  Optical searches assisted by the field of a laser pulse might allow for
exploring a variety of not yet detected dark matter candidates such as
hidden-photons and scalar minicharged particles. These hypothetical degrees of
freedom may be understood as a natural consequence of extensions of the
Standard Model incorporating a hidden $\rm U(1)$-gauge sector. In this paper,
we study the effects induced by both candidates on the propagation of a probe
electromagnetic waves in the vacuum polarized by a long laser pulse of moderate
intensity, this way complementing our previous study [JHEP \textbf{06}, $177$
($2015$)]. We describe how the absence of a spin in the scalar charged carriers
modifies the photon-paraphoton oscillations as compared with a fermionic
minicharge model. In particular, we find that the regime close to their lowest
threshold mass might provide the most stringent upper limit for minicharged
scalars. The pure-laser based experiment investigated here could allow 23for
excluding a sector in the parameter space of the particles which has not been
experimentally ruled out by setups driven by dipole magnets. We explain how the
sign of the ellipticity and rotation of the polarization plane acquired by a
probe photon--in combination with their dependencies on the pulse
parameters--can be exploited to elucidate the quantum statistics of the charge
carriers.
