  The interaction of intense laser beams with plasmas created on solid targets
involves a rich non-linear physics. Because such dense plasmas are reflective
for laser light, the coupling with the incident beam occurs within a thin layer
at the interface between plasma and vacuum. One of the main paradigms used to
understand this coupling, known as Brunel mechanism, is expected to be valid
only for very steep plasma surfaces. Despite innumerable studies, its validity
range remains uncertain, and the physics involved for smoother plasma-vacuum
interfaces is unclear, especially for ultrahigh laser intensities. We report
the first comprehensive experimental and numerical study of the laser-plasma
coupling mechanisms as a function of the plasma interface steepness, in the
relativistic interaction regime. Our results reveal a clear transition from the
temporally-periodic Brunel mechanism to a chaotic dynamic associated to
stochastic heating. By revealing the key signatures of these two distinct
regimes on experimental observables, we provide an important landmark for the
interpretation of future experiments.
