Control of light by curved space in nanophotonic structures

Light Propagation through Nanophotonics Wormholes

“…In Figs (2), (3), we see the behavior of the phase and group velocities for the same values of q and k x considered in [7]. We have considered realistic values of 100¯m for the length of the surface -centered around the wormhole's throat at z = 0-and 30¯m for its minimum radius -corresponding to the radius of the wormhole throat b 0 -and a wavelength in the optical regime λ = 780µm.…”

“…Now, we follow the mathematical analysis in [7]. In the coordinate system we are considering, the transverse electric modes do not have z component and, if we write the x component as where n = c/v is the refractive index, k is the wavenumber k = nω/c -ω being the frequency of the wave-and q plays the role of the propagation constant.…”

“…An important application is the design of nanophotonic devices where the propagation of electromagnetic fields in the visible regime mimics propagation on curved spacetime [4], thus enabling the study of general relativity properties in the laboratory [5,6]. A recent development [7] has been the experimental design of a 3D nanophotonic material emulating Flamm's paraboloid, which is a 2D spatial cut of the Schwarzschild spacetime metric embedded as a revolution surface in a 3D space. While, of course, this metric is perhaps the most paradigmatic example of curved spacetime due to its applications in the analysis of black holes, embedding techniques are a standard tool in general relativity and can be used to describe other spacetimes of interest [8].…”

“…As in the Schwarzschild case, the embedding diagram is a 2D spacelike cut of the full spacetime embedded as a surface of revolution in 3D space. The construction of this structure would require similar technology as the Flamm's paraboloid, which has been recently build up in the laboratory [7]. By considering realistic experimental parameters, we show that the phase and group velocities of waves propagating along the wormhole structure are significantly modified.…”

Gouy and spatial-curvature-induced phase shifts of light in two-dimensional curved space

“…Experimentally it can be realized by covering a thin layer of waveguide on surface [27]. In the latest decade various concepts have been reconsidered and reported, such as solitons [28], evolution of speckle pattern [29], spatially accelerating wave packets following nongeodesic trajectories [30,31], topological phases in curved space photonic lattices [32], phase and group velocity of wave packets [33], Wolf effect of light spectrum [34,35], etc. Specially, in a pioneering work [26], Schrödinger equation for linear propagation on curved space with constant Gaussian curvature is derived, which is in essence the wave equation under paraxial approximation, and one of whose solutions is the fundamental notion in optics, Gaussian beam.…”