Observation of photon sphere modes in black hole microcavity laser

One of interesting phenomena of a black hole (BH) in its vicinity due to its extreme curvature of spacetime is called a photon sphere (PS), a closed trajectory where photons get trapped and orbit. In this work, we design novel 3D microcavities and investigate lasing on modes localized on a PS, induced by attractive nature of BH. We explore these eigenmodes by conformally transforming a Schwarzschild BH metric into a 2D plane with varying refractive index. We analytically confirm the existence of PS modes by extending our previous theory of conformal transformations [PNAS 119, e2112052119 (2022)] into open systems, and solving the wave equation under a WKB framework. To numerically induce lasing of PS modes, we selectively pump the 2D cavity above the vicinity of the PS. The lasing process is revealed by a 3D finite-difference time-domain simulation coupled to the atomic population of a four-level atomic structure. A lasing mode localizing on PS is observed in its emission spectrum. Experimentally, the corresponding 3D curved surface, which is parabola-like, is fabricated by direct laser writing of dye-doped resin. The microcavity is selectively pumped on its waist by shaping the pump intensity profile, using a spatial light modulator. The effect of stability of ray trajectories on lasing properties of modes is still under investigation. The notion of BH microcavities inspires engineering of effective potential in microcavities and paves a new way to design modes with desired lasing characteristics.