  We demonstrate the application of a fiber-coupled quantum-dot-in-a-tip as a
probe for scanning electric field microscopy. We map the out-of-plane component
of the electric field induced by a pair of electrodes by measurement of the
quantum-confined Stark effect induced on a quantum dot spectral line. Our
results are in agreement with finite element simulations of the experiment.
Furthermore, we present results from analytic calculations and simulations
which are relevant to any electric field sensor embedded in a dielectric tip.
In particular, we highlight the impact of the tip geometry on both the
resolution and sensitivity.
