“…The periodic corrugation has the effect of coupling both sets of modes [12], in a way reminiscent of studies made for LandauZener manipulation of Rydberg atoms in the 90's [15], an analytical description that we are currently investigating. , [8,11,12], the coupled modes dispersion flattens out at the zone edge, being equally pushed downward by higher modes and pushed upward by lower modes. This is the critically coupled regime (CCR).…”