Bright and dark localized states in doubly resonant optical parametric oscillators

Localized dissipative states (LSs) are one example of the many types of emergent patterned states appearing in systems out of thermodynamic equilibrium [1] . The formation of LSs is generally related with the presence of bistability between two different states and the locking of front waves connecting them. In optics, this type of states can emerge in externally driven dispersive nonlinear cavities, due to a double balance between energy dissipation and driving on one hand, and dispersion and nonlinearity on the other hand. LSs have been shown experimentally in Kerr cavities [2] , where they have been found to underpin the formation of optical frequency combs [3] . Recently, they have been also discovered in quadratic-Kerr cavities [4] .