Lasing in a Mobius strip microcavity

 

A neat paper was just published in Physical Review Letters and highlighted as an Editor's Suggestion: Möbius Strip Microlasers: A Testbed for Non-Euclidean Photonics

 

In conventional microring lasers based on whispering gallery modes each lasing mode can be described semiclassically as a light ray that is reflected off the boundary between the outer edge of the high refractive index ring and the ambient medium. The ray returns to the same position after completing one cycle of the ring, forming a periodic orbit. Rays with a large angle of incidence with the outer edge will undergo total internal reflection and thus have extremely low losses. Thus, the rays follow the outer edge closely.

What happens if we add a twist to the ring to form a Mobius strip? Do the whispering gallery lasing modes survive?

 

No. The boundary of a Mobius strip forms a single closed curve; following the (concave) outer edge for one cycle you will end up at the (convex) inner edge, which cannot support whispering gallery modes.

 

The simplest periodic orbits supported by the Mobius strip involve alternating reflections off the inner and outer edges. The low angle of incidence makes these orbits highly lossy and unlikely to lase.

 

The authors fabricated Mobius strip cavities and measured their lasing spectra. The spacing between the peaks was used to obtain the optical path length of the lasing modes, revealing that they are neither whispering gallery modes nor the alternating reflection periodic orbits. Instead, they reveal a novel class of periodic orbit unique to three-dimensional Mobius strips, in which the ray only reflects off the outer edge (ensuring low losses), but also crosses the interior of the strip to avoid ending up on the inner edge.

The experimental observations are corroborated with numerical solutions of the Helmholtz equation and semiclassical computation of the periodic orbits. Future work will consider the full vectorial Maxwell's equations to unveil the role of polarization in this peculiar class of twisted cavities.