Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators

We report on the controlled light confinement in microtube bottle resonators formed by rolled-up strained semiconductor bilayers. We experimentally and theoretically discuss two important properties of this novel kind of microcavities: the axial light confinement and the mode splitting by broken rotational symmetry. Our model bases on the adiabatic separation of circular and axial mode propagation. The circular problem is solved by a simple waveguide model for the specific geometry along the microtube axis. These solutions act as a quasipotential in a quasi-Schrodinger equation for the axial propagation. We experimentally investigated microtubes with two different axial confinement mechanisms: lobes of varying winding number in the rolling edge and etched rings of a varying wall thickness along the microtube axis. For the microtubes with lobes, we observe a very good quantitative agreement with our model and show that axial mode dispersion can even be tailored by the shape of the lobe. For the microtubes with etched rings, we observe only a qualitative agreement. These microtubes exhibit a well pronounced mode splitting by broken rotational symmetry that is analyzed by two-dimensional finite-difference time-domain simulations. We observe an oscillating behavior of the amplitude of the splitting as well as of the quality factors of the split modes under variation of the winding number. We show that the splitting is connected to the axial confinement.