Aberration-driven tilted emission in degenerate cavities

The compensation of chromatic dispersion opened new avenues and extended the level of control upon pattern formation in the temporal domain. In this paper, 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 spatial domain. Our approach leverages the interplay between optical aberrations and the proximity to the self-imaging condition, which allows us to cancel or reverse paraxial diffraction. As an example, we show how spherical aberrations materialize into a transverse bi-Laplacian operator and, thereby, explain the stabilization of temporal solitons traveling 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.