Self-accelerating self-trapped nonlinear beams of Maxwell's equations.

Area of Science:

• Nonlinear optics
• Mathematical physics
• Wave propagation

Background:

• Exact solutions to Maxwell's equations with optical nonlinearities are crucial for understanding light-matter interactions.
• Nonlinear optical effects like self-trapping and backscattering significantly influence beam dynamics.
• Highly non-paraxial beams present unique challenges in theoretical and computational analysis.

Purpose of the Study:

• To present novel shape-preserving, self-accelerating beams that are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity.
• To investigate the role of nonlinearity, diffraction, and backscattering in maintaining beam acceleration along circular trajectories.
• To explore the potential for self-reflection and U-shaped trajectories in these nonlinear beams.

Main Methods:

• Analytical derivation of exact beam solutions incorporating nonlinear optical effects.
• Development of a projection operator technique to separate forward and backward propagating waves.
• Implementation of reverse simulation methods to analyze complex beam dynamics.

Main Results:

• Demonstrated shape-preserving, self-accelerating beams exhibiting circular trajectories under nonlinear conditions.
• Identified self-trapping and backscattering as key mechanisms for maintaining beam acceleration and shape.
• Established the significance of the backscattered wave in the dynamics of these non-paraxial nonlinear beams.

Conclusions:

• Nonlinear optical effects enable the creation of self-accelerating beams that resist diffraction and maintain their shape.
• The interplay between nonlinearity, diffraction, and backscattering dictates the circular trajectory of these beams.
• The study opens possibilities for observing self-reflecting beams forming 'U' shaped trajectories through nonlinear interactions.