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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;1 }. t/ T8 Z9 m0 {
k0 = 2*Pi/lamda;6 V. V0 t' _$ h* \4 ?5 Q9 C J7 y8 j* Y
n1 = 1.4677;(*纤芯折射率*): o1 H! @) o+ e$ R4 e+ k8 o' u6 b+ D! z* M
n2 = 1.4628;(*包层折射率*); V0 e) D3 B7 F0 O2 f$ J
n3 = 0.469 + 9.32*I;(*银折射率*)
. o\" G B5 i2 M6 F4 A2 {/ V
a1 = 4.1 10^-6;(*纤芯半径*)
\" U0 q2 _' T Z- K
a2 = 62.5 10^-6;(*包层半径*)* V; p8 R6 z2 f- S
d = 40 10^-9;(*金属厚度*)
. U$ D: ^& ]. t7 m& S
a3 = a2 + d;' O3 C9 v: a# i6 P; X; U- }
mu = Pi*4 10^-7;(*真空磁导率*)
epsi0 = 8.85 10^-12;(*介电常数*); s8 p$ p/ h4 @
# r. b8 ?) [3 U9 u
n4 = 1.330;: q' j1 Q8 ]3 D
9 M) [9 L$ b8 P) a1 ~
neffcl = neffclre + neffclim*I;5 ~+ _4 e# ^& n0 ~
8 g* A$ c; \3 V/ g: p
betacl = k0*neffcl;
. \' {* h+ @9 r7 x\" D) A7 k2 h
omega = 2*Pi*299792458/lamda;
+ }, c: K( T% l; f( \, V! Y
7 G9 W. I( o0 c) A/ ^* a: P
epsi1 = n1^2*epsi0;
& g, o5 k1 A. B2 t+ N
epsi2 = n2^2*epsi0;' R X0 b! B3 o% ]9 T
epsi3 = n3^2*epsi0;' | F+ `7 n! D3 @
epsi4 = n4^2*epsi0;
) X0 E0 G* h. F: K q
& }' K\" `: I) {% M- b0 Y1 F( {
u1 = k0*Sqrt[neffcl^2 - n1^2];7 q\" q) o0 I; R( h
u2 = k0*Sqrt[neffcl^2 - n2^2];
& f: q& I5 B* E
u3 = k0*Sqrt[neffcl^2 - n3^2];) \) i2 X. D( L( I, p0 l1 J! Y& L
w4 = k0*Sqrt[neffcl^2 - n4^2];
! ?8 G6 i: G! ]4 o( b2 ?* m) P
+ W) V/ R! J6 d h
Iua111 = BesselI[1, u1*a1];5 e/ v- b: s9 H& U
Iua121 = BesselI[1, u2*a1];/ Y+ `& j+ f8 a: W4 ?% I
Iua122 = BesselI[1, u2*a2];
5 g: z\" S* {! p
Iua132 = BesselI[1, u3*a2];
! Z2 p. d: N7 v$ f+ `
Iua133 = BesselI[1, u3*a3];
2 C9 `; t' n M. m/ h
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;3 N c9 e: e+ Z6 G& [/ m
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
1 y$ z$ I1 `% ~
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
# A! G2 m7 _$ {
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;* c4 K# \8 c: T6 @: q' }
/ C4 m1 H) Z1 G1 w/ \
Kua121 = BesselK [1, u2*a1];% i7 p/ e8 x9 Q! e, C, E7 q# v
Kua122 = BesselK [1, u2*a2];
( s# t: u) Q: A; u3 |
Kua132 = BesselK [1, u3*a2];8 F1 o8 B5 q0 C1 s; h
Kua133 = BesselK [1, u3*a3];2 H7 ~) Z- `' h* m
Kwa143 = BesselK [1, w4*a3];
3 R8 B8 V J* t' z, w
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
, W/ D( b: q) r$ k0 H
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;5 I2 M( Y& t6 n9 u7 ]) u% f
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;# E\" _ }7 {1 ]+ b% @
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
1 H, {/ S ` f; z% A
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;) a- p0 I' {$ d4 d: t' I4 T
5 g9 t: g7 [$ _. ^2 A: D$ [
H1 = (betacl*Kwa143*
3 D5 D% }$ v# a3 C
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*7 M5 Q! U5 s, i5 W+ a; [
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*2 x1 \5 p\" l9 y0 a
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*$ `6 Q |+ ]# B3 D2 B: ~' B9 T1 H
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
$ h. D# U3 ~2 r, @
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*! e2 T; v \+ Q3 _0 Q
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*. n/ m1 R* y W& _$ N
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
5 M# i9 { }+ K3 E1 Y
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);8 f, t7 ^! B8 H; q' S2 x
* W) s+ C0 C# _8 t\" B0 c, H1 d
H2 = (betacl*Kwa143** d0 a3 |0 r$ A
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*& C: t: k* @6 N) C5 i# S
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
& u& u4 g- S# }5 I& H0 n2 m
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
6 M/ C\" j {2 p, }) f
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*) A; D\" p. O3 U6 J+ v
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
# E! H7 L/ }/ I2 U
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
4 }+ N/ _. S5 e8 Y' y' m1 u
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*0 i$ o2 g4 I- Z: ~\" @; q
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; v$ }8 v) f1 d, `) e& p5 ?
# B3 e% I: J0 _\" |: L& H3 K9 @5 b
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*: Q( `2 L3 I! X' b5 v: n/ z1 J1 S* X
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
& D1 o) a# G8 l5 O2 C, Z
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*( ~) ^# y% l) Z$ i5 X
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
' \, g) f9 H- z( q( o
Kua122 - 0 E, [0 e+ X9 ?! |) Q1 W
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
. b5 R\" F/ |+ ~- m3 M8 ?
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
( R: V1 V! Q6 m9 l& D
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 1 A x) B$ F- X& ^3 d5 A0 n% ?; I
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
) H3 l+ d3 q- W# z
\" \2 v: A4 Z3 M2 [% J) O\" i9 |8 R
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*/ t. S% h, [8 z( A
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
; R8 \6 |\" F4 ]6 H7 `' c$ k& J* i
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*3 H3 Q5 i6 b6 O; H8 C
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
& Y& A* q$ e6 w8 M$ t2 I' |1 J5 p
Iua122 -
0 p: g4 z8 G1 k+ c5 x+ d. L
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
2 Y0 {4 T! q9 Q
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
& f5 d, v- t$ z8 v
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - . S; `2 {# A# V* Z
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);: u! C: _8 i2 Z: T' ^7 L! y
8 h6 |# z6 w& V; X; o- w0 S b: o, |
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*7 \% |9 D; l) d2 F3 Y' K1 a
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
: Q: R/ o/ b5 M' e. c$ f5 J! W
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
5 T* M6 `2 T1 T3 n# ^. P! d, r T
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -( ?) x2 A4 f& F( r( ]
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 3 H) t2 ^5 E2 _ e% l
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ' k2 U- d: `+ B! V
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 3 T9 o* @: u( h- `
w4^2/u3^2*Kwa143*IIua133);9 |# y& R. j, ^
* d$ f* t+ a/ u4 t
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
9 f) l) A& V0 O
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*8 S. g' v1 R* C$ q% _
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*% `4 l1 o8 o8 h+ x K8 b
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
9 z6 G7 v8 _ }6 Y4 q- {, ~+ y! t' f
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ) Z% O5 G/ m\" U7 p& W7 @- O
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - : y5 ]$ [: b. b$ ^% B4 K& J
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
! |& C( Q2 P! U) ?6 _7 [ y
w4^2/u3^2*Kwa143*IIua133);! P: b+ T% h0 }* O: l. I, t) f
' S x3 _) X8 D: ~! z3 i. N1 M
M3 = (betacl*Kwa143*
9 G$ g7 v0 o8 o+ F1 |# g
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - . B1 p( K& g( }
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*+ B! n( z9 P! \
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
/ r6 L$ q' n( q* k6 L# I
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
) A! i3 ~! V3 s' ]% }\" A% V
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
4 e4 S3 E p A5 a6 d+ v, {
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*& i5 U; n& n; h/ W/ A/ f\" t
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
: p/ G- p! T0 R/ S$ b
w4^2/u3^2*Kwa143*IIua133);7 M; t0 j; \5 F5 [0 r3 S: u$ D
# M( X7 k( M8 m9 I% C4 p1 W
M4 = (betacl*Kwa143*
\" v/ u, D% B0 r1 {' H
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
5 S: g- _; \, S/ T/ ~
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*\" c. q% j2 A2 @
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
3 i/ ]' W6 q2 {3 g\" V; g# {) X
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*, }4 f8 R. g! n( M. Q& b
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
3 r- S! H. V4 Y0 @1 ]- k\" B
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
3 X2 s* q+ C; I( z$ l
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - % W# `- b. e* C
w4^2/u3^2*Kwa143*IIua133);
& ^+ t\" m8 C9 N3 {9 D
7 A/ O! }6 C\" ?7 y7 }9 b5 }# T
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
7 t9 Z3 [: c, Q3 ~( K0 U) Q
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;* U5 m+ S7 e7 Z, C. |4 C. ?
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
\" o9 Y5 g* o) N r4 ? M2 O1 Y
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;/ r+ Z7 U6 I, q+ G0 [5 b' U
. h, u. T+ @; |# h
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;4 L0 @; Y* v; r' g7 ?
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;: T4 X0 z% |# }, K
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
$ [# D5 x2 l: X/ a: F
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;# k. Y0 z* ^/ N! L' _: W
6 o$ k Z) w9 j0 L2 j. V# Z. g1 |
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
W\" v0 H6 M6 p/ t- s7 T0 F
V1*M4);$ Y- o- Q, B; n3 l$ u
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
' m) S9 z* u\" T! U# C
V2*M2);
! x; M1 O$ W, w7 i o& S
: |7 S0 W- A5 E7 a% S( \& G
x = xicl1 - xicl2;
4 x8 m\" M/ p0 I9 E: f\" h5 u. Z
x1 = Re[x];
: O- `7 R- O5 i+ V
x2 = Im[x];$ b! U% k4 G3 {* ~
8 G: k7 Q4 S' U! b( p' l! w
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
6 U/ M1 {! L& n x/ i) U! C- q
]
7 r# Z7 G# P% G- |
+ l8 n( Y$ S, Z6 v5 _4 ]

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