Quartic Kerr cavity combs: bright and dark solitons

Area of Science:

• Nonlinear optics
• Cavity quantum electrodynamics
• Soliton physics

Background:

• Kerr cavities are fundamental systems for studying light-matter interactions and nonlinear phenomena.
• Localized states, such as solitons, are crucial for understanding optical signal processing and pattern formation.
• Dispersion management is key to controlling and stabilizing optical states.

Purpose of the Study:

• To theoretically investigate the dynamics, bifurcation structure, and stability of localized states in Kerr cavities.
• To analyze these states at the pure fourth-order dispersion point, comparing normal and anomalous group velocity dispersion regimes.
• To explore differences from standard second-order dispersion systems.

Main Methods:

• Theoretical analysis of nonlinear dynamics in Kerr cavities.
• Investigation of bifurcation structures and stability properties.
• Examination of both normal and anomalous group velocity dispersion regimes.

Main Results:

• In the anomalous dispersion regime, single and multi-peak localized states exhibit stability over an extended parameter range.
• Stable narrow bright solitons are identified in the normal dispersion regime.
• A novel scenario for spatial eigenvalues, leading to oscillatory tails in localized states, was discovered.

Conclusions:

• Fourth-order dispersion significantly alters the dynamics and stability of localized states compared to second-order dispersion.
• The anomalous regime offers a wider parameter space for stable multi-peak localized states.
• The newly identified eigenvalue scenario provides a unifying explanation for the observed oscillatory tails.