We consider the mean field model of the optical parametric oscillator (OPO) when the second harmonic of the OPO is driven externally by a spatially periodic pump field. Exact solutions for the first and second harmonics can be derived using Jacobi elliptic functions. These solutions can describe behavior that is both sinusoidally varying as well as front and pulse-like in the transverse direction. Numerical simulations show that for a wide range of parameter space these solutions are stabilized transverse field structures. Bifurcations can also occur which result in new nontrivial, but periodic, spatial structures.