Planar light bullets under conditions of second-harmonic generation

Area of Science:

• Nonlinear Optics
• Mathematical Physics

Background:

• Second-harmonic generation (SHG) is crucial for frequency conversion in nonlinear optics.
• Understanding spatiotemporal solitons in 2D media with anomalous dispersion is key for optical communications.

Purpose of the Study:

• To analytically and numerically investigate the dynamics of two-component spatiotemporal solitons in 2D media with anomalous dispersion.
• To determine the stability criteria and oscillation periods of these solitons.
• To explore the formation of light bullets and the effects of phase and group-velocity mismatch.

Main Methods:

• Averaged Lagrangian method for analytical approximation of soliton solutions.
• Variational approach to derive stability criteria and oscillation periods.
• Direct numerical simulations to validate analytical predictions and observe soliton dynamics.

Main Results:

• An approximate analytical solution for planar spatiotemporal two-component solitons was obtained.
• Decreasing soliton component amplitudes and increasing transverse coordinates lengthen temporal duration.
• A stability criterion and oscillation period for light bullets were derived.
• Stable propagation of solitons was demonstrated numerically over long distances.
• Formation of two-component light bullets was observed when initiating with a fundamental frequency pulse.
• Effects of phase and group-velocity mismatch on pulse propagation were investigated.

Conclusions:

• The averaged Lagrangian method provides accurate predictions for 2D spatiotemporal soliton dynamics in media with anomalous dispersion.
• The derived stability criterion and oscillation period are validated by numerical simulations.
• Stable light bullet formation and propagation are achievable, offering potential for advanced optical systems.