Optical Microcavities Formed by Semiconductor Microtubes Using a Bottlelike Geometry

We report on the realization of optical microtube resonators with a bottlelike geometry. The measured eigenenergies and the measured axial field distributions of the modes can be described by a straight and intuitive model using an adiabatic separation of the circulating and the axial propagation. The dispersion of the axial mode energies follows a photonic quasi-Schrödinger equation including a quasipotential which can be determined for the actual geometry of the microtube in a precise and simple way. We show that tailoring the geometry of the microtube bottle resonators enables the realization of a wide variety of mode distributions and dispersion relations.

Figure 1

(a) Sketch of a microtube bottle resonator exhibiting a parabolic lobe on its outside rolling edge. Red arrows illustrate the circular light propagation by multiple total internal reflections. (b) SEM image of a microtube bottle resonator. Yellow lines clarify the edges of the $U$-shaped mesa. (c) Magnified top view on the region marked in (b).

Figure 2

(a) Spatially integrated and (b) spatially resolved PL spectra of the microtube bottle resonator with a parabolic lobe. (c)–(d) Axial field distributions calculated within the adiabatic approximation. (c) Numerical solution for a finite potential obtained from SEM images of the microtube. (d) Analytical solution for an infinite parabolic potential for one group of axial modes. (e) FDTD simulation of the axial field distribution. Intensities in (b)–(e) are encoded in a color scale as depicted in the inset of (d). Horizontal axes in (b)–(e) give the relative position with respect to the extremum of the lobe. The dashed horizontal line at about 1.19 eV serves as a guide for the eye.

Figure 3

(a),(b) PL spectra of microtube bottle resonators with a (a) triangular and (b) rectangular lobe. The insets sketch the level spacings in a (a) triangular and (b) rectangular potential. (c)–(e) Axial mode dispersions for a (c) parabolic, (d) triangular, and (e) rectangular lobe. Measured (calculated) values are depicted as red circles (black squares). Connecting lines serve as guides for the eye.