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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
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- lamda = 1.55 10^-6;
8 L M. Y4 }/ _( m' Z - k0 = 2*Pi/lamda;+ D8 p6 T/ M4 s4 T
- n1 = 1.4677;(*纤芯折射率*)
9 b' }, Z0 C' v* ?0 ]# d e- ^ - n2 = 1.4628;(*包层折射率*)$ {3 D i4 A' \2 V* \% N, {
- n3 = 0.469 + 9.32*I;(*银折射率*)3 q6 q: h( x& T7 Z
- a1 = 4.1 10^-6;(*纤芯半径*)
# G2 z7 ^. m8 A0 E4 Y - a2 = 62.5 10^-6;(*包层半径*)$ v( ?9 h) m, a4 i6 C
- d = 40 10^-9;(*金属厚度*)
% ?- E! {! }( ~8 S% }# Y! Z - a3 = a2 + d;0 H. |; i6 Y6 ^7 \' b0 t( r
- mu = Pi*4 10^-7;(*真空磁导率*)
5 d+ y: y: I6 [6 `4 y- ]' c - epsi0 = 8.85 10^-12;(*介电常数*)& D* T( S\" ~) O2 m
' z1 ~2 H' Z9 O! \% V+ p [/ ]- n4 = 1.330;
& ?; |3 [ E$ G7 R: g\" j8 j
/ V# `3 h( z. g/ Q- neffcl = neffclre + neffclim*I;9 ?( k6 m2 @8 V. r! _/ D, a
- : ^+ v& t0 M; ?- C8 U
- betacl = k0*neffcl;
! a9 L' _9 y* z0 X7 f - omega = 2*Pi*299792458/lamda;& A. `2 R9 z& Y2 f$ c8 W
' Q+ v0 _3 G9 ~- epsi1 = n1^2*epsi0;& u0 R0 ?/ e/ w; G) l
- epsi2 = n2^2*epsi0;0 R0 ^) `4 r) H2 W' X\" f+ k
- epsi3 = n3^2*epsi0;1 G. y1 M# f& y4 q1 u
- epsi4 = n4^2*epsi0;$ k6 @: a7 N# z5 o# K+ h8 j
- 6 P+ T5 I; l6 j; W# Q$ ~4 N
- u1 = k0*Sqrt[neffcl^2 - n1^2];% M5 B0 P/ a, Q- i
- u2 = k0*Sqrt[neffcl^2 - n2^2];/ _5 ]& C! p4 h( Q# c1 a( Y
- u3 = k0*Sqrt[neffcl^2 - n3^2];
Z% U l+ {7 O) K - w4 = k0*Sqrt[neffcl^2 - n4^2];
4 s4 `$ q, E. n. W, e1 C# n* J - v, i* G; P' {/ c) C# e0 e
- Iua111 = BesselI[1, u1*a1];
; p8 M, }9 i# K. P- ^3 a - Iua121 = BesselI[1, u2*a1];9 O& k2 I' i0 b# {
- Iua122 = BesselI[1, u2*a2];% s `/ r. q9 Z8 l. E3 Z
- Iua132 = BesselI[1, u3*a2];
6 I& A0 x! J7 ?0 e* i$ p - Iua133 = BesselI[1, u3*a3];
' U: x1 Q j) o6 A - IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;\" G8 ]3 w: ?. P4 c+ E
- IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2; z b6 h. J0 |/ o& h) b/ U7 M; G4 U; w
- IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;+ `; b& K3 q Y+ }# Z
- IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;# v, t, z w8 h) ~0 f
- IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;5 m) }% Z6 u$ [- R
- / z' E: m+ }+ Q+ _
- Kua121 = BesselK [1, u2*a1];( a7 A' D6 L2 I2 \- C% _
- Kua122 = BesselK [1, u2*a2];
: ^$ t, ]2 r+ R - Kua132 = BesselK [1, u3*a2];' p3 W& B$ X( J/ h4 G- c
- Kua133 = BesselK [1, u3*a3];
. t5 R% o! J3 R - Kwa143 = BesselK [1, w4*a3];, n' U+ y' v. D5 K3 e/ m\" p0 d
- KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;+ J0 m! I5 S7 I' t0 O5 }; p: p& a
- KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;# D0 R+ N( U( L5 D0 @9 s/ C4 v
- KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;$ z( h+ h- J4 Z, @% m8 V$ F
- KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
0 _; V P0 S/ ~( Z1 V1 A - KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;3 j6 p3 r\" G* b8 T Y
8 w! Y% x, r/ M& t- H1 = (betacl*Kwa143*. L, u+ C+ |! P' ]+ h& u9 `
- Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*2 @5 x. }/ J- Z# _% N, y6 v
- Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*# T# C( U' d) B\" N
- Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*- s\" w+ f+ x/ @) L2 n9 S
- Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*( q+ }# l' h n! n7 f
- Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*. j& r/ c/ i4 d- v! }
- Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
5 v. z5 ?' ]! C6 c3 b - Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: p6 ^4 O* A# c- z; F! B( Y; M t
- Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& C- S) z8 V. A% X I; |
- ; ~8 \% E$ u! t0 P# A\" l
- H2 = (betacl*Kwa143*+ q3 ? |' E6 N2 @. Z0 i
- Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*9 J. B3 x f* w9 y: {$ t# R
- Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*. a\" E: M. v; E
- Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
5 @( p* B z9 A: [9 q J, b5 T4 C - Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
} e7 E! c% a+ j9 `- ] - Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
7 y [- R3 R- P - Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*3 b: G G: S7 r. [
- Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
9 _/ Q7 h& F- p - Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);$ b; z4 P( P\" F& [$ x: t. B2 ^
7 |. c+ u. ~) f$ K, o: \- H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*. q2 {. v' \ {3 y6 J3 L% o
- Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*; q, i4 C\" f8 o9 }1 _
- Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
$ e. Z2 j, B( [ - Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
0 w( E- t( ]0 Z: s' l5 l C - Kua122 - \" y* @9 n! o# i; `
- u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
9 v3 m6 o, d6 U0 j3 Z - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - }% e( o; i+ ]8 ?' T0 S; F7 p
- u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
b2 l0 [! n) s. P4 k: A ]1 q) g! t - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
; T% l3 q9 q5 o/ f) y
) j( f# v$ Y6 b8 Z. v- H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*0 B, j+ @6 B1 I* f; u3 G& e
- Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
; D/ k. }% e8 U4 c) `, x- [4 u - Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
2 }5 U' i$ N. X( [( K9 Z- \% w: i - Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
. I) y, j$ l! `( U5 x - Iua122 - 0 O8 y: q4 I* P, ]
- u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
5 j( a4 c7 W4 O\" v ? - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
8 s2 c! t/ o& J9 r& | - u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
0 q* n: R\" ?3 u- K @ - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);* \5 }& U, G/ O% E) S4 o6 }
+ L$ }! m7 {& S, i- M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
2 f, V6 r3 i7 R - Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*7 I& B& S3 p/ d0 a2 ^+ s7 p% }) x
- Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*$ I\" \0 c( D\" h4 V) p5 Y& t2 a
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -\" b& n7 v) N\" p% H, F
- u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 3 O- w5 T! w ^2 @
- w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - $ t9 o5 V7 I2 k6 D0 [
- u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - : U9 e\" Q$ ~5 O% S9 V! W
- w4^2/u3^2*Kwa143*IIua133);) X) X( @+ W+ O$ P3 @! k8 P
- * A: S, E2 r0 y7 L0 b$ G% k( G
- M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl* k4 \/ l8 }* U; O w- e
- Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*' N/ i1 |3 t. R5 D8 }; H! c
- Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*( m: q$ I\" d3 ^8 E% ]( @
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -; W+ c+ w7 D\" I t! @
- u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
4 v: z\" i7 o: o8 n: ]1 L - w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
8 \. V8 V7 N+ k, t6 S) z6 B - u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % m. W4 b3 A4 E- S
- w4^2/u3^2*Kwa143*IIua133);
& A\" E3 L3 ^0 m! B- G% C - 8 f, p! O2 x. s$ B
- M3 = (betacl*Kwa143*( H9 o: g\" s3 s7 \8 f; e. i
- Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
t5 Y) l- V1 @* s/ v - u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*( A0 I, ]. O4 ?, z/ `
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
$ N: d7 d- C( ~/ C& R2 T5 { - u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*8 x* I2 n6 |, K\" i% G+ i
- Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 2 N( d9 i* G8 k# @
- w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
' B% Y+ r0 y/ i I\" C$ N - Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - , c9 J4 Y% L2 q9 m
- w4^2/u3^2*Kwa143*IIua133);
/ e2 O' ]5 A( C8 ?: O
$ a* s; k- \4 F8 p& ?- M4 = (betacl*Kwa143*# \* I1 j( C/ ]# }+ e5 p2 ^# A, c
- Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - & P7 M7 }\" p6 y& d/ o, ^
- u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*0 p* Z3 d5 Y\" q- s1 p. J
- Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - * G\" w% V% |4 j& t
- u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*, P3 ?+ @( Q* H
- Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
* \6 X t- ^( e\" _1 _ - w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
; X7 O3 c5 t% Y5 L, t' y - Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - * i$ x) y4 U4 c6 z7 i* {
- w4^2/u3^2*Kwa143*IIua133);- K# }3 j% p7 i. S& V\" A\" d
/ d6 {! L9 L, N; ^1 M- R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
& k# M1 h, [1 E0 _ - T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
& {1 L1 W, _& S. S - U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
2 b& h! K& A G; @1 | - V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
; V, V$ F\" G% J9 C3 I, h
]6 p3 p' @# Z: `8 L\" C! R: i7 s- R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;% W5 i2 }6 c4 k! D
- T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
+ G, G* W' b7 s\" m2 j6 e - U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
) F) z. E* \* e) \* |6 h - V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
4 [2 y9 J: u( J* c: k - ' x+ ]$ q, s' C
- xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + # W+ i\" {6 g' S! G1 z ]- d' v2 @
- V1*M4); j- X0 \5 R9 ?: q. _
- xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
% ?7 g8 R$ ^7 B- \\" s* a\" I - V2*M2);/ `$ a: P4 y/ |* l9 T
- / U, w, t( J; l7 ? w' n
- x = xicl1 - xicl2;- |. ^% X6 H4 F$ c0 Z6 ^# y% Y [4 W
- x1 = Re[x];
* N& W: v2 S+ f* C: j - x2 = Im[x];
% x( q6 }' ]' [ N* b
, p9 e8 m s* l8 p* ]1 r* h- FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];0 B' K# L8 f9 m: P' F0 y/ V' P
- ]
2 `: l) }0 Y; N% O' B8 w - - n: g. u5 T( H2 E
复制代码 代码如上,结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}( [$ \# b7 p1 N2 F$ k) U
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
3 ^2 |! F7 Z0 @换成
$ b- S- @& u' ]# l# I5 h n" I- YFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
* G7 Y7 i5 x- }1 i+ X. e FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
2 k7 f7 t9 l$ s0 ?2 H ], Y0 s$ t) w0 D9 v" _) m: H! F. D% p) t
就会出现# ?; P% `/ ^! h
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.( v3 t x _3 L0 l! u
3 o5 {$ C5 n5 a) m6 `
请问是怎么回事?
8 e* b# M0 o9 K/ u9 T4 V$ o. c$ v4 q H9 d8 w: F
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