Abstract
The transverse pattern formation in singly and doubly resonant optical parametric oscillators (OPOs) is investigated. The study is based on the derivation and analysis of the amplitude equation for these two cases of OPOs. It is shown that the amplitude equation of a singly resonant OPO (the complex Ginzburg-Landau equation) is similar to that of a class A laser. The doubly resonant OPO is described by a Swift-Hohenberg equation analogous to the amplitude equation obtained recently in the optical bistability. The spontaneous structure formation of OPOs is also demonstrated numerically.