Paraxial light in a Cole-Cole nonlocal medium: Integrable regimes and singularities

Boris Konopelchenko, Antonio Moro*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)


Nonlocal nonlinear Schrödinger-type equation is derived as a model to describe paraxial light propagation in nonlinear media with different 'degrees' of nonlocality. High frequency limit of this equation is studied under specific assumptions of Cole-Cole dispersion law and a slow dependence along propagating direction. Phase equations are integrable and they correspond to dispersionless limit of Veselov-Novikov hierarchy. Analysis of compatibility among intensity law (dependence of intensity on the refractive index) and high frequency limit of Poynting vector conservation law reveals the existence of singular wavefronts. It is shown that beams features depend critically on the orientation properties of quasiconformal mappings of the plane. Another class of wavefronts, whatever is intensity law. is provided by harmonic minimal surfaces. Illustrative example is given by helicoid surface. Compatibility with first and third degree nonlocal perturbations and explicit solutions are also discussed.

Original languageEnglish
Article number59490C
Pages (from-to)1-12
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Publication statusPublished - 1 Dec 2005
Externally publishedYes
EventNonlinear Optics Applications - Warsaw, Poland
Duration: 31 Aug 20052 Sept 2005


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