Generation, Dynamics, and Interaction of Quartic Solitary Waves in Nonlinear Laser Systems

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the inputs to these systems. Therefore, I numerically analyze the generation of localized states arising from dominant quartic dispersion where noise is added on the inputs to the laser system and the resulting robustness of these states. In addition, I also examine the interaction of solitary waves with dominant quartic dispersion in different media and how these results can differ from the conventional case of dominant quadratic dispersion. The results show that the behavior that is exhibited for the quadratic case for generation of pulses is maintained and furthermore, there are increased opportunities for stable localized states in quartic Kerr media

Generation, Dynamics, and Interaction of Quartic Solitary Waves in Nonlinear Laser Systems

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the inputs to these systems. Therefore, I numerically analyze the generation of localized states arising from dominant quartic dispersion where noise is added on the inputs to the laser system and the resulting robustness of these states. In addition, I also examine the interaction of solitary waves with dominant quartic dispersion in different media and how these results can differ from the conventional case of dominant quadratic dispersion. The results show that the behavior that is exhibited for the quadratic case for generation of pulses is maintained and furthermore, there are increased opportunities for stable localized states in quartic Kerr media

Quartic Kerr cavity combs: bright and dark solitons

[EN] We theoretically investigate the dynamics, bifurcation structure, and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are analyzed, highlighting the main differences from the standard second-order dispersion case. In the anomalous regime, single and multi-peak localized states exist and are stable over a much wider region of the parameter space. In the normal dispersion regime, stable narrow bright solitons exist. Some of our findings can be understood using a new, to the best of our knowledge, scenario reported here for the spatial eigenvalues, which imposes oscillatory tails to all localized states.PPR acknowledges the European Union's Marie Sklodowska-Curie grant 101023717. SH and AA have been supported by NSF RTG grant DMS-1840260 and AA was supported by grant NSF/DMS-1909559. SH and AA also benefited from discussions with Dr. Ross Parker. YVK and CM gratefully acknowledge discussions with Professor L. Torner.Parra-Rivas, P.; Hetzel, S.; Kartashov, Y.; Fernández De Córdoba, P.; Conejero, JA.; Aceves, A.; Milián Enrique, C. (2022). Quartic Kerr cavity combs: bright and dark solitons. Optics Letters. 47(10):2438-2441. https://doi.org/10.1364/OL.45594424382441471