1.5波長ダイポール

By 平野拓一

<< Graphics`Colors`

\( (*\ モ - メント法の結果\ *) \)
ivec = {{0.0013062531145648074`, 
              2.5995748241589567`}, {0.002273467469405078`, 
              2.605046915751126`}, {0.0031824890605324`, 
              2.6103180815431246`}, {0.004024930908946023`, 
              2.615656239998546`}, {0.004804442415433602`, 
              2.621099050238991`}, {0.0055185978691421`, 
              2.6266847527655592`}, {0.006163780691275122`, 
              2.6324481633378047`}, {0.006735930346006162`, 
              2.6384260321853943`}, {0.007231060468242848`, 
              2.644659115714557`}, {0.007645538928034487`, 
              2.65119410004406`}, {0.007976265750447553`, 
              2.658085691069274`}, {0.008220792479999895`, 
              2.6653991951371214`}, {0.008377405374964128`, 
              2.6732138971053114`}, {0.008445183873848199`, 
              2.6816276415175717`}, {0.008424040806895777`, 
              2.690763213576078`}, {0.008314748426534938`, 
              2.700777446801719`}, {0.008118953293488615`, 
              2.7118745517173575`}, {0.007839182895811845`, 
              2.724326158653273`}, {0.007478847537179725`, 
              2.7385023877982055`}, {0.007042242844033708`, 
              2.754921717674382`}, {0.006534562207307211`, 
              2.7743343212573928`}, {0.005961937108862292`, 
              2.797868100946252`}, {0.0053315431103635146`, 
              2.827299501685435`}, {0.004651858609087104`, 
              2.8655912927610045`}, {0.003933299288541094`, 
              2.9180536516071487`}, {0.0031898750671042024`, 
              2.9951204315804656`}, {0.0024440540343437294`, 
              3.1198205238135985`}, {0.0017435074808881373`, -2.9333989085647003`}, {0.0012233431123040523`, -2.460343806902702`}, {0.0011866023631810813`, -1.726764421821871`}, {0.0016668310119624398`, -1.212638106102854`}, {0.002356105052770327`, -0.9617529902807641`}, {0.003100396208893127`, -0.8272169563074253`}, {0.003846344951465431`, -0.7442650205723123`}, {0.004569776432969295`, -0.6872983815570058`}, {0.0052560514128605325`, -0.6448702646933067`}, {0.005894465424975296`, -0.6111949157131299`}, {0.006476369578702703`, -0.5830345256151526`}, {0.006994451653477579`, -0.5584105098178591`}, {0.007442430919565037`, -0.5360064183395715`}, {0.007814907972417113`, -0.5148586396216045`}, {0.008107245253588804`, -0.49416780996911364`}, {0.008315469724059693`, -0.47316368266624464`}, {0.008435179626469839`, -0.45073439031018836`}, {0.008466851549858719`, -0.4265987982288778`}, {0.00834496191113369`, -0.380990343677043`}, {0.00846685154985871`, -0.42659879822887786`}, {0.008435179626469818`, -0.45073439031018897`}, {0.008315469724059648`, -0.47316368266624603`}, {0.008107245253588745`, -0.4941678099691155`}, {0.007814907972417049`, -0.5148586396216074`}, {0.007442430919564952`, -0.5360064183395756`}, {0.006994451653477491`, -0.5584105098178642`}, {0.006476369578702604`, -0.5830345256151593`}, {0.005894465424975191`, -0.6111949157131386`}, {0.005256051412860424`, -0.6448702646933177`}, {0.004569776432969178`, -0.6872983815570206`}, {0.003846344951465309`, -0.7442650205723327`}, {0.0031003962088930093`, -0.8272169563074544`}, {0.0023561050527702134`, -0.9617529902808113`}, {0.0016668310119623577`, -1.2126381061029372`}, {0.001186602363181075`, -1.726764421822011`}, {0.001223343112304157`, -2.4603438069028063`}, {0.001743507480888283`, -2.933398908564738`}, {0.0024440540343438856`, 
              3.1198205238135857`}, {0.0031898750671043533`, 
              2.9951204315804616`}, {0.003933299288541245`, 
              2.918053651607147`}, {0.004651858609087241`, 
              2.865591292761005`}, {0.00533154311036364`, 
              2.827299501685436`}, {0.005961937108862401`, 
              2.797868100946253`}, {0.006534562207307309`, 
              2.774334321257394`}, {0.007042242844033792`, 
              2.754921717674383`}, {0.007478847537179802`, 
              2.738502387798206`}, {0.007839182895811914`, 
              2.724326158653274`}, {0.008118953293488669`, 
              2.711874551717358`}, {0.008314748426534985`, 
              2.700777446801719`}, {0.008424040806895811`, 
              2.690763213576078`}, {0.008445183873848234`, 
              2.6816276415175717`}, {0.00837740537496417`, 
              2.673213897105311`}, {0.00822079247999995`, 
              2.665399195137121`}, {0.007976265750447612`, 
              2.6580856910692736`}, {0.007645538928034546`, 
              2.6511941000440595`}, {0.007231060468242904`, 
              2.6446591157145565`}, {0.006735930346006222`, 
              2.6384260321853934`}, {0.006163780691275177`, 
              2.632448163337804`}, {0.005518597869142142`, 
              2.6266847527655584`}, {0.004804442415433636`, 
              2.62109905023899`}, {0.004024930908946058`, 
              2.615656239998545`}, {0.0031824890605324273`, 
              2.6103180815431237`}, {0.0022734674694051024`, 
              2.6050469157511253`}, {0.001306253114564816`, 
              2.599574824158956`}};

c = 3*(10^8);
λ0 = 1. ;
k0 = ((2 π)/λ)0;
h = 1.5*λ0/2;
nn = Length[ ivec ];
cur[n_, t_] := 
        ivec[[n, 1]]*Cos[t + ivec[[n, 2]]];

grapdist = {Red, AbsoluteThickness[2], 
          Line[Table[{100*
                  ivec[[i, 
                      1]], ((i - 1)/(nn - 1))*(2*h) - 
                  h}, {i, 1, nn}]]};
Show[ Graphics[grapdist] ];

charges[n_, t_]:=Module[{r = (2*h)/50},
{{Gray,Rectangle[{-r,-h-2*r},{r,h+2*r}]},
  
{Yellow, 
                    Table[Disk[{0, ((i - 1)/(n - 1))*(2*h) - 
                            h + 100. *(2*h/(n - 1))*
                              cur[IntegerPart[((i - 1)/(n - 
                                        1))*(nn - 1)] + 1, t]}, 
                        r], {i, 1, n} ]}}
];
Table[
      Show[ Graphics[ {grapdist, charges[15, t]} ], 
        AspectRatio -> Automatic ], {t, 0, 2 Pi - 0.001, 
        2 Pi/8}]

微小ダイポールの放射電界

\(\(r\&^ . x\&^ = 
        Sin[θ]\ Cos[φ];\)\)
\(\(θ\&^ . x\&^ = 
        Cos[θ]\ Cos[φ];\)\)
\(\(\(φ\&^ . x\&^ = Sin[φ];\)\(
\)
    \)\)
\(\(r\&^ . y\&^ = 
        Sin[θ]\ Sin[φ];\)\)
\(\(θ\&^ . y\&^ = 
        Cos[θ]\ Sin[φ];\)\)
\(\(\(φ\&^ . y\&^ = Cos[φ];\)\(
\)
    \)\)
\(\(r\&^ . z\&^ = Cos[θ];\)\)
\(\(θ\&^ . z\&^ = Sin[θ];\)\)
\(\(φ\&^ . z\&^ = 0;\)\)

er[i_, r_, θ_, t_] := 
        2*Cos[θ]*(Cos[k0*(c*t - r) + ivec[[i, 2]]]/(((k0*r))^2) + Sin[k0*(c*t - r) + ivec[[i, 2]]]/(((k0*r))^3));
etheta[i_, r_, θ_, t_] := 
        Sin[θ]*(Cos[k0*(c t - r) + ivec[[i, 2]]]/(((k0*r))^2) - ((1/((k0*r))) - (1/(((k0*r))^3)))*
                Sin[k0*(c t - r) + 
                    ivec[[i, 2]]]);
ex[i_, r_, θ_, φ_, t_] := 
        Sin[θ] Cos[φ] er[i, r, θ, t] + 
          Cos[θ] Cos[φ] etheta[i, r, θ, 
              t];
ey[i_, r_, θ_, φ_, t_] := 
        Sin[θ] Sin[φ] er[i, r, θ, t] + 
          Cos[θ] Sin[φ] etheta[i, r, θ, 
              t];
ez[i_, r_, θ_, φ_, t_] := 
        Cos[θ] er[i, r, θ, t] + 
          Sin[θ] etheta[i, r, θ, 
              t];
energy[xo_, yo_, zo_, t_] := 
      Module[{xs = 0, ys = 0, zs = 0, r, θ, φ, exsum = 0, 
          eysum = 0, 
          ezsum = 0}, 
Do[
zs = (i - 
                      1)/(nn - 1)*(2*h) - 
              h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
            ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
            ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
exsum += 
            ivec[[i, 1]]*
              ex[i, r, θ, φ, t]; 
eysum += 
            ivec[[i, 1]]*
              ey[i, r, θ, φ, t]; 
ezsum += 
            ivec[[i, 1]]*
              ez[i, r, θ, φ, t]
, {i, 1, 
            nn}
]; 
(exsum^2) + (eysum^2) + 
          (ezsum^2)
]

アニメーション

Table[
      DensityPlot[
        energy[0, x, y, t], {x, -2, 2}, {y, -2, 
          2}, 
ImageSize -> {200, 
            200}, 
ColorFunction -> (Hue[-0.7*(# - 1), 1, 1] &), 
Mesh -> 
          False, 
FrameTicks -> 
          None, 
PlotPoints -> 
          100, 
Epilog -> {White, 
            Rectangle[{-h/10. , -h}, {h/10. , h}]}], {t, 
        0, (π/(c k0)) - 
          0.001*(π/(c k0)), (π/(c k0))/
          8}]