Non-Euclidean photonics: pseudosphere and black hole microlasers

Hyperbolic surfaces are surfaces with negative curvature. Theoretical studies of such surfaces have been extensive over the past century. In particular, within the context of quantum chaos, hyperbolic surfaces can exhibit strong chaotic behavior [1]. The literature is rich with theoretical results on quantum chaos in hyperbolic surfaces [2]. However, there are very few experimental studies validating these theoretical results [3]. The recent rise of three-dimensional (3D) printing at the microscale, particularly using Direct Laser Writing (DLW), offers new opportunities to explore light propagation on hyperbolic surfaces. On these non-Euclidean surfaces, light rays propagate between points by following the shortest path, known as a geodesic.