We combine two-photon lithography and optical tweezers to investigate the Brownian
fluctuations and propeller characteristics of a microfabricated helix. From the analysis
of mean squared displacements and time correlation functions we recover the components
of the full mobility tensor. We find that Brownian motion displays correlations between
angular and translational fluctuations from which we can directly measure the hydrodynamic
coupling coefficient that is responsible for thrust generation. By varying the distance
of the microhelices from a no-slip boundary we can systematically measure the effects
of a nearby wall on the resistance matrix. Our results indicate that a rotated helix
moves faster when a nearby no-slip boundary is present, providing a quantitative insight
on thrust enhancement in confined geometries for both synthetic and biological microswimmers.
