Abstract
The real world embraces nonlinearity and disorder and works with their mutual interplay. All the natural and artificial bodies are nonlinear and disordered, especially in the interaction with strong fields, the pivotal topic of this thesis. Here, we will explore several features of this interplay: we will discuss new intriguing phenomena (like the use of nonlinearity to control the stability of light localizations, the emission through two-levels laser action, the first observation of competitive laser spectra by granular media, etc.), that open up novel avenues for research in several fields, from medical imaging to nonlinear optics. In this preface, we give an overview about these two mechanisms, with special emphasis on localization phenomena.
Fortunately, we are living in a nonlinear world. While linearization beautifies physics, nonlinearity provides excitement in physics Y. R. Shen
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- 1.
The restoring force, related to the Coulomb field of the ion core and that binds the electron to its equilibrium position, is not simply elastic and, hence, the energy levels are no longer equidistant.
- 2.
We assume no free charges present and no magnetization of the medium.
- 3.
The first reported observation of solitons was made by J. S. Russel in 1984 by studying water waves but, once first observed and understood, the solitary waves are found in every branch of the physics of wave propagation [1, 2, 3, 4, 5]. He wrote
I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation
—Report of the fourteenth meeting of the British Association for the Advancement of Science, York, September 1844 (London 1845), pp. 311–390, Plates XLVII–LVII.
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Folli, V. (2012). Introduction. In: Nonlinear Optics and Laser Emission through Random Media. Springer Theses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4513-1_1
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DOI: https://doi.org/10.1007/978-94-007-4513-1_1
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