Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results
Abstract
:1. Introduction and the Basic Models
2. Basic Soliton Families in the One-Dimensional Fractional Medium
2.1. Stationary States and Analysis of Their Stability
2.2. The Quasi-Local Approximation for Modes Carried by a Rapidly Oscillating Continuous Wave
2.3. The Scaling Relation and Variational Approximation (VA) for Soliton Families
2.4. Numerical Findings
3. Further Results for Nonlinear Modes in One-Dimensional Fractional Waveguides
3.1. Systems with Trapping Potentials
3.2. Dissipative Solitons Produced by the Fractional Complex Ginzburg-Landau Equation (CGLE)
4. Vortex Modes in Two-Dimensional (2D) Fractional-Diffraction Settings
4.1. Stationary Vortex Solitons
4.2. Dynamics of Vortical Clusters
4.3. Stabilization of 2D Solitons by the Trapping Potential
5. Conclusions
Funding
Acknowledgments
Conflicts of Interest
References
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Malomed, B.A. Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results. Photonics 2021, 8, 353. https://doi.org/10.3390/photonics8090353
Malomed BA. Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results. Photonics. 2021; 8(9):353. https://doi.org/10.3390/photonics8090353
Chicago/Turabian StyleMalomed, Boris A. 2021. "Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results" Photonics 8, no. 9: 353. https://doi.org/10.3390/photonics8090353
APA StyleMalomed, B. A. (2021). Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results. Photonics, 8(9), 353. https://doi.org/10.3390/photonics8090353