Theoretical seminar | 10 March 2021

We will discuss the problem of the topological properties of fields on a dielectric Möbius strip, and how to approach it. Two different suitable approaches found in the literature, the metric approach and the Berry phase approach, are strongly interrelated. We will look at this relationship, as well as delve into the mathematical structure behind the Berry phase. We will also briefly discuss the results of numerical simulation of a Möbius strip of finite thickness and with several twists.

Ma LB, Li SL, Fomin VM, Hentschel M, Götte JB, Yin Y, Jorgensen MR, Schmidt OG. Spin-orbit coupling of light in asymmetric microcavities. Nat Commun. 2016 Mar 18;7:10983. doi: 10.1038/ncomms10983.

Li, Zehao & Ram-Mohan, Ramdas. (2012). Quantum mechanics on a Möbius ring: Energy levels, symmetry, optical transitions, and level splitting in a magnetic field. Physical Review B. 85. 10.1103/PhysRevB.85.195438.

Geometry, topology and physics, M. Nakahara(Kinki U., Osaka), 2003, Published in: Boca Raton, USA: Taylor & Francis (2003) 573 p