Einstein beams are coherent optical beams generated by the conditions of gravitational lensing. In the ray picture, Einstein beams are formed by the intersection of light rays deflected by a lensing mass, similar to non-diffracting Bessel beams, but with the difference that adjacent rays diverge slightly. When accounting for the wave properties of light, they form beam-like diffraction patterns that preserve their shape but expand as the light propagates. The addition of a topological charge to the light, leads to more complex patterns carrying orbital angular momentum. For symmetric lensing conditions, Einstein beams carry modes described by confluent hypergeometric functions, which can be approximated by Bessel functions. A theoretical analysis of this is presented here. In astrophysical observations, many of these features can only be inferred because conditions of coherence and alignment make them difficult to observe. Studies of Einstein beams in the laboratory can be used to inform astrophysical observations and discover new non-astrophysical laboratory applications.
We used spatial light modulation to deflect coherent light beams into trajectories specified by gravitational lensing. We programmed symmetric and asymmetric lensing objects, including adding orbital angular momentum. In the far field we observed Einstein rings and arcs for symmetric lensing objects, and various types of Einstein arcs for asymmetric lensing objects, similar to what is seen in astronomical observations. In the near field we observed the caustics produced by gravitational lensing, not possible in astronomical observations, which consisted of Bessel patterns for symmetric objects, and Mathieu-like patterns and astroids for asymmetric objects.
We use a spatial light modulator (SLM) to mimic the effect of gravity and steer the light from a laser to observe Einstein rings with a laboratory camera. The derived programming of the phase of the SLM follows a logarithmic dependence with impact parameter. As expected, we also observe arcs when the source and lensing object are not in line with the observer. Measurements for distinct parameters are consistent with the expectations. The coherent optical beams that are programmed to follow gravitational lensing trajectories have a transverse mode consistent with Bessel functions, yet they do not exhibit the non-diffracting properties of Bessel beams: they expand linearly with the propagation distance. The addition of a vortex phase also produces patterns that coincide with Bessel modes of order given by the topological charge of the vortex..
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