Abstract
Wave packets of light have been made to travel in a curved space along geodesic paths, generating optical analogues of general-relativity phenomena. A new analysis of the curved-space generalization of the Maxwell equations shows that wave packets can also travel along nongeodesic paths while changing and recovering their shapes periodically.
Highlights
We present shape-preserving spatially accelerating electromagnetic wave packets in curved space: wave packets propagating along nongeodesic trajectories while periodically recovering their structure
Far, in all of these experiments and theoretical studies on general-relativity concepts with EM waves, the wave packets were propagating on geodesic trajectories, which are naturally the shortest path, analogous to straight lines in flat geometry
We show that wave packets can exhibit periodically shape-invariant spatially accelerating dynamics in curved space, propagating in nongeodesic trajectories that reflect the interplay between the curvature of space and interference effects arising from initial conditions
Summary
Shape-invariant wave packets that are exact solutions of Maxwell’s equations [39]. Experimental demonstrations of such beams followed soon thereafter [40,41,42], along with further theory and experiments demonstrating additional families of nonparaxial accelerating beams [43,44,45]. Consider EM waves that are restricted to exist in a 2D curved surface This physical situation can be achieved by covering the surface area of a 3D shape (a sphere, for example) with a thin homogenous layer of a material with a higher refractive index. The wave equation for the electric field is derived from Eqs. (1) [15]:
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