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In this work we implement theoretical proposal of Smolyaninov and Narimanov (Phys. Rev. Lett. 105, 067402 (2010)) who demonstrated that extraordinary light waves in hyperbolic metamaterials exhibit “two times” physics behavior. This behavior is observed via experimental study of gravity-like nonlinear optics of iron/cobalt-based ferrofluid hyperbolic metamaterials. In addition to conventional temporal coordinate, the spatial coordinate oriented along the optical axis of the metamaterial also exhibits timelike character, which leads to very unusual “two times” physics behavior in these systems.
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Vera N. Smolyaninova, Jonathon Cartelli, Bryan Augstein, Mary Sajini Devadas, I. Smolyaninov, "Experimental observation of effective gravity and two times physics in ferrofluid-based hyperbolic metamaterials," Proc. SPIE 11460, Metamaterials, Metadevices, and Metasystems 2020, 1146011 (20 August 2020); https://doi.org/10.1117/12.2569342