Oscillator strengths for optical transitions in a hollow cylinder

Abstract

The oscillator strengths for optical transitions between the lowest-order single-electron energy subbands are obtained within the dipole approximation as functions of the axially applied magnetic field. Confinement of the electron is by the magnetic field potential as well as by some fictitious potential of the quantum wire with a spatial variation across the cylinder thickness. The radiation field is taken as that of the circularly polarized light along the axis of the cylinder. Within the framework of the dipole approximation, the only allowed transitions associated with this polarization are those between the electron-energy subbands whose azimuthal quantum numbers differ by unity. As a result of the Zeeman splitting of the non-zero azimuthal-quantum number states, several branches of the oscillator strengths emerge from the zero-field branch on taking into account the possible permutations of the sign of the relevant azimuthal quantum numbers. The main prediction is the enhancement of the oscillator strengths for transitions between the subbands whose energy gaps open up on increasing confinement of the electron due to the magnetic field potential.