Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato–Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that three-dimensional (3D) dissipative structures occur in a strongly nonlinear regime where modulational instability is subcritical. We provide a detailed analysis on the formation of optical 3D crystals in both the super- and sub-critical modulational instability regimes, and we highlight their link to the formation of light bullets in diffractive and dispersive Kerr resonators. We construct bifurcation diagrams associated with the formation of optical crystals in both monostable and bistable regimes. An analytical study has predicted the predominance of body-centered-cubic (bcc) crystals in the intracavity field over a large variety of other 3D solutions with less symmetry. These results have been obtained using a weakly nonlinear analysis but have never been checked numerically. We show numerically that indeed the most robust structures over other self-organized crystals are the bcc crystals. Finally, we show that light-bullets and clusters of them can occur also in a bistable regime.

使用平均场 Lugiato-Lefever 方程 [Gopalakrishnan、Panajotov、Taki 和 Tlidi，Phys. 牧师莱特。126, 153902 (2021)]。结果表明，三维 (3D) 耗散结构出现在调制不稳定性为亚临界的强非线性区域中。我们详细分析了超临界和亚临界调制不稳定性状态下光学 3D 晶体的形成，并强调了它们与衍射和色散克尔谐振器中轻型子弹形成的联系。我们构建了与单稳态和双稳态光学晶体形成相关的分叉图。一项分析研究预测了体心立方 (bcc) 晶体在腔内场中的优势，而不是对称性较差的各种其他 3D 解决方案。这些结果是使用弱非线性分析获得的，但从未进行过数值检验。我们从数值上表明，与其他自组织晶体相比，确实最坚固的结构是 bcc 晶体。最后，我们表明，在双稳态中也可以出现光弹和它们的簇。