QED vacuum nonlinearity in Laguerre-Gauss beams

We investigate in detail the stimulated photon emission in pulse-shaped Laguerre-Gauss beams of arbitrary mode decomposition within the framework of Euler-Heisenberg effective theory. We elaborate on the analytic structure of the photon emission amplitude and identify its dominant and sub-dominant parts by analyzing each signature's phase scaling. We identify three distinct nonlinear signatures: the orbital angular momentum (OAM) flip ($\ell:1 \rightarrow -1$) , higher harmonic generation ($\ell:1 \rightarrow 2$) and harmonic reduction ($\ell:1 \rightarrow 0$). We estimate signal photon yield for each signature under various pulse collision scenarios we explain in detail. We also outline a prospective experimental setup that may probe these signatures.