Analytical three-dimensional solutions of Schrodinger equation in fiber with nonlinear refractive index

D. Y. Dakova; R. N. Bozhinova; L. I. Pavlov

doi:10.1117/12.726998

5 March 2007 Analytical three-dimensional solutions of Schrodinger equation in fiber with nonlinear refractive index

D. Y. Dakova, R. N. Bozhinova, L. I. Pavlov

Proceedings Volume 6604, 14th International School on Quantum Electronics: Laser Physics and Applications; 66041N (2007) https://doi.org/10.1117/12.726998
Event: 14th International School on Quantum Electronics: Laser Physics and Applications, 2006, Sunny Beach, Bulgaria

Abstract

The solutions of vector Nonlinear Schrodinger Equation (NLSE) in fiber with nonlinear dispersion and nonlinear refractive index of the type of n₂ ∝ (x² + y²) are presented in the report. Exact analytical 3D+1 soliton solutions of NLSE are obtained in Cylindrical Coordinate System {0;&rgr;;&Jgr;;z} which axis OZ coincides with geometrical axis of the &rgr;² = x² + y² ≠ 0. In the case of (x² + y²) → 0 is solved corresponding linear equation. It has been found the connection point between exact analytical solutions of both types of equations - vector nonlinear Schrodinger and corresponding linear equations. The obtained analytical solutions of both types of equations in cylindrical coordinates are represented and in Cartesian coordinates. Following the results the main application of these 3D+1 solitons is in realizing of stable waveguide propagation of laser pulses with random intensities in nonlinear fibers.

Citation Download Citation

D. Y. Dakova, R. N. Bozhinova, and L. I. Pavlov "Analytical three-dimensional solutions of Schrodinger equation in fiber with nonlinear refractive index", Proc. SPIE 6604, 14th International School on Quantum Electronics: Laser Physics and Applications, 66041N (5 March 2007); https://doi.org/10.1117/12.726998

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