Earth-Lens Telescope for Distant Axion-like Particle Sources with Stimulated Backward Reflection

We propose a novel telescope concept based on Earth’s gravitational lensing effect, optimized for the detection of distant dark matter sources, particularly axion-like particles (ALPs). When a unidirectional flux of dark matter passes through Earth at sufficiently high velocity, gravitational lensing can concentrate the flux at a distant focal region in space. Our method combines this lensing effect with stimulated backward reflection (SBR), arising from ALP decays that are induced by directing a coherent electromagnetic beam toward the focal point. The aim of this work is to numerically analyze the structure of the focal region and to develop a framework for estimating the sensitivity to ALP–photon coupling via this mechanism. Numerical calculations show that, assuming an average ALP velocity of 520 km/s—as suggested by the observed stellar stream S1—the focal region extends from $9\times {10}^9$ m to $1.4\times {10}^{10}$ m, with peak density near $9.6\times {10}^9$ m. For a conservative point-like ALP source located approximately 8 kpc from the solar system, based on the S1 stream, the estimated sensitivity in the eV mass range reaches $g/M=\mathcal{O}\left({10}^{-22}\right){\mathrm{GeV}}^{-1}$. This concept thus opens a path toward a general-purpose, space-based ALP observatory that could, in principle, detect more distant sources—well beyond $\mathcal{O}\left(10\right)\mathrm{kpc}$—provided that ALP–photon coupling is sufficiently strong, that is, $M\ll M_{\mathrm{Planck}}$.