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Recent progress in the study of the non-classical macroscopic state of light sheds light on the characterization of high-gain spontaneous parametric down-conversion (SPDC). However, the theory of high-dimensional entangled photon pairs with SPDC in this high-gain regime is far from being complete. Here, we present a numerical study of the effect of the phase-matching function on the OAM entanglement in high-gain SPDC. We use a recently developed classical model of high-gain SPDC to compute the OAM spectrum of the entangled photon pair and examine how the OAM entanglement depends on various physical parameters determining the phase-matching function. Our study offers guidelines for quantum state engineering with bright sources of photon pairs entangled in high-dimensional OAM spaces.