Metric Signature Transitions in Optical Metamaterials

We demonstrate that the extraordinary waves in indefinite metamaterials experience an ($--++$) effective metric signature. During a metric signature change transition in such a metamaterial, a Minkowski space-time is created together with a large number of particles populating the space-time. Such metamaterial models provide a tabletop realization of metric signature change events suggested to occur in Bose-Einstein condensates and quantum gravity theories.

Figure 1

(a) Schematic views of the “wired” and “layered” metamaterials. Panels (b) and (c) show calculated $\mathrm{Re}(\epsilon )$ and $\mathrm{Im}(\epsilon )$ of the wired metamaterial made of silica glass and gallium wires ($\mathrm{Im}{\epsilon }_{x,y}\ll \mathrm{Im}{\epsilon }_z$, not shown). This medium demonstrates metric phase transition in the visible frequency range when gallium wires are converted from the solid to liquid state. The case of $N_{\mathrm{Ga}}=0.1$ volume fraction of gallium has been considered. The range of frequencies for which the effective metric signature changes from the Minkowski ($-,+,+,+$) to the 2T physics ($-,-,+,+$) is shown by the dashed lines.

Figure 2

Photon energy $dE/d\omega$ (normalized per unit volume) emitted during the femtosecond light-induced metric signature phase transition in the gallium-based metamaterial from Fig. 1. Inset: Hyperbolic dispersion relation allowing unbounded values of the wave vector due to which the photonic density of states diverges.