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Self-similar parabolic beam generation and propagation
Guoqing Chang1, Herbert G Winful, Almantas Galvanauskas
1FOCUS Center and Center for Ultrafast Optical Science, University of Michigan, 2200 Bonisteel Boulevard, Ann Arbor, Michigan 48109-2099, USA.
Summary
Researchers solved nonlinear Schrödinger equations analytically and numerically, finding self-similar parabolic beams in (2+1) dimensions. This demonstrates stable beam propagation in nonlinear media with gain and negative nonlinear index.
Area of Science:
- Nonlinear Optics
- Mathematical Physics
Background:
- Nonlinear Schrödinger equations model light propagation in various media.
- Spatial solitons in bulk media with nonsaturating nonlinearities are typically unstable in (2+1) dimensions.
Purpose of the Study:
- To analytically and numerically solve (1+1)- and (2+1)-dimensional amplified nonlinear Schrödinger equations.
- To investigate the possibility of self-similar beam propagation in (2+1) dimensions.
Main Methods:
- Analytical solutions using asymptotic analysis.
- Numerical simulations of the nonlinear Schrödinger equations.
Main Results:
- An asymptotic solution was found for self-similar propagation with parabolic amplitude and phase profiles.
- Self-similar parabolic beams were shown to be possible in (2+1)-dimensional media with gain and a negative nonlinear index.
Conclusions:
- The findings extend the understanding of beam propagation beyond (1+1) dimensions.
- Stable self-similar parabolic beam propagation is achievable under specific conditions in nonlinear media.