Estudio de solitones de helmholtz en interfaces no lineales sobre sistemas de procesamiento paralelo

Résumé

The character of this Thesis is two-fold, since the work has been developed within two different scientific fields such as nonlinear optics and parallel computing. As regards parallel computing, efficient parallel implementations of nonlinear beam propagation methods are presented. Within nonlinear optics, this Thesis has based on the Helmholtz theory of spatial solitons to provide a framework for studying the behaviour of soliton beams at the planar boundary separating two Kerr-type media. Numerical results obtained through massive parallel simulations fully agree with the theoretical predictions of the model presented in this Thesis. Both the Split-Step Fourier and the Nonparaxial Beam Propagation methods, used in the numerical integration of the Nonlinear Schrodinger equation and the Nonlinear Helmholtz equation, respectively, have been parallelized. Special attention has been focused on the parallelization of the computational core of both methods, constituted by the calculation of an operator in the spectral domain by means of successive forward and backward Fast Fourier Transforms. Both computational and communication savings are reduced in relation to other alternatives based on the use of the state-of-the-art parallel routines. Performance test carried out in both distributed and shared memory systems have exhibited a high performance for all problems and hardware configurations tested. Soliton reflection and refraction at nonlinear interfaces is studied in terms of the Helmholtz theory. Unlike previous paraxial analysis, whose validity is restricted to vanishingly small angles of propagation, this approach preserves the full angular content of the problem. Such angular character is present in one of the main contributions of this Thesis, namely a generalised Snell law that governs the behaviour of both bright and dark solitons impinging on a nonlinear interface at arbitrary angles. In the case of bright solitons, substantial differences in relation to existing paraxial studies have been highlighted. The analysis presented for dark soliton refraction, however, constitute a first approach to a problem hardly addressed before.