  We present theoretical and experimental results of coherent population
trapping spectra on a multi-level $^{40}$Ca$^+$-type configuration, adding a
third beam to the standard two-laser $\Lambda$ system to avoid undesired
optical pumping. We show that the extra laser can preserve the nature of the
dark resonances or introduce decoherence depending on its power. Experiments
are carried out using a single trapped $^{40}$Ca$^+$ ion in the
$S_{1/2}-P_{1/2}-D_{3/2}$ manifold. Theoretically, the problem is solved with a
Floquet-like expansion of the Liouvillian that correctly predicts all of the
measured spectra without the need of full time integration. As a first
application of the multilaser technique, we show that the richer spectra
obtained can be used as a vectorial polarimeter of one of the beams, allowing
one to measure the electrical field at the ion position in any spatial
direction. We also explain how our setup could realize a thermometer with
tunable sensitivity and no laser-linewidth dependence.
