Photon pairs generated via spontaneous parametric down-conversion (SPDC) can exhibit entanglement in the Laguerre-Gaussian (LG) mode basis, which enables high-dimensional free-space quantum communication by exploiting the high-dimensional space spanned by the LG modes. For such free-space quantum communication, the brightness of the quantum light source plays an important role due to the atmospheric turbulence and photon loss. A variety of studies have analyzed the SPDC brightness by decomposing biphoton states into LG modes, but they have often relied on a degenerate state, a narrow-spectral-bandwidth approximation, or a thin-crystal approximation. However, these approaches are unsuitable for nondegenerate type-0 SPDC with a periodically poled nonlinear crystal, which offers higher brightness due to its superior nonlinear coefficients. In this study, we examine the spectrum of photon pairs in specific LG modes generated by a type-0 periodically poled potassium titanyl phosphate crystal while avoiding the constraints imposed by the aforementioned assumptions. In addition, we investigate the optimal focal parameters of the pump, signal, and idler to maximize the brightness for a given LG mode. Our findings show that it is not feasible to simultaneously optimize the brightness for different LG modes with a single pump focal parameter. The results of this study provide a comprehensive framework for developing high-brightness quantum light sources and contribute to the advancement of high-dimensional free-space quantum communication.

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• Photon pairs & parametric down-conversion