Abstract
We investigate theoretically and experimentally the development of instabilities in passive ring cavities with stepwise longitudinal variation of the dispersion. We derive an extended version of the Lugiato-Lefever equation that permits to model dispersion oscillating cavities and we demonstrate that this equation is valid well beyond the mean field approximation. We review the theory of Turing (modulational) and Faraday (parametric) instability in inhomogeneous fiber cavities. We report the experimental demonstration of the generation of stable Turing and Faraday temporal patterns in the same device, which can be controlled by changing the detuning and/or the input power. Moreover, we experimentally record the round-trip-to-round-trip dynamics of the spectrum, which shows that Turing and Faraday instabilities not only differ by their characteristic frequency but also by their dynamical behavior.
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