Section 3.2: Expressing isotropic medium using the Hodge operator for a Lorentz metric

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

AA = -eps IdentityMatrix[3];
BB = 1/mu IdentityMatrix[3];
CC = 0 IdentityMatrix[3];
DD =CC;

kappa = emABCDToKappa[AA, BB, CC, DD];

Express medium using the Hodge operator

kappa2 = Sqrt[ eps/mu] emHodge[DiagonalMatrix[{-1/(eps mu),1,1,1}]];

Simplify[Union[Flatten[kappa2-kappa]],{eps>0,mu>0}]

Extra:  Compute Tamm-Rubilar tensor density for this kappa

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