Classical model of spontaneous parametric down-conversion

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic ``vacuum'' seed field. analytically show that second-order spatiotemporal correlations generated from DFG process replicate those signal SPDC. Specifically, for low gain, is consistent with quantum calculation photon's reduced density matrix; high model's predictions are in good agreement our experimental measurements far-field intensity profile, orbital angular momentum spectrum, wavelength spectrum SPDC increasing strengths. further theoretically successfully captures SU(1,1) interference induced coherence effects both gain regimes. Intriguingly, also correctly predicts linear scaling visibility object transmittance low-gain regime---a feature often regarded quintessential signature nonclassicality coherence. Our may not only lead to fundamental insights into classical-quantum divide context coherence, but can be useful theoretical tool numerous experiments applications based on