Localization problem in optics: Nonlinear quasiperiodic media

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Abstract
We have presented a detailed numerical study of the localization problem in a nonlinear quasiperiodic structure for normal incidence of plane-polarized light. The main conclusions are as follows. Strong surface localization, which is observed for forbidden states (transmission coefficient T≃0) in the linear theory, is strongly affected even by weak nonlinearity, resulting in inhibition of localization, while the extended states corresponding to allowed regions (T≃1) in the linear theory retain their distribution pattern. Depending on nonlinearity, forbidden regions may exhibit critical-state behavior. The evidence of bulk localization is apparent from the nature of solitonlike field distributions for allowed regions. The bulk localization, which is a result of a delicate interplay between dispersion and nonlinearity, persists for a very large number of layers in contrast to linear theory. The bulk localized states have been shown to be self-similar.