平行平板の解析

2006/12/9 平野拓一（東京工業大学）

TE(H)

m=(({{0, kc[1], 0, 0}, {0, 0, -kc[2]*Sin[kc[2]*b], kc[2]*Cos[kc[2]*b]}, {Cos[kc[1]*a], Sin[
                  kc[1]*a], -Cos[kc[2]*a], -Sin[kc[2]*a]}, {-kc[1]*Sin[kc[1]*a], kc[1]*Cos[kc[1]*a], kc[2]*
                  Sin[kc[2]*a], -kc[2]*Cos[kc[2]*a]}}));

Det[m]  //  Simplify

kc[i_] := (Sqrt[k[i]^2 - (β^2)]);
dh[β_] := (Cos[
              a kc[2]] (Cos[b kc[2]] kc[1] Sin[a kc[1]] + 
                Cos[a kc[1]] kc[2] Sin[b kc[2]]) + 
          Sin[a kc[2]] (-Cos[a kc[1]] Cos[b kc[2]] kc[2] + 
                kc[1] Sin[a kc[1]] Sin[b kc[2]]))

dh[β]  /.  {a -> 0, kc[1] -> 0}

f = 50. *(10^9);
c = 2.998*(10^8);
λ0 = c/f;
k0 = ((2*π)/λ)0;
k[i_] := k0*(Sqrt[μr[i]*ϵr[i]]);

a = 0;
b = 165. *(10^(-6));
μr[1] = 1. ;
ϵr[1] = 1. ;
μr[2] = 1. ;
ϵr[2] = 1. ;

Plot[Abs[dh[β]], {β, 0, k[2]}]

TM(E)

m=(({{1, 0, 0, 0}, {0, 0, Cos[kc[2]*b], Sin[kc[2]*b]}, {Cos[kc[1]*a], Sin[
                  kc[1]*a], -Cos[kc[2]*a], -Sin[kc[2]*a]}, {-kc[1]*Sin[kc[1]*a], kc[1]*Cos[kc[1]*a], kc[2]*
                  Sin[kc[2]*a], -kc[2]*Cos[kc[2]*a]}}));

Det[m]  //  Simplify

kc[i_] := (Sqrt[k[i]^2 - (β^2)]);
de[β_] := 
      Cos[a kc[2]] (Cos[b kc[2]] kc[2] Sin[a kc[1]] + 
              Cos[a kc[1]] kc[1] Sin[b kc[2]]) + 
        Sin[a kc[2]] (-Cos[a kc[1]] Cos[b kc[2]] kc[1] + 
              kc[2] Sin[a kc[1]] Sin[b kc[2]])

de[β]  /.  {a -> 0}

f = 50. *(10^9);
c = 2.998*(10^8);
λ0 = c/f;
k0 = ((2*π)/λ)0;
k[i_] := k0*(Sqrt[μr[i]*ϵr[i]]);

a = 0;
b = 165. *(10^(-6));
μr[1] = 1. ;
ϵr[1] = 10. ;
μr[2] = 1. ;
ϵr[2] = 10. ;

Plot[Abs[de[β]], {β, 0, k[2]}]