- s9 W8 W( F, \\" `
d = 40 10^-9;(*金属厚度*)
- `$ _4 ^2 W5 x, J) {
a3 = a2 + d;
* Q$ |' }# A) P5 H! ?) h9 s5 R
mu = Pi*4 10^-7;(*真空磁导率*)! h: g2 h7 `5 x# G Q0 g
epsi0 = 8.85 10^-12;(*介电常数*)
+ |9 ?7 c\" V1 r: G8 B9 r9 y
- d' a4 x& K( t A8 Q; a. H3 p
n4 = 1.330;
! d7 _8 q9 R# @$ o
0 t9 c9 T3 m% \! R6 ` O0 m
neffcl = neffclre + neffclim*I;
. T4 n* u9 T0 T* j4 p8 _
& G. L1 m& n5 r6 }) P: n+ x2 r% I- |
betacl = k0*neffcl;
+ }\" t% i Y/ M5 p5 ?
omega = 2*Pi*299792458/lamda;
: H/ b* W7 h' m
0 w6 h6 ?( x6 a+ K! b! q F+ d
epsi1 = n1^2*epsi0;+ V! U# O' ^% ^
epsi2 = n2^2*epsi0;
) ?, ]2 S: R9 ^; B- b5 t5 d
epsi3 = n3^2*epsi0;# s+ l% G+ d8 i! ^3 G
epsi4 = n4^2*epsi0;
3 C, d! y\" J' x% {) n- j
w: [$ a: N2 `( l0 o4 [
u1 = k0*Sqrt[neffcl^2 - n1^2];
6 q% l\" S8 C8 c# u
u2 = k0*Sqrt[neffcl^2 - n2^2];; F6 I* u7 r& n$ A+ d
u3 = k0*Sqrt[neffcl^2 - n3^2];2 t; x# j/ w3 ?4 t
w4 = k0*Sqrt[neffcl^2 - n4^2];5 V% @' `2 o- S3 h9 L* T
4 z0 W' Z/ e, L/ r8 d- u
Iua111 = BesselI[1, u1*a1];4 L8 c8 c7 }- J! x0 q
Iua121 = BesselI[1, u2*a1];) i K g, ~: l- y- E# ?& \0 s
Iua122 = BesselI[1, u2*a2];( [. o' l9 O+ N3 i1 \: G6 b& g
Iua132 = BesselI[1, u3*a2];9 M) @. r1 C. g5 m5 e) x; f
Iua133 = BesselI[1, u3*a3];5 m* a5 v: ` w9 a8 A# K
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;0 o( Q5 d5 I' R
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;) P# m) ~4 L$ J6 |$ {5 A: W3 J1 [
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
0 ]7 A( d- T6 x3 S0 u
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;# @8 n' U/ J$ [) K
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
& `2 Q4 z+ j5 C- E
5 v6 p5 I9 H\" ?5 z9 M6 ?( @! L% Y0 I, y
Kua121 = BesselK [1, u2*a1];
\" {, b- M( d& O0 e2 Y/ E& O# X& V7 o
Kua122 = BesselK [1, u2*a2];
7 w2 \9 y& |( g2 ^; S% @3 o' }& @
Kua132 = BesselK [1, u3*a2];3 t9 b0 v9 |+ \% t5 d
Kua133 = BesselK [1, u3*a3];
$ N0 ~- Y6 U* c
Kwa143 = BesselK [1, w4*a3];
* B; p) Q* X- D# n5 w
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
& u& v B, I8 u- w1 ]\" G
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
! ^1 F3 g: y9 ?6 H4 `
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;/ T- q3 c; D& c
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
! U\" ^+ E6 K* L# }# c/ C* n, {
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
6 e! K# v: r+ I3 B
1 X- t+ y/ p, t4 P: v a\" z; W
H1 = (betacl*Kwa143*
3 @& s0 S# E# F) z$ k2 _7 K2 Z
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*8 k6 I s% {' X8 q5 R
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143* U& K2 O9 W! V8 X4 Z1 I1 `
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*# g. }& m& H8 \. B) B
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
' M& l9 C0 Y$ L& t& }: f
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*\" P% ^# i/ Z4 K( F
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*8 M0 r* P8 }0 ^( r* Q. y+ I\" g9 s4 e
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: {1 H- ]& g) P+ A
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
; e1 ` l\" U5 H\" n. `- v. L1 G
f$ ?, d/ W% b: P7 _/ `
H2 = (betacl*Kwa143*' y2 Z) U6 L1 u6 t& o8 Z9 C- Y# c
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
$ j2 `! R5 w7 e/ z. P# V U
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
- ^3 Y8 f* v, b% q8 D6 L
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
' p p3 g: N6 X
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
\" f: y5 `0 |( V* G
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*/ f& U) L+ \5 J5 d
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
* g2 ]; A r C* m- U& `) {
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*) i8 E4 u' {; T p- O
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);( W3 Q1 c; ^1 G X- d- a
8 Q) g+ _& G. L; e; G: U4 d
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
) B! Q; O) O/ B- j/ Y+ I
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
7 J, W\" `+ q& l) k5 a* Q& ^\" S
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
2 x* I& y7 s5 j; o) N+ J2 }# [
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
! |9 \\" _0 A; j- S0 g\" m
Kua122 - ; x$ G2 W/ {' @. F; D
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 0 R, o+ [\" J& k\" s+ l
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
% ]2 O* ?0 s5 v+ \
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
' D! N- h/ Q) j9 O3 I- O
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
7 w6 k, h1 r2 z3 ]2 f, _8 _\" h: ^
! d4 V# o7 O0 u( ?
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
# ]5 B& h8 m) O9 c0 @& T
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
' c6 t' p4 ?9 A3 \
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*/ g! N2 ]8 ~9 ^\" h
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
\" r/ v0 g$ p6 t, a8 O
Iua122 -
2 H. K. i/ }9 X2 E
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
2 C: G7 x& W1 f& ?) P( S
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
2 Q/ o k# V\" H: Q6 E
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 1 }% h+ n( b9 n4 f0 `
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 g l! ]: F/ w( V$ [+ G0 u7 o J
! K% p, E2 \/ t+ C: Q4 ~
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*$ `, s8 q) Q+ u% Z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
$ Z2 z. ^# H7 M6 w# q* x
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*7 G7 Q% O( Y h
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -6 P4 h& _4 P: j2 T$ M7 W- n' P
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - $ ^# o+ J/ v- K% N0 E
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
/ _ k( u { v* p
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
\" t6 q% k Z! j- T1 U# P
w4^2/u3^2*Kwa143*IIua133);6 X. X- z$ X; T3 R. C# b
+ K# t! k: z4 I\" a6 \ I
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
+ Q$ T/ v9 I; W$ {2 [9 f4 z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
0 S( \, O1 _- O) w
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
- q, I, X. S6 R' w
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 - C! ]4 Y* J* D& v- N* c3 j
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
: f' U) _; W& V8 O- `$ ]
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 5 I9 c& D. P- d- o6 P
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
/ Q. Z0 R4 b# O/ c7 |
w4^2/u3^2*Kwa143*IIua133);
1 \- Z/ K$ m8 M7 @0 I( r+ v, `
; v) n& [0 P; @& ]; D
M3 = (betacl*Kwa143*: B* c, D4 _5 K! L, F1 a2 Q2 u
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
) Y6 Q/ d# K8 \5 D# `- ^4 Y
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*# k; Z/ _. n$ ^# S7 F% h1 q
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
- \: Y8 ?: i& i0 F# {% b
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*2 j: f+ {. J2 n8 a1 L) F
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
1 m9 X' U6 w$ |$ p
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*9 k, `- ^6 X4 n
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
: {3 F% H8 i# u% q8 z, r& K3 h
w4^2/u3^2*Kwa143*IIua133);2 e' w0 g. i% ?( \4 \) z
' w) g( F0 r( e+ b! B6 N B3 `& \
M4 = (betacl*Kwa143*5 Q9 N( {$ o z$ A0 Y
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
( S\" e: y; J$ J, f e! F\" T' ]! O
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
! ~6 W1 b5 \& D\" n# M/ z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
5 v! ], l0 a* u
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
; ^+ ?7 y* }( K6 k. {
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
, C) C0 W/ c0 K& U$ E Y- s9 m U
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*( w6 q% r5 |% l! _+ \
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 3 w9 Z( d\" g\" v8 }
w4^2/u3^2*Kwa143*IIua133);/ X6 k$ ?; V& b/ U8 O
5 r+ u+ ?: N7 |- Z9 b
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
* F# m) I+ _! Y# X
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;: I9 \9 g% j e\" v5 ^, X
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
4 X! s$ M \; D4 y$ ]: ?* e7 r
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
( H( k/ s9 B4 `4 `1 }* ]* r& ?
! E1 L4 f% \$ [- _
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;; Q7 d1 x/ b* R; R) p- v/ B# u
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;% M8 P1 `/ n; y7 o
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;: ]6 N ^8 ?- w8 R* g% f
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;( w/ Z/ [% `( J9 Y6 k, m4 C
1 I( m& G0 t8 O1 x2 \. J
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
& e2 A7 B: d8 T! S# h
V1*M4);
# h, a7 H# K0 }# Z R9 o4 y' b
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
/ e, ?0 T\" x: z- x _$ u
V2*M2);
+ Y3 F: [6 O# P
\" @+ m4 I' i* O2 p: c
x = xicl1 - xicl2;' Q8 i* m* N( w; X) ~/ t) _# m
x1 = Re[x];
, ?: P6 I5 `. i
x2 = Im[x];# m/ h$ w/ K6 H# Y' |$ e\" {\" i$ F
4 C m$ }9 s- h6 D2 d' Q
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
. a6 G* o$ t1 N: C- S/ m: G
]# w: n; Y: R- k% o. @( ^# P: ~
9 Q1 v) [) Y: h' E

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