Analytical treatment of spectral properties and signal–idler intensity correlations for a double-resonant optical parametric oscillator far below threshold

Cavity-enhanced spontaneous parametric down-conversion has found multiple realizations over the past years in order to generate narrow-band single-photons that can interact efficiently with atomic resonances. In this paper, we present a theoretical treatment of down-conversion inside a resonator far below threshold and provide specific analytical expressions for quantities like the single-photon spectrum and the signal–idler cross-correlation function. Additionally, we show a measured second-order signal–idler cross-correlation function from a double-resonant optical parametric oscillator far below threshold and include a comparison of our theoretical results with experimental data in order to support our results.