Abstract
Formation of one-dimensional spatial structures in degenerate optical parametric oscillation due to diffraction effects is discussed and their analogy with parametrically excited localized structures studied in hydrodynamics is illustrated. It is shown that, when the emergence of roll paterns is inhibited by cavity constraints, localized structures in the form of bright or dark solitary waves for the signal field may be generated for appropriate detunings of the pump field from a cavity resonance. The dark waves exist when bifurcation is supercritical and are stable close to threshold, whereas bright waves spontaneously arise in the subcritical case for large pump detunings and below threshold for oscillation due to a modulational instability of the homogeneous state.
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