Spatiotemporal nonlinear optical self-similarity in three dimensions

Area of Science:

• Nonlinear optics
• Mathematical physics

Background:

• The (3+1)D nonlinear Schrödinger equation models light propagation in various media.
• Self-similar solutions are crucial for understanding stable light propagation.
• Controlling light structures is key to advanced optical technologies.

Purpose of the Study:

• To introduce novel spatiotemporally expanding self-similar solutions.
• To investigate solutions with and without initial vorticity.
• To explore potential for collapse-free nonlinear optical phenomena.

Main Methods:

• Solving the (3+1)D nonlinear Schrödinger equation with gain.
• Analyzing self-similar solutions in the absence of initial vorticity.
• Analyzing self-similar solutions with nonzero initial vorticity.

Main Results:

• Demonstrated expanding self-similar light bullets with parabolic intensity and linear chirp.
• Found expanding vortex torus solutions with central phase singularities for nonzero vorticity.
• Identified self-similar structures that expand without collapse.

Conclusions:

• Expanding self-similar light structures offer a new paradigm in nonlinear optics.
• These solutions provide a route towards collapse-free spatiotemporal nonlinear optics.
• The findings are relevant for developing advanced optical systems and controlling light propagation.