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Noise-sustained convective structures in nonlinear optics
No full textEvidence of noise-sustained patterns in nonlinear optical systems is given. They are found in passive optical cavities, filled by Kerr type nonlinear media, when the angle of incidence of the pump beam is not zero, in a regime of convective instability. These patterns arise as a macroscopic manifestation of dynamically amplified noise, with amplification factors of up to 10(5). We characterize the difference between noise-sustained and deterministic patterns in terms of statistical properties of the field spectral intensity
Growth dynamics of noise-sustained structures in nonlinear optical resonators
No full textThe existence of macroscopic noise-sustained structures in nonlinear optics is theoretically predicted and numerically observed, in the regime of convective instability. The advection-like term, necessary to turn the instability to convective for the parameter region where advection overwhelms the growth, can stem from pump beam tilting or birefringence induced walk-off. The growth dynamics of both noise-sustained and deterministic patterns is exemplified by means of movies. This allows to observe the process of formation of these structures and to confirm the analytical predictions. The amplification of quantum noise by several orders of magnitude is predicted. The qualitative analysis of the near- and far-field is given. It suffices to distinguish noise-sustained from deterministic structures; quantitative informations can be obtained in terms of the statistical properties of the spectra
Noise-Sustained Structures in Nonlinear Optical Cavities: Theory and Future Perspectives
No full textTwo-dimensional noise-sustained structures in optical parametric oscillators
No full textThe problem of two-dimensional (2D), transverse, noise-sustained pattern formation is theoretically and numerically studied, in the case of an optical parametric oscillator, for negative signal detuning. This gives a complete analysis of a 2D, convective, pattern forming system which is also relevant to more general 2D physical systems. For the optical parametric oscillator, the transversal walk-off due to the nonlinear crystal birefringence, exploited to phase match the frequency down-conversion process, turns the instability to convective up to a certain threshold. In this regime, noise-sustained patterns can be observed. These structures are a macroscopic manifestation of amplified microscopic noise which, in the context of optics, can be of quantum nature. Directly observable properties of the near and far field as well as statistical properties of the spectral intensity help to distinguish noise- from dynamics-sustained structures. Moreover, the analysis indicates that the walk-off term breaks the rotational symmetry of the 2D model. This causes a preferential selection of the stripe orientation, which would be otherwise random, the modulus of the wave vector being the only restricted value. At the convective threshold an entire set of spatial modes becomes unstable, whereas the threshold of absolute instability depends on the relative orientation of the mode. Beyond the threshold for absolute instability, this causes the coexistence, in the linear regime of evolution, of modes that are absolutely unstable, and others that are only convectively unstable. The numerical solutions of the dynamical equations of the system under study confirm the analytical predictions for the value of the instability thresholds and the kind of pattern selected. Moreover, they allow us to investigate the nonlinear regime showing qualitatively the coexistence of modes with different types of instability and giving a quantitative characterization of the transition from noise-sustained to dynamics-sustained structures
Space inversion symmetry breaking and pattern selection in nonlinear optics
No full textPattern formation in nonlinear optical cavities, when an advection-like term is present, is analysed. This term breaks the space inversion symmetry causing the existence of a regime of convective instabilities, where noise-sustained structures can be found, and changing the pattern orientation and the selected wavevector. The concepts of convective and absolute instability, noise-sustained structures and the selection mechanisms in two dimensions are discussed in the case of optical parametric oscillators and a Kerr resonator. In the latter case, in which hexagons are the selected structure, we predict and observe that stripes are the most unstable structures in the initial linear transient. In the nonlinear regime of the absolute instability these stripes destabilize and hexagons form. Their orientation is dictated by that of the transient stripes and therefore by the advection term. In the convective regime we predict and observe disordered noise-sustained hexagons, preceded in space by noise-sustained stripes
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