b, Simulated dynamics of a pulse displayed at cross-sections of the paraboloid waveguide for different times. In agreement with Fig. 2c,d, the group velocity is decreasing while propagating towards the bottleneck. f, Comparison of geodesic trajectories calculated from the Schwarzschild metric (equation (8)) (solid lines) and FDTD simulation results (open circles), for beams launched at different angles with respect to the z axis (see legend).Įxperimental results on light manipulation via space curvatureĪ, Calculated group velocity extracted from the width evolution of a Gaussian beam in the experiment. e, Geodesic trajectory of a beam launched at an initial tilt angle relative to the symmetry axis. d, Scanning electron microscope image of the surface waveguide. Yellow indicates the evolution of the beam width, which narrows due to the curvature of space. After the bottleneck, the beam reappears and experiences broadening (white lines indicate the borders of the waveguide). The beam narrows as it propagates towards the bottleneck of the structure and power escapes to outside the surface waveguide, when the beam gets near the bottleneck, the power inside the waveguide is considerably depleted. Exploiting Einstein’s theory of general relativity, the curved space associated with specially designed nanophotonic structures is shown to be able to manipulate light propagation.Įxperimental observation of the evolution of an optical beam in the microstructured surface waveguideĪ, Schematic of the coupling scheme of the light to the paraboloid waveguide. b, Curvature effects on diffraction. This generic concept can serve as the basis for curved nanophotonics and can be employed in integrated photonic circuits. Finally, our structure exhibits tunnelling through an electromagnetic bottleneck by transforming guided modes into radiation modes and back. Our construction allows control over the trajectories, the diffraction properties and the phase and group velocities of wavepackets propagating within the curved-space structure. We demonstrate this concept by studying the evolution of light in a paraboloid structure inspired by the Schwarzschild metric describing the space surrounding a massive black hole. We present a new class of nanophotonic structures with intricate design in three dimensions inspired by general relativity concepts, where the evolution of light is controlled through the space curvature of the medium. Conventional nanophotonic structures are fabricated in planar settings, similar to electronic integrated circuits. Nanophotonics is based on the ability to construct structures with specific spatial distributions of the refractive index.
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