  We recently reported on a proof-of-principle experiment demonstrating optical
trapping of an ion in a single-beam dipole trap superimposed by a static
electric potential [Nat. Photonics 4, 772--775 (2010)]. Here, we first discuss
the experimental procedures focussing on the influence and consequences of the
static electric potential. These potentials can easily prevent successful
optical trapping, if their configuration is not chosen carefully. Afterwards,
we analyse the dipole trap experiments with different analytic models, in which
different approximations are applied. According to these models the
experimental results agree with recoil heating as the relevant heating effect.
In addition, a Monte-Carlo simulation has been developed to refine the
analysis. It reveals a large impact of the static electric potential on the
dipole trap experiments in general. While it supports the results of the
analytic models for the parameters used in the experiments, the analytic models
cease their validity for significantly different parameters. Finally, we
propose technical improvements for future realizations of experiments with
optically trapped ions.
