SetDirectory["~/writing/WIP/KappaLib/"];
<<KappaLib.m

Example 5.3: We show that there are complex medium that have the same Fresnel surface as the flat Minkowski metric

Ax=(({{-(1/(2 (z^2))), 0, 0}, {0, -2 z, 0}, {0, 0, -z}}));
Bx=-Ax;
Cx=(({{(I/(3 (z^2)))-I z, 0, 0}, {0, -(I/(6 (z^2)))+I z, 0}, {0, 0, -(I/(6 (z^2)))}}));
Dx=Cx;
kappa=emABCDToKappa[Ax,Bx,Cx,Dx];

Simplify[emKappaToFresnel[kappa,{xi0,xi1,xi2,xi3}]]

emTrace[kappa]

Simplify[emDet[kappa]]

Extra:

Solve[(-5+126 (z^3)-684 (z^6)+648 (z^9))==0,z]

%//N

One zero is z=6^(-1/3)

kappa0=kappa//.z->(1/(6^(1/3)));

{A0,B0,C0,D0}=emKappaToABCD[kappa0];

Simplify[A0]//MatrixForm
Simplify[C0]//MatrixForm

emDet[kappa0]
Simplify[emKappaToFresnel[kappa0,{xi0,xi1,xi2,xi3}]]