Sagnac SPDC Entanglement Sources

Counterpropagating nonlinear-optical down-conversion paths yielding polarization-entangled photon pairs. The main concepts are phase matching, Bell fidelity, visibility. Each must be defined in the context of a concrete physical model, mathematical representation, or experimental task. Terminology alone does not establish the behavior of the system.

A polarization Sagnac interferometer drives nonlinear down-conversion in counterpropagating directions, coherently combining alternatives that can produce an entangled two-photon polarization state. Phase matching and the overlap of spectral, spatial and temporal modes determine whether the alternatives are distinguishable. A Bell-state polarization reconstruction alone may not reveal source drift, background coincidences or spectral correlations. Pump, signal and idler wavelengths must match the actual crystal and coating specification.

Model pair-generation amplitudes and analyzer probabilities, calculate accidental-subtracted as well as raw coincidences, and reconstruct a physical density operator from calibrated projection counts. Include drift reversals and systematic analyzer offsets as independent validation tests. Compare brightness, heralding, Bell visibility and fidelity at the same collection and optical-filter settings.