Absorption of hybrid fibre modes by Cs atoms in quadrupole transitions

The rate of the absorption of light endowed with orbital angular momentum by the process of upward quadrupole transitions in Cs atoms is evaluated when the Cs atoms are localised in the vicinity of the outer surface of an optical fibre. The coupling is between the quadrupole tensor components and the gradients of the vector components of the electric field of a hybrid fibre mode. Values of the absorption rates are obtainable for quadrupole transitions assuming a moderate laser power and experimentally accessible parameters, we find that the processes of absorption of the hybrid modes by the Cs atoms proceed at rates of the order $0.1 \gamma$ where $\gamma^{-1}$ is the lifetime of the upper state involved in the quadrupole transition.