Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization (2212.13052v1)

Abstract: We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light-bullets, are the only existing and stable states for a given set of parameters. This property is extremely rare, if not unknown, in passive nonlinear physical systems. As a result, the excitation of the cavity with any input field leads to the deterministic formation of a target soliton or breather, with a spatiotemporal profile that unambiguously corresponds to the given cavity and pumping conditions. In addition, the tuning of the potential width along the temporal direction results in the existence of a plethora of stable asymmetric solitons. Our results may provide a solid route towards the observation of dissipative light bullets and three-dimensional breathers.

• The paper presents a novel methodology using a 3D parabolic potential to excite robust, stable 3D high-order solitons and breathers in driven dissipative systems, modeled by a Kerr cavity.
• The introduction of this 3D potential uniquely stabilizes 3D solitons, making them the sole attractors for given parameters, challenging previous ideas about their stability in passive systems.
• Tuning the potential allows deterministic excitation of desired stable asymmetric and high-order solitons and breathers, with potential applications in robust optical frequency comb generation.

Robust Three-Dimensional High-Order Solitons and Breathers in Driven Dissipative Systems

This paper presents a comprehensive approach for the excitation of robust three-dimensional (3D) high-order solitons and breathers in passively driven nonlinear cavities, using an optical Kerr cavity with diffraction and anomalous dispersion as the model system. The authors introduce a novel methodology that involves the incorporation of a 3D parabolic potential, which is critical in breaking translational symmetry and ensuring the formation of stable light-bullets. This is an intriguing development, given that 3D soliton stability is often elusive due to effects such as higher-order perturbations leading to decay or collapse.

Key Findings

• Unique Stability: The paper demonstrates that the introduction of the 3D parabolic potential causes the cavity system to stabilize 3D solitons as the only existing attractors for given parameters. The deterministic formation of a specific soliton or breather with an unequivocal spatiotemporal profile derives solely from the cavity and pumping conditions. This challenges prior understanding that considered such stability rare or difficult to attain in passive dissipative systems.
• High-Order and Asymmetric Solitons: The tuning of the potential along the temporal direction yields a variety of stable asymmetric solitons. This process facilitates the deterministic excitation of desired solitonic states from arbitrary inputs.

Methodology and Results

The paper introduces a general model in the form of a master equation that encompasses driven Kerr cavities with 3D potentials:

$$\partial_t A = i \nabla^2 A - i(x^2 + y^2 + C\tau^2)A + i|A|^2A - (\alpha + i\delta)A + P$$

Here, $A$ is the electric field amplitude, with the parameters and coefficients representing group velocity dispersion, diffraction, and loss, among others. The authors highlight that despite the non-linear complexities, stable light bullets are achieved, and their forms are elaborated through rigorous path-continuation methods and time propagation simulations.

The findings indicate a rich bifurcation structure of stable states, with potential applications extending to robust frequency comb generation in optical systems. The breathers that emerge exhibit perfectly periodic oscillations over extensive simulation timelines, underscoring their stability.

Implications and Future Research Directions

The research establishes a significant paradigm shift in the understanding and generation of high-order 3D solitons in nonlinear systems. This work not only provides a theoretical foundation for soliton stability in dissipative systems but also opens avenues for experimental demonstration and technological applications, such as in optical frequency combs and advanced photonic devices.

Moreover, the results may have implications beyond optics, potentially informing studies in Bose-Einstein condensates and plasma physics, where similar dissipative structures are of interest. Future research could explore the practical realization of these findings in microcavity contexts, with an emphasis on leveraging this knowledge for enhanced coherent light sources and communication technologies.

Conclusion

This paper's approach to ensuring the robust excitation and stabilization of 3D solitons within driven Kerr cavities marks a significant advancement in nonlinear dynamics. The integration of 3D potentials effectively mitigates the traditional challenges faced in soliton stabilization, providing a pathway for continued exploration and application across various domains of physics.