We analyze the process of photon-pair generation via spontaneous parametric down-conversion in a quadratic nonlinear asymmetric waveguide coupler. The two waveguides have different geometry, such that light coupling only occurs within a narrow bandwidth of one of the generated (signal) photon modes, while the other (idler) photon together with the pump stay localized in one (driven) arm of the coupler. We demonstrate that such a setup represents a powerful and flexible tool for engineering spectral properties of generated photon pairs. Mode hybridization and dispersion of coupling can be utilized for shifting the balance between group velocities of interacting pump, signal, and idler fields, subsequently leading to a significant increase of spectral factorizability (purity) of photons. We also show that for interaction lengths shorter than one beat length, generated pairs with signal photon being localized in the auxiliary (not pumped) arm of the coupler appear to be spectrally localized in both signal and idler components. The bandwidth of such intrinsic filtering of generated photons can be controlled by several geometrical parameters.
An effective-medium approach is used to derive a set of coupled-mode equations describing quadratic parametric interactions in a one-dimensional inhomogeneous medium of finite length. The solutions for both copropagating and counterpropagating interactions are used to study the quantum-mechanical process of spontaneous parametric down-conversion (SPDC). An example is studied in which the inhomogeneous medium is a photonic crystal. The effect that device geometry has on both the efficiency and bandwidth of SPDC is explored. With appropriate design, we find that it is possible not only to enhance the efficiency of SPDC, but also to generate broadband copropagating and narrowband counterpropagating down-converted light. A setup is proposed with the potential to act as a source of entangled photon pairs.
Spatial correlations of photon pairs from spontaneous parametric down-conversion (SPDC) underpin quantum imaging and entanglement certification. We present the first systematic study of spectral filter bandwidth effects on transverse spatial correlations in bulk Type-I BBO for degenerate and non-degenerate configurations. In the far field, the degenerate conditional momentum width is pump-limited and filter-invariant, while non-degenerate configurations exhibit monotonic growth in both marginal and conditional momentum widths -- with the walk-off axis
≈100 times more sensitive than the non-walk-off axis. In the near field, we identify a previously unreported flat-dip-rise profile: the conditional position width narrows by
≈10% at an optimal bandwidth
Δdip≈1.35ΔλSPDC before rising due to geometric displacement. When the filter is placed on the idler arm, the dip shifts by the exact factor
(λi/λs)2. Both results are universal for any non-degenerate SPDC source, requiring only a finite crystal length,
dθ/dλ=0, and incoherent spectral averaging. The Reid EPR uncertainty product is consistently smaller on the walk-off axis -- a structural advantage of bulk birefringent geometry absent in quasi-phase-matched sources. The optimal filter bandwidth
ΔF=Δdip is determined entirely by the intrinsic phase-matching bandwidth of the crystal and is directly readable from the X-entanglement spectral width of the source.