半波長ダイポール

By 平野拓一

<< Graphics`Colors`

\( (*\ モ - メント法の結果\ *) \)
ivec = {{0.0015993914407161295`, -0.638326039248772`}, {0.0027831608122753076`, -0.6325631210094189`}, {0.003901425945848874`, -0.626899099492919`}, {0.004943792355583696`, -0.6210407749991087`}, {0.005915568720751507`, -0.6149339167612491`}, {0.006814306518962076`, -0.6085180370926005`}, {0.007635948282381321`, -0.6017301860351156`}, {0.008375699124354924`, -0.5944970505766951`}, {0.009028639464416678`, -0.586729335457548`}, {0.009590034347251829`, -0.5783140102107232`}, {0.01005550072072821`, -0.5691022309455882`}, {0.010421052498610209`, -0.5588863529252784`}, {0.010683083515825849`, -0.5473679964174963`}, {0.010837141645569558`, -0.5339289636856862`}, {0.010883995930053006`, -0.518519737056533`}, {0.010745778116230915`, -0.4873006127297302`}, {0.010883995930052999`, -0.518519737056533`}, {0.010837141645569539`, -0.5339289636856862`}, {0.01068308351582582`, -0.5473679964174962`}, {0.010421052498610183`, -0.5588863529252782`}, {0.010055500720728179`, -0.5691022309455882`}, {0.009590034347251798`, -0.578314010210723`}, {0.009028639464416646`, -0.586729335457548`}, {0.008375699124354883`, -0.594497050576695`}, {0.007635948282381277`, -0.6017301860351156`}, {0.006814306518962035`, -0.6085180370926004`}, {0.00591556872075147`, -0.6149339167612489`}, {0.004943792355583666`, -0.6210407749991085`}, {0.0039014259458488502`, -0.6268990994929189`}, {0.002783160812275291`, -0.6325631210094186`}, {0.00159939144071612`, -0.6383260392487717`}};

c = 3*(10^8);
λ0 = 1. ;
k0 = ((2 π)/λ)0;
h = λ0/4;
nn = Length[ ivec ];
cur[n_, t_] := 
        ivec[[n, 1]]*Cos[t + ivec[[n, 2]]];

grapdist = {Red, AbsoluteThickness[2], 
          Line[Table[{20*
                  ivec[[i, 
                      1]], ((i - 1)/(nn - 1))*(2*h) - 
                  h}, {i, 1, nn}]]};
Show[ Graphics[grapdist] ];

charges[n_, t_]:=Module[{r = (2*h)/50},
{{GrayLevel[0.8],Rectangle[{-r,-h-2*r},{r,h+2*r}]},
  
{Blue, 
                  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[10, t]} ], 
        AspectRatio -> Automatic ], {t, 0, 2 Pi - 0.001, 
        2 Pi/8}]

Hue のテスト

ContourPlot[(Sqrt[(x^2) + (y^2)]), {x, -1, 1}, {y, -1, 1}, 
      ColorFunction -> (Hue[-0.7*(# - 1), 1, 1] &), 
      ContourLines -> False, Contours -> 40]

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}, 
        ColorFunction -> (Hue[-0.7*(# - 1), 1, 
                1] &), 
Mesh -> 
          False, 
FrameTicks -> 
          None, 
PlotRange -> {0, 
            0.002}, 
PlotPoints -> 
          100, 
Epilog -> {White, 
            Rectangle[{-h/6. , -h}, {h/6. , h}]}], {t, 
        0, (π/(c k0)) - 
          0.001*(π/(c k0)), (π/(c k0))/
          8}]