Towards a piecewise-homogeneous metamaterial model of the collision of two linearly polarized gravitational plane waves

We considered the experimental realization of a Tamm medium that is optically equivalent to the collision of two linearly polarized gravitational plane waves as a piecewise homogeneous metamaterial. Our formulation was based on the homogenization of remarkably simple arrangements of oriented ellipsoidal nanoparticles of isotropic dielectric-magnetic mediums. The inverse Bruggeman homogenization was used to estimate the constitutive parameters, volume fractions, and shape parameters for the component mediums. The presented formulation is appropriate for the regions of spacetime where the two gravitational plane waves interact, excluding the immediate vicinity of the nonsingular Killing-Cauchy horizon at the focusing point of the two plane waves.