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

Boris Konopelchenko; Antonio Moro

doi:10.1117/12.621824

5 October 2005 Paraxial light in a Cole-Cole nonlocal medium: integrable regimes and singularities

Boris Konopelchenko, Antonio Moro

Proceedings Volume 5949, Nonlinear Optics Applications; 59490C (2005) https://doi.org/10.1117/12.621824
Event: Congress on Optics and Optoelectronics, 2005, Warsaw, Poland

Abstract

Nonlocal nonlinear Schroedinger-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.

Citation Download Citation

Boris Konopelchenko and Antonio Moro "Paraxial light in a Cole-Cole nonlocal medium: integrable regimes and singularities", Proc. SPIE 5949, Nonlinear Optics Applications, 59490C (5 October 2005); https://doi.org/10.1117/12.621824

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