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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 U0 R, B! F/ F: [3 {. F
k0 = 2*Pi/lamda;
J L6 k2 b& @# b7 P0 c
n1 = 1.4677;(*纤芯折射率*)1 s' ]6 a; p\" Z8 u
n2 = 1.4628;(*包层折射率*)# t0 V# g A1 K% }/ X\" K0 R3 P
n3 = 0.469 + 9.32*I;(*银折射率*)
. Y- F8 r% D' y; T\" U
a1 = 4.1 10^-6;(*纤芯半径*); {% c1 z, v) [# s2 {
a2 = 62.5 10^-6;(*包层半径*)8 s; t) h\" X7 z* o8 P3 b
d = 40 10^-9;(*金属厚度*)) y z# V+ M* E$ O
a3 = a2 + d;5 D+ j) ~\" o8 ^) V, D
mu = Pi*4 10^-7;(*真空磁导率*)\" m# c5 q; q# }% ~/ n y$ |9 i
epsi0 = 8.85 10^-12;(*介电常数*)
0 v* J# ]/ V6 @) s& o' `
+ W6 Z$ x5 a: P
n4 = 1.330;
\" S# r\" Z8 ]\" S/ A
1 e, u! w& a7 ^7 d
neffcl = neffclre + neffclim*I;/ V$ k$ Z6 c7 H' ?2 D
+ K) L5 {- c0 y' A
betacl = k0*neffcl;. ^6 B/ H* D. o6 y\" y# D/ L6 ^
omega = 2*Pi*299792458/lamda;4 ~) E: L8 a/ U3 {' C$ q9 V' M
) M% o3 a; |( N f F3 ^
epsi1 = n1^2*epsi0;) U# l3 D0 [; \7 x- N
epsi2 = n2^2*epsi0;# i2 w9 Z3 Y# a8 y
epsi3 = n3^2*epsi0;* d7 ~2 ]8 e# f, N\" A* R
epsi4 = n4^2*epsi0;3 x7 J6 x4 n; y
6 D0 i5 j; F* _+ B& R( U
u1 = k0*Sqrt[neffcl^2 - n1^2];
8 u1 ` X: l. n' F. ^
u2 = k0*Sqrt[neffcl^2 - n2^2];+ a: W& `* Q. G
u3 = k0*Sqrt[neffcl^2 - n3^2];\" w5 X T; s1 }$ |* j5 W
w4 = k0*Sqrt[neffcl^2 - n4^2];% E& Z3 T) S) t% [. G5 F' S9 D* h
2 w: O4 W% U7 k! Q+ g' z\" U
Iua111 = BesselI[1, u1*a1];
: W/ H0 D- \& v8 ~! q8 `) @
Iua121 = BesselI[1, u2*a1];4 y. Z5 J. i3 u
Iua122 = BesselI[1, u2*a2];
* ^) I) a( }& V, U! X# @ B7 l% R
Iua132 = BesselI[1, u3*a2];
. w, ]: V\" {- f9 Z( a
Iua133 = BesselI[1, u3*a3];, Z\" ` ]# \\" @. `
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
) L/ e7 E$ b+ X' v ^$ w; U
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
6 `% I |2 ]# }; F& b- ^! C
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;7 n1 N0 t$ Q+ d) I2 q3 A% D$ A- k; p7 n F
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
9 |\" x1 ]7 G* @& D\" g3 E1 t$ ?
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
5 ?& y1 s: }' I: ~9 _+ e0 J. C5 i; d
. k/ h* p. H; C* c B) x* Q( j
Kua121 = BesselK [1, u2*a1];
- D: g5 I1 ~4 V
Kua122 = BesselK [1, u2*a2];
/ j+ T: m( i* f& X. R+ I& ^9 x3 V
Kua132 = BesselK [1, u3*a2];9 }. \. |' T+ b0 K* a
Kua133 = BesselK [1, u3*a3];
+ Z6 d; u; X% Y
Kwa143 = BesselK [1, w4*a3];) }4 q' ?# @! H& o6 \\" b0 [- p
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;( X A4 }* K9 m
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;2 I6 w2 K- Q6 b* k: b
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
8 M# c- `% K, u
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;; E- h. M) D% d( n. D6 T; e! O4 W+ ~
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
! `. Y( u0 `- U2 s; ?/ T* [% v D
& T& w* P: P# i/ R
H1 = (betacl*Kwa143*9 M\" l! G* ^ r; u9 j' l! g9 h\" }
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*, p- }& k2 T- a2 M) z0 ?
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
/ s# {2 M$ n+ I7 j% v& a
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*; Z7 |( i% k3 I- T
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132* A u4 N% L0 G1 D
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
$ U( p1 q. j\" m+ g) g
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*9 q. k0 ?4 ~5 a: }& `
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*& A% [ _! v6 b( U1 j2 B. M
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);% P T; c/ U3 u7 k% X, }+ A) h
9 H4 E/ N4 A. a; H
H2 = (betacl*Kwa143*, O/ I, p T* D+ ]/ y
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*& g9 e( @2 @3 @* H
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*- _( d8 ?! k\" o
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*1 ?+ H) D7 w% q: m3 z
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
$ ~% b3 `& r# T: d3 y# E& W
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* b* \( F! B( c: t. J9 g+ Q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' S8 x, w) @2 Z4 }# H
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*7 h1 i5 Z. V8 l5 C! g6 [. T' l
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& E5 h6 _0 C* C
& b4 L- z; p+ A' E2 n
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
, Z! o3 @* C) ~: V, W( t
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
! A; o0 r) M* _; A7 p6 _
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143* W) |) a5 F# @* r5 {
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
/ ?8 d! s. e6 s5 z( G
Kua122 - 0 ?0 [) V6 U1 l. F7 Y6 e
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
# k9 Q# j7 F. _) V
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
6 |\" R, @$ v0 I% c6 R: I7 l9 m$ @
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - \" W8 l4 p1 @1 |# e6 E; y
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; t9 v: b8 L- x& E, @: X0 @
+ [) U3 A9 Q3 W4 h% u, |1 l
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
5 z' T6 X6 C3 p- ?1 k2 I
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*; z& p. |' \: A; Y- d1 V
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*3 e% w\" _0 o8 }' g/ P# l
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
& f$ g, h4 R2 u
Iua122 - : T' U; h1 }- f4 [4 g
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
& o8 i$ S$ y( n
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
; A! z+ g. U# G5 o- @% g
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
$ ]0 w7 v! _# q' ?
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);' K; g v1 p\" C. {, g, `. n
/ m\" \8 N& t( F2 s, f5 J+ A$ y6 K
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*3 @/ o# \. J1 q% e s7 s
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*+ T, K4 n4 O% g% s
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*2 E8 P, ~7 l7 e: j) w' o* Q) {
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
+ a6 ?( t) c5 O$ o# @: z5 u
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ' Z k' P) }3 v0 X$ b! q
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
9 X7 Z0 u3 F% D! t
w4^2/u3^2*Kwa143*IIua133);
) B( D5 |, E& W2 s) z, X
. g$ K- W6 M* T7 ]# l
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*3 d0 w: E. A; A4 l; O
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
' e8 X9 h% z# X9 }) E
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
2 L5 m; \$ e- s2 Z Z* R\" q
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
4 e, @3 M' C2 U) K0 Q3 k# J
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
7 p' F9 R# h' y V1 P$ L
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
8 s2 v, x5 j# S
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
, P$ ~4 q! ]% S1 v
w4^2/u3^2*Kwa143*IIua133);
. b# B: `% |) Q\" d- ?. `# Q- ~4 v
- x1 ^/ `0 I! Z+ b; j4 V, {
M3 = (betacl*Kwa143*# o\" T1 C+ Y, u$ l) y1 \
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - - y: V+ ^$ i% I) p( ?8 S
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
7 q4 @4 |$ H: H6 j) l- d
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
/ W% N\" F6 \9 n5 o
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
, l# F\" d5 p6 p/ ^4 @* J$ G, D# S
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
; p# K, P6 v( P9 C& Q2 w% P* P
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
4 l; w0 ~ l6 u' |\" A9 e0 ~# v
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
- q2 V1 c* F# D
w4^2/u3^2*Kwa143*IIua133);
3 u4 r3 A! ?% @& i$ F* t* y5 h% H
, U3 @9 n4 E1 J9 t: g/ Z
M4 = (betacl*Kwa143*
' [' }6 J% B\" ^0 l* J7 E; H
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
/ o+ u9 J* I* J3 C* @/ p( e
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*( d! _\" ]' U$ |+ P
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 6 R$ I. f\" B; W% n) U5 X1 v$ I9 N% W
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
) A3 J# J# R7 R0 D
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ; B6 B) o: t5 ^6 S/ i4 t
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*6 w1 X- ^+ z' R( |4 u# o1 c
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
; A' G0 {+ L$ _. d
w4^2/u3^2*Kwa143*IIua133);) ?; C3 T0 l; K u7 S5 X# n$ T6 Q
# ?$ b: J' t. z6 y
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;5 k, {) K$ G; D2 L* j2 f
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;* j( C. n\" `4 S; ~, y; C
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
6 X. a& |: t: n1 [1 y9 k, G5 N
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
% c( R/ t+ }( _6 i( l6 R
% j7 f. c+ Q7 m' Z$ E
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;3 E: w# P: I, m& P4 y9 L
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
\" a0 y, J% I( }( L1 D
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;* K+ N1 r. U5 E
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
9 Y/ r$ S! r' Y! q5 l3 t* T$ E
; ~! \! r2 K Q! {5 s9 S
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
/ d) f0 S/ i4 a4 ]) C+ M. z; V3 ]% a
V1*M4);% c1 \; @, t& F3 N
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + - B2 U( D3 z& }- a
V2*M2);7 R8 v/ r, Y( I m3 F\" H$ W8 K
( I, x2 t$ P+ r/ ~* a
x = xicl1 - xicl2;
; v: \: e7 z- {1 L. [- n0 B
x1 = Re[x];4 K. C* w: x& B% h
x2 = Im[x];
2 Z I5 Y! H# p' Y/ @7 u6 S; a' ^3 J
4 w8 m4 b% o\" {; U H+ ^
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];+ Y% r7 z* o7 F7 o D
]6 L+ l( a5 }! v% q9 C4 @
7 i, l8 T4 i R# ~* @

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