  We investigate theoretically how the proximity effect in
superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling
manifests in the density of states and critical temperature. To describe a
general scenario, we allow for both Rashba and Dresselhaus type spin-orbit
coupling. Our results are obtained via the quasiclassical theory of
superconductivity, extended to include spin-orbit coupling in the Usadel
equation and Kupriyanov--Lukichev boundary conditions. Unlike previous works,
we have derived a Riccati parametrization of the Usadel equation with
spin-orbit coupling which allows us to address the full proximity regime.
First, we consider the density of states in both SF bilayers and SFS trilayers,
where the spectroscopic features in the latter case are sensitive to the phase
difference between the two superconductors. We find that the presence of
spin-orbit coupling leaves clear spectroscopic fingerprints in the density of
states due to its role in creating spin-triplet Cooper pairs. Unlike SF and SFS
structures without spin-orbit coupling, the density of states in the present
case depends strongly on the direction of magnetization. We show that the
spin-orbit coupling can stabilize singlet superconductivity even in the
presence of a strong exchange field $h \gg \Delta$. This leads to the
possibility of a magnetically tunable minigap: changing the direction of the
exchange field opens and closes the minigap. We also determine how the critical
temperature $T_c$ of an SF bilayer is affected by spin-orbit coupling and
demonstrate that one can achieve a spin-valve effect with a single ferromagnet.
We find that $T_c$ displays highly non-monotonic behavior both as a function of
the magnetization direction and the type and direction of the spin-orbit
coupling, offering a new way to exert control over the superconductivity of
proximity structures.
