Numerical Framework for Type-I SPDC Using Python: Photon Emission and Entanglement Analysis

This study introduces a novel Python-based numerical framework for simulating spontaneous parametric down-conversion (SPDC) in a Type-I nonlinear BBO crystal. Unlike conventional analytical treatments, the present work provides a detailed three-dimensional mapping of the photon emission cone, explicit derivation of the entangled two-photon state, and systematic evaluation of phase-matching conditions. The results confirm the generation of polarization-entangled Bell states and demonstrate violation of the Bell–CHSH inequality, thereby reinforcing the nonlocal character of quantum mechanics. The close agreement between the simulated outcomes and reported experimental data validates the originality and robustness of the approach. Beyond its immediate results, this framework lays the groundwork for future development of an integrated simulation platform for diverse SPDC experiments, offering a valuable tool for both researchers and students in quantum optics.