  We investigate $\phi$ meson photoproduction on the nucleon and the
\nuclide[4]{He} targets within a dynamical model approach based on a
Hamiltonian which describes the production mechanisms by the Pomeron-exchange,
meson-exchanges, $\phi$ radiations, and nucleon resonance excitations
mechanisms. The final $\phi N$ interactions are included being described by the
gluon-exchange, direct $\phi N$ couplings, and the box-diagrams arising from
the couplings with $\pi N$, $\rho N$, $K\Lambda$, and $K\Sigma$ channels. The
parameters of the Hamiltonian are determined by the experimental data of
$\gamma p \to \phi p$ from the CLAS Collaboration. The resulting Hamiltonian is
then used to predict the coherent $\phi$-meson production on the
\nuclide[4]{He} targets by using the distorted-wave impulse approximation. For
the proton target, the final $\phi N$ rescattering effects, as required by the
unitarity condition, are found to be very weak, which supports the earlier
calculations in the literature. For the \nuclide[4]{He} targets, the predicted
differential cross sections are in good agreement with the data obtained by the
LEPS Collaboration. The role of each mechanism in this reaction is discussed
and predictions for a wide range of scattering angles are presented, which can
be tested in future experiments.
