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Proceedings Paper

Description of caustic structures in non-linear media: envelope of characteristic trajectories for the non-linear Schrodinger equation
Author(s): J. C. Juarez-Morales; G. Martinez-Niconoff; J. Munoz-Lopez
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Paper Abstract

We describe the mode solutions for the Helmholtz Equation using the operator formalism. The study is extended to the structural solution for the focused non-linear Schrödinger equation (NLSE). With this treatment, we obtain for the NLSE a reduced partial differential equation, whose characteristic solution has an eikonal structure which allows us a geometrical analysis. Focusing region in non-linear media is described by means of an envelope region of eikonal trajectories establishing similar behaviors with caustic structures. In particular, if the boundary condition consists of a slit shape curve, the focusing profile corresponds with the evolute of the curve. In general, the profile satisfies a non-linear partial differential equation whose structure remains non-variable under changes of variables which may represents scaling or rotations. This feature permits us to extend the analysis to other kind of focusing regions, such as focusing vortex.

Paper Details

Date Published: 14 September 2007
PDF: 7 pages
Proc. SPIE 6669, Seventh International Conference on Solid State Lighting, 66691F (14 September 2007); doi: 10.1117/12.732202
Show Author Affiliations
J. C. Juarez-Morales, Instituto Nacional de Astrofísica, Óptica y Electrónica (Mexico)
G. Martinez-Niconoff, Instituto Nacional de Astrofísica, Óptica y Electrónica (Mexico)
J. Munoz-Lopez, Instituto Nacional de Astrofísica, Óptica y Electrónica (Mexico)


Published in SPIE Proceedings Vol. 6669:
Seventh International Conference on Solid State Lighting
Ian T. Ferguson; Nadarajah Narendran; Tsunemasa Taguchi; Ian E. Ashdown, Editor(s)

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