Analogue gravity in hyperbolic metamaterials

Abstract

Sub-wavelength confinement of light in nonlinear hyperbolic metamaterials due to formation of spatial solitons has attracted much recent attention because of its seemingly counter-intuitive behavior. In order to achieve self-focusing in a hyperbolic wire medium, a nonlinear self-defocusing Kerr medium must be used as a dielectric host. Here we demonstrate that this behavior finds natural explanation in terms of analogue gravity. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2+1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. In order for the effective gravitational constant to be positive, negative self-defocusing Kerr medium must be used as a host. If gravitational self-interaction is strong enough, spatial soliton may collapse into a black hole analogue.

16 pages, 2 figures, this version is accepted for publication in Phys. Rev. A

References in corpus (3)

• Optical Hyperlens: Far-field imaging beyond the diffraction limit
• Magnifying superlens in the visible frequency range
• "Planck-scale physics" of vacuum in a strong magnetic field

Cited by in corpus (18)

• Hyperbolic Metamaterials with Bragg Polaritons
• Nonlinear optics of photonic hyper-crystals: optical limiting and hyper-computing
• Anomalous diffraction in hyperbolic materials
• Holographic duality in nonlinear hyperbolic metamaterials
• Observation of the acceleration of light in a tapered optical fiber
• Analogue quantum gravity in hyperbolic metamaterials
• Demystifying the Holographic Mystique
• Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors
• Squeezed gravitons from superradiant axion fields around rotating black holes
• Covariant kinematics of light in media and a generalized Raychaudhuri equation
• Experimental model of topological defects in Minkowski spacetime based on disordered ferrofluid: magnetic monopoles, cosmic strings and the spacetime cloak
• Fine tuning and MOND in a metamaterial multiverse
• Experimental observation of effective gravity and two times physics in ferrofluid-based hyperbolic metamaterials
• Metamaterial model of tachyonic dark energy
• Quasibound states of massive charged scalars around dilaton black holes in $2+1$ dimensions: Exact frequencies
• Fractional charges and Misner-Wheeler charge without charge effect in metamaterials
• Thermodynamics of effective Minkowski spacetime in self-assembled hyperbolic metamaterials
• Metamaterial model of a time crystal