We study the formation of localized patterns arising in doubly resonant dispersive optical parametric oscillators. They form through the locking of fronts connecting a continuous-wave and a Turing pattern state. This type of localized state can be seen as a slug of the pattern embedded in a homogeneous surrounding. They are organized in terms of a homoclinic snaking bifurcation structure, which is preserved under the modification of the control parameters of the system. We show that, in the presence of phase mismatch, localized patterns can undergo oscillatory instabilities which make them breathe in a complex manner.

We study the appearance of localized patterns in degenerate optical parametric oscillators in a doubly resonant configuration. We find that in some parameter regimes these states undergo oscillatory instabilities which make them breathe.

Self-pulsing is an ubiquitous phenomenon arising in coupled nonlinear systems. We here experimentally study the self-pulsing dynamics occurring in two coupled fiber ring resonators. Our results are supported and extended by a detailed bifurcation analysis.

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