For incidence in the critical region, the propagation of gaussian lasers through triangular dielectric blocks is characterized by the joint action of angular deviations and lateral displacements. This mixed effect, known as composite Goos-Haenchen shift, produces a lateral displacement dependent on the axial coordinate, recently confirmed by a weak measurement experiment. We discuss under which conditions this axial lateral displacement, which only exists for the composite Goos-Haenchen shift,

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... resents an oscillatory behavior. This oscillation phenomenon shows a peculiar behavior of light for critical incidence and, if experimentally tested, could stimulate further theoretical studies and lead to interesting optical applications.