  A search for sub-eV scalar fields coupling to two photons has been performed
via four-wave mixing at a quasi-parallel laser collider for the first time. The
experiment demonstrates the novel approach to search for resonantly produced
sub-eV scalar fields by combining two-color laser fields in the vacuum. The aim
of this paper is to provide the concrete experimental setup and the analysis
method based on specific combinations of polarization states between incoming
and outgoing photons, which is extendable to higher intensity laser systems
operated at high repetition rates. No significant signal of four-wave mixing
was observed by combining a $0.2\mu$J/0.75ns pulse laser and a 2mW CW laser on
the same optical axis. Based on the prescription developed for this particular
experimental approach, we obtained the upper limit at a confidence level of 95%
on the coupling-mass relation.
