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  • TA的每日心情
    郁闷
    2015-6-6 15:06
  • 签到天数: 5 天

    [LV.2]偶尔看看I

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    1#
    发表于 2015-6-2 12:57 |只看该作者 |正序浏览
    |招呼Ta 关注Ta |邮箱已经成功绑定
    1. lamda = 1.55 10^-6;* M7 `3 b+ H: I; Y
    2. k0 = 2*Pi/lamda;
      4 Z' V, V; s# @3 f! e\" e$ t5 |
    3. n1 = 1.4677;(*纤芯折射率*)+ k4 j$ X4 W( Z* F) R
    4. n2 = 1.4628;(*包层折射率*)
        i) r  V% O' o1 k5 q
    5. n3 = 0.469 + 9.32*I;(*银折射率*)( O* ~6 u& [+ `3 ~6 t: P\" D( g/ l
    6. a1 = 4.1 10^-6;(*纤芯半径*)
      9 a& g- E' }  `& L$ E  z2 ^. B
    7. a2 = 62.5 10^-6;(*包层半径*)- x; W) ^8 f5 a3 l- u
    8. d = 40 10^-9;(*金属厚度*)
      & o4 K# w5 Q, X1 A  R7 g
    9. a3 = a2 + d;: W. ?0 `6 t* y' {' n+ S
    10. mu = Pi*4 10^-7;(*真空磁导率*)( s  N7 O  g7 G3 b, q# ]
    11. epsi0 = 8.85 10^-12;(*介电常数*)# ]% B  L( j! i* Z

    12. ' V; h! i! y0 c' V; w: B' b2 F
    13. n4 = 1.330;
      9 \* v( O, S7 f3 m
    14. 2 T+ i\" {$ W, Q9 t& B2 U% z
    15. neffcl = neffclre + neffclim*I;/ I2 e  F% u, r) ^: u+ c7 Y! h7 T

    16. 9 R- G5 f% c4 k4 o7 {2 w+ y
    17. betacl = k0*neffcl;
      6 ?/ r\" p( y. l) K$ z( w
    18. omega = 2*Pi*299792458/lamda;
      6 X1 J  ]+ a! m2 ^

    19. - f6 `6 H- p% B
    20. epsi1 = n1^2*epsi0;
      + y  Q. y$ p: D9 N3 Z
    21. epsi2 = n2^2*epsi0;4 E' D7 J5 y* n4 J8 v  N  S
    22. epsi3 = n3^2*epsi0;
      * K5 i- Y& c5 q; d& R4 h$ U
    23. epsi4 = n4^2*epsi0;
      . }4 U; P: B  L& Y$ t( G

    24. % F\" \) ^% G9 x3 p% F8 E
    25. u1 = k0*Sqrt[neffcl^2 - n1^2];
      6 N. H/ ~; G8 o) ]- u
    26. u2 = k0*Sqrt[neffcl^2 - n2^2];
      - t5 A\" K% a% Z* k7 P- \
    27. u3 = k0*Sqrt[neffcl^2 - n3^2];
      . q; U( [6 p: R; R1 V% `
    28. w4 = k0*Sqrt[neffcl^2 - n4^2];7 q6 A$ Z  n# ]3 c\" B0 n  h

    29. ' }9 R3 ^6 |& M
    30. Iua111 = BesselI[1, u1*a1];
      1 T6 k/ J1 s1 D( B- Z( }- x
    31. Iua121 = BesselI[1, u2*a1];
      # |; }( M$ |' @, r: P! E5 H& Z. j1 J# [/ e
    32. Iua122 = BesselI[1, u2*a2];# X, r: Y: F* c\" t\" H8 [: b
    33. Iua132 = BesselI[1, u3*a2];
      ( C4 Z4 _/ L\" i1 y( Q: [  N9 Q
    34. Iua133 = BesselI[1, u3*a3];0 z  {5 ]7 ]* J: V. q) y5 P\" c) Q3 f
    35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;/ F4 l8 E& U4 ^% m( K$ Y
    36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;5 X& k3 A  d, n& F: k/ O' [- i
    37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;/ b/ B\" v# e$ s: G\" \
    38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
      0 R3 O+ d$ w3 ]: a; S: ?, D  B
    39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
      4 F; L\" [6 f- `( U9 A7 b
    40. 8 }9 z9 j7 i% a2 u# e  x  n
    41. Kua121 = BesselK [1, u2*a1];\" J7 s; L; ?$ d4 f9 U6 s
    42. Kua122 = BesselK [1, u2*a2];8 s! W- V+ l  D. _: N* ^
    43. Kua132 = BesselK [1, u3*a2];8 |' }+ l* {) {7 j' K
    44. Kua133 = BesselK [1, u3*a3];6 ?+ f1 S  u& E# ~8 L- T
    45. Kwa143 = BesselK [1, w4*a3];
      8 ]- h# R8 H1 z/ C3 `8 t
    46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;. I- V5 G$ C\" g& V. K9 x5 M5 s: C
    47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
      6 Z8 w/ t& h  U5 U
    48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;* l1 i  Y) G, U# @
    49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
      ! B8 K5 v# g$ p) h; p
    50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
      % n2 |; s, M. _9 e
    51. , @+ C  p( d\" K) W6 u- B
    52. H1 = (betacl*Kwa143*4 ~% Y5 R0 m$ ]3 Z# N; z  I; c
    53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
      : \+ ^! D9 f. k5 K
    54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*3 s  B: {9 M) {. J& a, g0 k
    55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" Q* d  i4 u5 }+ e' `# A* {
    56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
      # e; u  F1 m- e1 v6 S& |
    57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
      / W' b- Y- w7 T0 }8 h. z
    58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
      4 g8 j+ A1 p3 S; h. r
    59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*& V- I7 h+ j- G# {% u+ v
    60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
      , P/ o) y$ F2 F! p4 h
    61. 1 }0 y/ W& ]; a! v; F+ W4 d; @4 M
    62. H2 = (betacl*Kwa143*% E1 B9 u& ~1 S0 g\" @
    63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
      : L' Z) i\" T0 \) E
    64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
      $ l( [/ M  g, B9 }
    65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" N% b, v5 r0 V+ z
    66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
        J/ v8 H: y7 V+ H0 D\" p. `# |
    67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
      1 G' L0 i; g) ~\" I
    68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*$ L4 ^+ W4 b+ d& |- w0 X
    69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
      9 C6 K\" L7 w+ x
    70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! Z- G. p. P) H6 J9 h+ W
    71. ! }$ q& C8 L, D2 t) y0 _* G$ A
    72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
      - F9 c6 K* W) t
    73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*4 `4 q- ]: G; H/ A
    74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
      ! x- ^( H8 f' N% V, {1 I
    75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 T7 O7 _( q0 f2 ]( e3 a
    76.        Kua122 - : a) d7 Y4 {' M$ x& k/ x$ ^- {; r. X
    77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
        z5 P# j; F3 S5 q% X# r1 l
    78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
      # E  [& s; }& m9 K* F# B, v
    79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - : B2 X2 I  N0 F4 F2 I% W# L
    80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);  @. s6 R  Q2 d# g  j0 _$ Z# ?

    81. 4 _( K3 Y- q2 F5 g( ^
    82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
      ) H9 e. Z( e; H$ S
    83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
      # @% h2 L! K5 ?. ^( q. J% {6 L( @  R
    84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*- Z+ l- c* p8 r5 ^) ?: _. c
    85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*7 A2 D, t: p. E2 u) e
    86.        Iua122 -
      9 ?) Q* Z0 \: h7 K( ~
    87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - # _4 [/ I- _\" W6 s; u0 e
    88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - \" w\" ^' U# E8 w+ Y9 X
    89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
      # ~6 r+ i8 o3 b- Y
    90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; A; d/ ^& s$ Y2 F% n
    91. # n% ?+ N1 b& d6 h* Y\" Q  S) q9 D( u
    92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
      / a$ E; [% G' p1 i+ T
    93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
      - H$ p# b  _* [\" w# @: G# X& O& i
    94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*\" P( }. k4 |% V( T& H; x# W9 Z
    95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
      ) I' p& D- i) w4 j. M
    96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
      8 {' |  S. _. }- D0 E0 Z5 k8 G( J8 n
    97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
      ) J' b; n8 h) L
    98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - - z! L1 }2 W; d9 I* T
    99.       w4^2/u3^2*Kwa143*IIua133);
      / Z. Y# A! A. o- A\" V' ^# q$ x
    100. \" W) k2 S; ~7 \; R# \
    101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
      $ K1 e7 K( b1 S\" y$ G) l
    102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
      ! R- i* _; s$ N; D5 e8 C- j' P
    103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*- q* M$ o  k\" Z\" r# W
    104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -4 K( r: A7 M2 o* ?% M' \
    105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
      ; J* X# l: F6 T; R/ ?
    106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
      0 c; K( K7 k6 \9 M. B7 N  s
    107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - \" H( h: F( W, G6 H% r, u
    108.       w4^2/u3^2*Kwa143*IIua133);\" r4 x9 z& ~; ^) ?9 |% u

    109. + X' j. l0 C\" u8 @\" s
    110. M3 = (betacl*Kwa143*  k! C' A/ A$ t9 \. `# r; h$ o
    111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
      / X% L' ]1 a  ?: F; A- d: A
    112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
      ! K: M7 r1 V1 o( b& x8 o
    113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
      ' z* B- U  r0 M3 N* A/ m
    114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132** B( R; [5 O8 @  L6 E\" ~% j
    115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
        }& ~, M- j  I0 n3 ~- I. G
    116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*  K8 p8 B& N. ?7 g: Y
    117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
      0 ]4 y3 [2 F+ H+ p6 V
    118.       w4^2/u3^2*Kwa143*IIua133);$ o( V! B; {9 {
    119. ; O8 V0 e  U\" p& k& o
    120. M4 = (betacl*Kwa143*5 Z* T% z9 ?% i. C
    121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
      , L8 a- [; o0 C- \2 ^* n2 h
    122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*+ N  P$ a( ~8 R6 E+ O9 N3 e3 E2 i& F
    123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - / j2 [9 `- a1 @- j3 O
    124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*) g7 c5 s9 p- S: q# T3 M. _\" h
    125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
      2 N' A) r! q1 A  m
    126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*$ E# g. N\" }; l6 |9 C7 M$ i
    127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
      ' C$ c, _* ], M9 O6 {0 ~' P
    128.       w4^2/u3^2*Kwa143*IIua133);
      2 w- \2 Z, F( l5 h

    129. 9 @/ V- N0 o8 h9 c4 R$ a, c
    130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;; t$ v+ i# h; |- U/ i
    131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;6 K4 w7 `  W4 w  Y! F
    132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;7 X  K1 F9 u8 r
    133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;8 t9 [! r9 ?6 M; \/ [
    134. ) `% m5 X7 G9 n1 F+ P
    135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
      , V& {' y$ h/ @; b* U. F  L+ [
    136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;  E# y4 {8 N* w& j# ]
    137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
      * _  D9 G- w2 z' J, ?1 F
    138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;/ m$ f. n; L+ N7 r$ X
    139. 5 `, g. p5 V) Y/ z4 ^\" |7 X
    140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
      ( @, z: q7 {+ _( K5 ]+ P
    141.      V1*M4);- y; I: K; K- p! ^
    142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
      3 T- A' q( s0 @7 V3 M
    143.      V2*M2);$ `$ t2 a7 u! i

    144. % }( A' ~\" g' s
    145. x = xicl1 - xicl2;: p$ c  l  g# N3 @+ u
    146. x1 = Re[x];) }# ~, ?, }1 C: h. p) J  A% E3 t
    147. x2 = Im[x];
      6 E% y8 e$ n1 w. j# K- y) M

    148. . x( }& ?* Q0 V
    149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];7 F1 O: f' z+ _% N; }- W+ h
    150. ]' ^) k\" B5 t9 J
    151. ( v\" V4 E3 W3 F& t
    复制代码
    代码如上,结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
    ; }6 |3 ]) z4 c7 x/ i/ [但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];0 K0 R0 ^) _4 S( D
    换成
    9 U/ P- p* B, @4 i' v  aFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
    ! ~, g" n8 q, X$ ?9 ]- p/ A FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
    ! C/ z* G+ ?; ` ]
    9 @  n8 C, |3 G就会出现
    8 Q& G' p, ?5 g( j! yFindRoot::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.
    & Z4 a* z' B5 V& h+ D; q) l8 i! T
    请问是怎么回事?
    ) V4 g) H! H2 F0 W0 \8 O, Z/ m8 }  w; ^) G9 x( ^  u: j% ?7 c
    zan
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