Fortunato Tito Arecchi

Pattern formation in extended media

High-dimensional optical dynamics results from the competition of many degrees of freedom, either space-like as in extended media, or time-like as in delayed dynamics. In both cases competition gives rise to patterns similar to those observed in fluids, hence the name of "dry hydrodynamics".

1990: The gradual transition from a small to a high number of competing modes is characterized by the passage from periodic and chaotic alternation (PA, CA) where one single mode per time is present, to space time chaos (STC) where many modes coexist at the same time. These phenomena, first observed in[179], are explained in terms of cavity symmetries.
1991: A heterodyne method introduced to detect phase singularities or vortices of the optical field[185] allows the description of optical pattern formation in terms of vortex statistics. The different scaling of the vortex statistics with the cavity size provides a discrimination between two regimes, one in which patterns are imposed by the boundary and one where patterns are intrinsic of the medium, as in chemical Turing morphogenesis[202].
1992: High dimensional chaos in a strongly confined medium, as a single mode laser cavity, results by introducing a feedback with a delay longer than the intrinsic correlation time of the laser dynamics[195].
1995-1997: Morphogenetic mechanisms analogous to those of fluid mechanics, are shown by the onset of different crystal and quasi-crystal symmetries, depending on the boundary constraints[224]. As the system is driven far away from threshold, many of these "pure" symmetries are excited simultaneously, but rather than quenching each other, they coexist in different regions, giving rise to a multi-domain structure[250] ( later called chimeras) or they lock into a single super-structure.
1999: Ref.[274] reports the scaling behaviour of defects after a rapid passage from below to above threshold in a nonlinear optical system. This corresponds to the rapid passage from many uncorrelated domains to an asymptotic single coherence area; however the asymptotic state is reached for long times, and immediately at the end of the switch pulse one finds a collection of frozen defects, due to the critical slowing down at the transition point. Such a feature is common to all extended critical phenomena; it had been hypothesized for cosmological defects (Kibble-Zurek ) and observed also in liquid helium.

2007-2009: Liquid crystal light oscillators provide evidence of spatio-temporal pulses[354] and of localized giant phenomena[385] called Optical Rogue Waves (review[426]).

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