Résumé
The compensation of chromatic dispersion opened new avenues and extended the level of control upon pattern formation in the \textit{temporal domain}. In this manuscript, we propose the use of a nearly-degenerate laser cavity as a general framework allowing for the exploration of higher contributions to diffraction in the \textit{spatial} domain. Our approach leverages the interplay between optical aberrations and the proximity to the self-imaging condition which allows to cancel or reverse paraxial diffraction. As an example, we show how spherical aberrations materialize into a transverse bilaplacian operator and, thereby, explain the stabilization of temporal solitons travelling off-axis in an unstable mode-locked broad-area surface-emitting laser. We disclose an analogy between these regimes and the dynamics of a quantum particle in a double well potential.