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升级   25.26% TA的每日心情 | 郁闷 2015-6-6 15:06 |
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签到天数: 5 天 [LV.2]偶尔看看I
 |
- lamda = 1.55 10^-6;
9 y3 n/ l& `6 O& s, i - k0 = 2*Pi/lamda;1 o\" O4 [! F( d
- n1 = 1.4677;(*纤芯折射率*)
+ ^1 B2 z- F) X, ~6 j - n2 = 1.4628;(*包层折射率*)
/ e% b; w0 Z0 ]9 @ - n3 = 0.469 + 9.32*I;(*银折射率*)
( U& R' d1 u/ v. T; c - a1 = 4.1 10^-6;(*纤芯半径*); v7 ~4 p% S+ z\" t% M7 w
- a2 = 62.5 10^-6;(*包层半径*); M5 i0 a2 `\" p5 o# S3 q
- d = 40 10^-9;(*金属厚度*)\" o2 m7 x5 g( r) _, r
- a3 = a2 + d;
1 B* W3 N& J' a. L+ |( [ - mu = Pi*4 10^-7;(*真空磁导率*)( R8 E2 t6 T+ c2 i: {8 a
- epsi0 = 8.85 10^-12;(*介电常数*)9 C ~* X( A! ~$ v+ m* S
- + i7 H3 P. K G
- n4 = 1.330;' }) ^; K2 i1 a+ N1 l
- ; U' ?4 b* m\" S& f' ]9 S
- neffcl = neffclre + neffclim*I;
: f8 K5 Q4 ?1 ~' ~1 n/ h% j
* i# \- F; h1 F- o) v9 C4 u- betacl = k0*neffcl;) o1 d. K- l2 I0 v$ Q
- omega = 2*Pi*299792458/lamda;* q/ l# U+ O! X4 k' B, q
- + s- _4 x6 m! ?& ]\" G
- epsi1 = n1^2*epsi0;& R1 N\" L& Y( ?- L6 D1 P5 L
- epsi2 = n2^2*epsi0;5 g! ^( Y1 `+ }+ }; D
- epsi3 = n3^2*epsi0;
. E$ F- R\" H5 z$ A0 J - epsi4 = n4^2*epsi0;0 ^( R/ `, b5 l$ t' I$ Q( z* k
! g2 ?0 O. Q, o) K- Q9 m1 u8 m5 U- u1 = k0*Sqrt[neffcl^2 - n1^2];
. S# S% }9 {\" s$ @: J - u2 = k0*Sqrt[neffcl^2 - n2^2];& `5 p) a4 D4 X4 R7 Q% b+ T3 M
- u3 = k0*Sqrt[neffcl^2 - n3^2];
. ?2 f. K! y0 Z, v - w4 = k0*Sqrt[neffcl^2 - n4^2];1 U7 w8 a* m1 `: C; }9 D2 G! L+ }' X
- \" h3 c5 B$ x' G8 J
- Iua111 = BesselI[1, u1*a1];* B! i8 l& e8 P\" I
- Iua121 = BesselI[1, u2*a1];
. q- X) R& Y5 Y2 }8 k - Iua122 = BesselI[1, u2*a2];
6 f+ y& H/ x& | - Iua132 = BesselI[1, u3*a2];9 r* f; D. q! ?9 u
- Iua133 = BesselI[1, u3*a3];# I( w# L+ q2 N, N' ^0 n- K- ^
- IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;* ^- t r* u5 {3 ~
- IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
2 |5 V8 ]; D* d0 F+ E& v0 e - IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
4 T( N' p) m% n! |% E2 v - IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;9 J' W( Z1 J8 } d5 {. ?\" ^& l1 @/ I, f
- IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
& y5 x3 V8 X/ U9 v
: R) x\" u* l/ E# I) V+ @- Kua121 = BesselK [1, u2*a1];& g5 l8 _% g% }7 f3 I
- Kua122 = BesselK [1, u2*a2];\" A( x\" n4 Z* E0 b
- Kua132 = BesselK [1, u3*a2];0 D5 G% V! u\" S6 o' a: [
- Kua133 = BesselK [1, u3*a3];
0 v5 h. n$ H6 E( X/ q5 s9 \ - Kwa143 = BesselK [1, w4*a3];
+ Z3 h$ V- `) T! \ - KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;9 m0 q/ F, {) W# h* k
- KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;# d\" K5 W8 t o\" C G
- KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
8 Y7 B( a+ B$ k3 F+ r) X - KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;) D1 g6 `, w* I* u; I
- KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
7 ^7 f; W2 t8 V1 f% H0 x' q
6 d! ^% Q0 Z/ a8 \. u$ S1 }& h- H1 = (betacl*Kwa143*( z% o) ?9 U+ l8 @ j3 ?$ N# G
- Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*; l! ?. y% t( o/ G
- Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
0 C+ p3 ]* f6 G3 \ - Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
1 Z6 x$ o, B+ E/ r0 J* S4 N& E - Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*, e; {' z\" X, ~; o. t6 s g
- Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*7 T W! ~, U- P
- Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
6 n# a& \8 B& G1 V7 o - Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* }1 ]$ K. d) B( |
- Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);$ K* s' D7 ? \1 w8 ^
: J; [' L; D3 }7 r' ^7 [: o. ^5 Q- H2 = (betacl*Kwa143*
1 B1 y: T* N4 G+ o* Z - Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*% k* [6 ^4 D6 H( j( ^% n2 }. [
- Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
- Z1 q, {4 h; ~0 R: p! _0 @, u - Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
n3 y2 O; E0 p - Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*' v. @, e [* M& c; G$ \8 b
- Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*) Z7 Y9 M6 a+ D2 u
- Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
. U& i9 v- I9 R) D' Q - Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, B! ]. M& M4 n U# u
- Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);' G+ [% U- T4 Z7 M' @+ e- g
- + ]. ^3 s. C6 v2 c: Z\" \
- H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
: k6 m4 W0 u1 G5 v - Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*9 J\" o2 ?& `' Z7 k; T) ?
- Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*# Y4 H$ E; E; B6 _. }( g6 ^4 t
- Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*2 e4 v\" }0 G! }1 H8 f
- Kua122 -
+ d# O9 M; V5 y0 K\" {! ?9 v - u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
5 U2 ^ m9 x a7 N - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 3 u( R* B\" L0 j, M4 E- ~3 H m3 ?
- u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - * w7 i+ n) t( l+ z+ T$ H' S$ t
- w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
$ o! m\" B5 \2 @' C/ X1 ^ - & S$ }; O( I, Y4 K
- H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
& ?! ~8 C1 j' d' f% [0 Z$ ~$ ~ - Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*: g! I0 M; t; i
- Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*$ x* F$ m W M _4 C3 D+ u
- Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
$ r( Q' y2 {1 N+ m; I$ ?# I' Q ` - Iua122 - \" }' v d( s4 @
- u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
$ E$ }$ X* O( t5 {- v - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
; P5 X( U. W x+ D/ H. C+ \* ~) Y - u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
3 H; `# i$ S$ H' W' p5 k - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
h0 N0 N5 {: _2 ?
$ |0 ]0 G) ^+ Y& D) Y. N+ z# |* \- M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*& ?1 c2 f& i# f
- Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*% B7 x5 I7 R# v
- Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*% K% U& H- C9 e. I
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
! s\" O& u3 I) c) u+ v - u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
, ?* y v- d8 P. D8 p& y - w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
6 l2 e7 B7 E3 F! Y7 S8 n - u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
- U c' f! y\" L' u$ G\" j9 R: \ - w4^2/u3^2*Kwa143*IIua133);
/ ?: z- S2 V5 e3 ?) @ - & c2 d! i+ w! e/ I$ J# \
- M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
, u3 I! j\" t$ ?# Z# k4 Z - Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
]) H! Q, H0 |& M3 d\" N9 h - Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143* N# u& n6 F\" h& ^- I2 o8 h
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
: F8 Q3 K/ }# v. O9 Y' a# Q - u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 3 I8 Z) b3 A& `: I0 ~
- w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
! G1 @+ t5 h2 D& @/ `! j/ S5 h - u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % d\" A$ ~% M* e- S; Q; [
- w4^2/u3^2*Kwa143*IIua133);1 s7 T0 J; b9 v6 V0 Q8 r/ f+ b
- 3 Q f, O% P# j) C( l+ Z
- M3 = (betacl*Kwa143*
4 Y# k- q9 y3 ~5 k$ \. ~ - Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
8 ?$ y0 [* n8 @' L; z+ @; } - u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*\" {$ s8 v$ Z/ `% v/ T
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 8 Z+ R+ K! p0 Q. R& H# w
- u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*' h+ c: O3 P& t+ j' x
- Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - , r4 r9 ]; P6 O* B0 i
- w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132** E5 @' E3 H9 A2 j- y
- Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
# q9 A. c! p. |: O - w4^2/u3^2*Kwa143*IIua133);
& i( e6 |# M5 }; t) @% T& b$ N - - j% d( W% `% H! z9 v
- M4 = (betacl*Kwa143*1 Q) W) \6 [\" m* F\" d8 p1 b( w$ `7 Z
- Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 7 P3 S\" k$ }. d$ F K
- u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
. y i5 E4 M, i& D* ~ - Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - , Q$ V' F% n0 Y5 a
- u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
: l: T0 P3 z* J( v$ M* c8 M# A& s4 T - Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
9 m% @: Q' d& v\" y9 n5 A - w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*, c! A1 e& K) O
- Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - X5 I2 }) f5 A9 A\" D9 V' T
- w4^2/u3^2*Kwa143*IIua133);
, F; d5 \8 c- j5 ~! g9 j - \" q& o! I- W+ F5 x\" R$ t1 C8 s
- R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;- p\" N7 ]7 Y8 b- v- J8 O% R% Q
- T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;- x+ L9 y$ |( e
- U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
4 m( [+ u) |# ?7 x6 b6 j - V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
1 ^5 ~1 z. A+ n7 \% ~0 S: b - 3 }3 @$ Q1 ?! F
- R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;; U2 n, ~; a8 o! K* E0 \8 u
- T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
$ h1 O* i [ u& A1 X - U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;: C' R1 O' O: K- c
- V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;; ^9 {6 e0 t7 k! o; C
- ( p( H# _, c5 p7 z! g0 G
- xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
0 @$ z0 |4 i* R1 [, v# X+ O, B% y - V1*M4);
9 Q- W2 E0 c% K' T! | @ - xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
4 `% q$ a+ U+ W$ P; P - V2*M2);
# }4 S9 E6 L( g3 \% q - P) X, j+ I$ o& i% h' v7 v
- x = xicl1 - xicl2;
7 B8 q/ V% R# B, k& h: v5 O; R, q - x1 = Re[x];
3 z) u& A\" f& n6 }- c - x2 = Im[x];
5 k: n4 Y. }: c
3 R) E; h w3 \5 I- FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
0 u4 l5 e6 _! h! o+ P) R - ]
\" _* G4 f6 I8 y6 R3 ~ - 2 O+ R/ V0 X) Q; @
复制代码 代码如上,结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
# t/ K7 y, [; O6 T. C8 \但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
2 o/ S* G- ^1 F x. q7 g _$ H& Z换成
1 \! W9 N8 Z0 G+ D; J1 F+ [For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;1 N2 E! T# t. \4 T0 p8 i& m
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];) ]7 s& t6 T8 O3 N3 F
]
1 ]4 M* C8 V* L4 G1 N# N( w就会出现
1 `6 S4 P0 N7 b# M2 e1 iFindRoot::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.
% u8 \- \* W: f# G" x6 V- o' N. C& a) t; D# P7 P, n" F% G: ]
请问是怎么回事?
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