We investigate polarizations of gravitational waves in generalized theories of gravity
whose action contains a nonminimal coupling (NMC) between an exponential function
of f(R) gravity and the matter field. Specifically, we consider two classes of such models.
In the first case, we assume an explicit NMC between the matter Lagrangian density and
curvature while in the second case, we consider the exponential f(R) gravity coupled
to the trace of the stress-energy tensor of a scalar field. Using the Newman–Penrose
quantities, we show that these models can be considered as suitable choices in order to
produce new polarization modes.