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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;
\" Q' [& [. m% R% i% i& L
k0 = 2*Pi/lamda;' u3 t# D; u1 J
n1 = 1.4677;(*纤芯折射率*)/ ^# u- J6 }! Q t* [
n2 = 1.4628;(*包层折射率*)
5 Z3 W3 Z% J$ }' V3 b& h* N! {# {6 E. \
n3 = 0.469 + 9.32*I;(*银折射率*)
C5 a; }. e/ ^9 E7 z
a1 = 4.1 10^-6;(*纤芯半径*)2 ]' T$ e1 W& C
a2 = 62.5 10^-6;(*包层半径*)
! N' |4 v1 |2 r z\" @
d = 40 10^-9;(*金属厚度*)% J7 ?) g3 `\" ^. ~5 t% k) J
a3 = a2 + d;) ~# U8 u3 {6 V$ E( ]
mu = Pi*4 10^-7;(*真空磁导率*)# D: F; i7 m P; ~* `; y. {4 I
epsi0 = 8.85 10^-12;(*介电常数*)
- J( ]' d+ V2 d0 e
2 {' W' @2 m3 r5 Q# R( T% y' r; R
n4 = 1.330;: c( e/ B3 M+ ]7 s1 T
2 y! |/ E! y$ D( l
neffcl = neffclre + neffclim*I;
# ?& y( V3 H8 ^1 h0 a
! u$ l8 \# {' W
betacl = k0*neffcl;
& P0 k5 ]4 M\" N. a5 o
omega = 2*Pi*299792458/lamda;/ J7 j\" m) G. N, {: t9 l5 c1 K
1 I1 x( |. z% M7 {8 b
epsi1 = n1^2*epsi0;
5 @- z( u0 A6 H: [2 t
epsi2 = n2^2*epsi0;( \2 |3 }3 L. I' Z ?6 F' o
epsi3 = n3^2*epsi0;
) Q# J$ N6 d' b, x6 h2 t9 p( k
epsi4 = n4^2*epsi0;
0 Q8 z+ E\" D! t, ]
5 {6 B3 K H5 w% p+ v0 y4 i
u1 = k0*Sqrt[neffcl^2 - n1^2];
( C- j$ r0 Q* p7 _
u2 = k0*Sqrt[neffcl^2 - n2^2];
3 z# s. e# T$ n* o0 Q& f/ H
u3 = k0*Sqrt[neffcl^2 - n3^2];
0 R' y) d2 Y\" p
w4 = k0*Sqrt[neffcl^2 - n4^2];- m* q- \: e7 b/ `9 @6 ]
* a! `, E. N( `5 T0 }% {: P+ |# a/ o
Iua111 = BesselI[1, u1*a1];
% G; m. D\" f+ d7 Z1 V) ~) }3 N
Iua121 = BesselI[1, u2*a1];
9 p- L, G) g) {+ Q
Iua122 = BesselI[1, u2*a2];
p( j8 q+ ?2 _+ v. F8 p, `' X( W
Iua132 = BesselI[1, u3*a2];9 _6 j7 f/ |\" i
Iua133 = BesselI[1, u3*a3];
6 W' J8 f9 g* @* w& Y* A5 {6 L
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;; j/ O# q) o: E+ q5 ?* }: P4 \: J! e/ M4 |
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;$ k; A0 _# C; C! O+ ]0 I+ N- w
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;0 |* q# M {; D: r) O/ {
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;( x+ |3 B& W, N! k% A' M
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
! t$ I! G* D; S9 x1 t/ x
7 I& n6 @% j l1 u, G
Kua121 = BesselK [1, u2*a1];
t7 ]6 `! c. I- _0 f' w/ p
Kua122 = BesselK [1, u2*a2];- q1 L' f! l8 U* C2 T) O Y# C3 D
Kua132 = BesselK [1, u3*a2];, i% y0 L\" P7 o( F4 V
Kua133 = BesselK [1, u3*a3];
( ]! m5 H2 V0 ^% `$ u# _- f
Kwa143 = BesselK [1, w4*a3];9 j) |# b( G4 m- E: {
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;6 C7 }/ H( J/ S; X/ h: v. P
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
# ?4 }9 m( i- I, ]3 I& d# M
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;# D& G\" F9 c o2 ~7 n% v
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
V1 q% S7 P4 f% M$ J8 H
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
* q8 K |' r6 H3 z( K! n1 E8 e4 o
, K& C\" q% C9 o
H1 = (betacl*Kwa143*
5 S\" m6 c6 E& B. b; h
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
# u( {; Q1 |\" ?4 W) v
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*6 f9 ~# |& M5 ?% m1 c/ `\" Q
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
6 t, X* I' }7 P# v# H
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
. ]; F; S+ [6 G6 @3 e
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: u( h# `3 Y7 |* t5 V& w
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
' p; M+ N P6 y: W0 E1 v! B
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*' V1 O# j+ w5 C% {0 k0 F; G% w\" i
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);5 T) V5 ?- H' L. G, U% M
5 b7 e* N; q! c, l4 v
H2 = (betacl*Kwa143*
' U; p& [5 h$ ~; ^9 c: D
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
1 ?% M! c\" N4 o- g
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
$ i3 `+ E9 {7 c8 `2 Z! ~
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
\" a2 `$ L8 z, p- O9 P3 c1 G
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
! D( y# }3 s/ G\" o
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
* o3 L p' n4 ?# S# m
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*9 [8 M3 {( f4 r! r1 n( t# x
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
( I- k# W R# L; U
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);1 H2 W/ \* j: s. Q, f- ~
' ~5 r. o' Q+ I# |
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*6 h6 A/ ~) ~8 b3 e\" d% N l- u
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*/ Z* m8 m4 M5 M/ `/ u+ u+ ^
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
\" P: q, p' s2 T) E
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*$ r5 Q# [5 B* G2 z8 b
Kua122 - ) F0 D ^' y5 f$ R1 c) E& U
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 9 R1 p$ U! j! o- P) Z; L% P# ?
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
' n; o- T* T7 r/ G) d l6 X
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);6 X+ l- P\" H4 J/ t3 q
1 g: c4 _! k7 ~6 J! i: ^! I
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
8 ^' L4 r7 e& f* T; _6 Y
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
5 O* R' O/ l* x9 B
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*7 d% R$ {8 A# b; d
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*1 s g3 h: A; i& t# C
Iua122 -
* R/ y. g2 m3 U: F\" }1 p
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
2 s8 X( i2 ]; D4 u L* K3 j
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 9 u( F4 Y! c1 _0 D1 g G4 }
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - / y7 K; F |! p6 V1 k, b
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);' d/ z% t2 l$ Y& [; A! J
8 u9 o+ j0 c4 _( C' y* _% ?# |0 A
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*( W4 t) I; d. U) k( E# U+ d6 j
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*# i2 ?! W! n U8 l: J) Z# Q
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*7 V: f+ G/ t0 m: C3 e. K' M9 m6 {) r# [
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -! D! \7 d& E/ B, Q
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ; R/ ^/ [: i- Y\" y4 n
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - - {) K% o5 `! l7 ^0 S
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - + T( N8 h9 Q; L$ U\" f
w4^2/u3^2*Kwa143*IIua133);
# X! m6 {! n+ ?) W# [; N
& t# X, z- k# t2 y- v( B
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
* a: D) ^/ \3 U. U3 O, e
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
i1 ?, r4 s0 }; S6 Z
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
m# s\" j8 e5 V$ o; T
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
- n% f9 y) I1 P- _/ I
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
4 M* }* C! w6 U6 _' G/ A7 ~
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - . |( f# @, y* r\" n. z* o: g
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
. q/ F3 U: R0 Z- _5 S
w4^2/u3^2*Kwa143*IIua133);$ A4 k! A4 f1 f
- h- T n% x- m. K ?
M3 = (betacl*Kwa143*
s. ^+ B; F1 }
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
1 o @) ^7 e( g0 W
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
1 J& N- X0 D/ Z1 U% o# _5 }
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - / O- J$ }8 ?0 } G5 o$ D
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132* G# |' N1 P. J# m! X1 B
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - . d T$ Q' b- d9 z\" T
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*: T W6 i- U; u0 }% z; ?& a
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
* Q1 {. D) U3 @) [8 u
w4^2/u3^2*Kwa143*IIua133);
3 O- v+ p+ t u8 o
9 D$ V* E$ D- j6 l
M4 = (betacl*Kwa143*2 C! ^8 k$ w# Z: D! m6 S
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
, t K1 N' s2 ~% N* M0 V+ A% O3 L
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*8 C6 P6 W) f' r\" ?
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
9 X( ~) I: t# V# U( s3 `
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
$ V1 Y+ W! N) G- y2 s* f& i
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 4 G8 \' s$ Y- `1 b1 ?, ]; Q
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*: k. j }0 B5 x9 ] P
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
1 O/ i0 J+ G$ W: b+ G' u Y
w4^2/u3^2*Kwa143*IIua133);. d: q8 D# `- `9 L4 }# N5 Q: H
' f' J9 f7 ^8 a2 \& L( V. k1 Z4 C7 o
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
) U S/ X* j1 o9 X2 l
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
\" Y% G5 l4 c$ S# c9 e, o' o
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;3 Y% {: ^& s: Y2 r* u7 I1 ~
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
; J. q' C% r% I, D( L
' ~, p7 t3 l8 ^! u6 h( O1 N
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
: ~1 K K: M+ A; N
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
/ G* H7 z/ u& D* d9 v* |
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
8 V; O6 f) F3 l\" Z/ d7 k
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;3 D9 @2 j! e T* w/ u0 U- Q
) r- M, Q! _8 t0 h b
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + $ \, \% ?2 v2 s# K2 Q& U) D( r
V1*M4);5 |0 s: R5 @. a2 v1 A& |4 d1 y$ V8 M
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
6 R* F, m9 U* V% i* l
V2*M2);
1 V% A( V* o! Y( x0 P$ y3 c
, a, v* g) @ Q3 ^\" q5 b- ~
x = xicl1 - xicl2;% @$ w! Q$ T) B9 F7 h `) F
x1 = Re[x];2 \% C; N( |7 p7 c# \8 n. Q
x2 = Im[x];
, a4 ?$ ?1 h5 I9 z i2 r& }) \
5 h7 }3 D6 k( F8 w& S5 p
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
0 p4 A& V, e }( ? x
]3 {\" r: K: v& j: [% C% Q( m
, q. q6 I2 m4 x4 D' ^; U

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