M\"obius strip microlasers: a testbed for non-Euclidian photonics

We report on experiments with Mobius strip microlasers which were fabricated with high optical quality by direct laser writing. A Mobius strip looks like a ring with a twist and exhibits the fascinating property that it has only one boundary and a one-sided nonorientable surface. Hence, in contrast to conventional ring or disk resonators, a Mobius strip cavity cannot sustain Whispering Gallery Modes (WGMs). Comparison between experiments and FDTD simulations evidenced that the resonances are indeed not of whispering gallery type, but localized along periodic geodesics. This finding is supported, on the one hand, by an extension of the effective index approximation to curved layers, and on the other hand, by an algorithm to systematically identify the periodic geodesics.