Abstract
The main aim of this thesis is the study of the interaction between nonlinearity and disorder, the pivotal processes underlying the localization of light. Knowing how the manipulation of an optical system by modifying the mutual competition between disorder and nonlinearity can result in localized wave-forms is an intriguing challenge and a significant target of modern optics. In this section, we discuss the Nonlinear Schroedinger equation (NLS), a paradigmatic universal nonlinear model that describes several physical phenomena in the framework of several disciplines, from the nonlinear optics to the quantum condensate. In a simple way, this equation allows to understand how the nonresonant nonlinearity (specifically the Kerr effect) can promote the formation of localized wave-forms through the balance of two opposite effects: wave dispersion and nonlinear response. The NLS represents the starting point to study the complex interplay between nonlinearity and disorder.
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Notes
- 1.
Once the disorder is added to the system, the permittivity, and hence the refractive index, will become explicitly dependent on the spatial coordinate, \(\epsilon=\epsilon(r,E).\)
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Folli, V. (2012). Nonlinear Schroedinger Equation. In: Nonlinear Optics and Laser Emission through Random Media. Springer Theses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4513-1_2
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DOI: https://doi.org/10.1007/978-94-007-4513-1_2
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