Aberration stabilized light bullets in normal dispersion injected Kerr resonators

We investigate three-dimensional light bullets (LBs) in an optically injected, vertically emitting Kerr-Gires-Tournois interferometer operating in the normal dispersion regime. In the uniform field limit, the dynamics is governed by a generalized Lugiato-Lefever equation with third-order dispersion, paraxial diffraction, and fourth-order diffraction, stemming from lens and mirror aberrations close to the self-imaging condition. Using direct numerical simulations, we show that without aberration only transversely drifting, tilted multi-peak localized states (LSs) are stable in two dimensions, whereas no stable LBs exist in three dimensions. However, a small negative spherical aberration stabilizes a rich multistable family of two-dimensional LSs, including straight and tilted multi-peak LSs, oscillating states, and complex bound states, which persist even for negative paraxial diffraction. We identify an Andronov-Hopf bifurcation followed by a homoclinic transition toward tilted states, accompanied by hysteresis. Finally, we demonstrate that stable straight and tilted LBs exist in three dimensions in the presence of aberration, the latter forming a continuous family parametrized by the transverse tilt direction.