Stability and dynamics of transverse field structures in the optical parametric oscillator near resonance signal detuning

An order parameter equation is derived for an optical parametric oscillator near the resonance signal detuning limit in two dimensions. The parametric mixing between signal and pump fields with cavity diffraction leads to a quintic, fourth-order evolution equation of the Swift-Hohenberg type which supports the formation of cavity solitons, plane waves and periodic structures. The formation, interaction and stability of each of the nontrivial spatial structures is considered via extensive numerical simulations. Stable optical structures are created which can be used as the basis for a wide range of all-optical technologies