  In the framework of the Inert Higgs Doublet model (IHDM), we have
investigated, in the center of mass frame, the neutral Higgs-boson pair
production in the presence of an intense and circularly polarized laser field
via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow H^{0}A^{0})$ at
the lowest order. By using the scattering matrix method, we have derived the
analytical expression of the differential cross section. The latter is
numerically integrated over the solid angle to obtain the total cross section.
Then, we have shown how this total cross section depends on the outgoing
particles mass for different number of exchanged photons. Next, we have
illustrated its variation as a function of the centre of mass energy for
different neutral Higgs-boson masses. Finally, we have indicated how it changes
as a function of the laser field amplitudes for both different number of
exchanged photons and different neutral Higgs-bosons masses.
