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    Optical echoes of light near an analog black hole

    Suting Ju, Jingxuan Zhang, and Li-Gang Wang*

    • *Contact author: lgwang@zju.edu.cn

    Phys. Rev. A 113, 063517 – Published 11 June, 2026

    DOI: https://doi.org/10.1103/728x-xlc9

    Abstract

    The light deflection under a strong gravitational field, referred to as strong gravitational lensing, provides a powerful probe of spacetime geometry. Besides, laboratory analog models are employed to study the effects of curved spacetime and explore the design of optical devices. Here, applying the framework of analog gravity, we investigate pulse echoes from a pointlike source on two curved surfaces of revolution derived from Schwarzschild spacetime, the Flamm paraboloid, and the surface of the two-dimensional Fermat metric, and reveal the interplay between the photon sphere and the pulse. We calculate the echo response using analytical geodesic solutions and the Huygens-Fresnel principle. Particularly, when the spatial scale of pulse duration is comparable to the photon sphere, continuous echo tails appear along bright interference fringes in temporal response. Analysis in both the temporal and frequency domains reveals that these echo tails are a signature of resonance between the incoming pulse and the photon sphere. This work provides a wave-optics perspective on pulse interference and echo formation in curved geometries, offering a tabletop platform for exploring the simulation of strong gravitational lensing phenomena.

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