We present two methods for the precise independent focusing of orthogonal linear polarizations of light at arbitrary relative locations. Our first scheme uses a displaced lens in a polarization Sagnac interferometer to provide adjustable longitudinal and lateral focal displacements via simple geometry; the second uses uniaxial crystals to achieve the same effect in a compact collinear setup. We develop the theoretical applications and limitations of our schemes, and provide experimental confirmation of our calculations.

We present a source of near-infrared photon pairs based on the process of spontaneous parametric downconversion (SPDC), for which the joint signal-idler quantum state is designed to be factorable in the frequency-time and in the transverse position-momentum degrees of freedom. Our technique is based on the use of a broadband pump and vector group velocity matching between the pump, signal, and idler waves. We show experimentally that a source based on this technique can be configured for the generation of: i) pure heralded single photons, and ii) polarization-entangled photon pairs which are free from spectral correlations, in both cases without resorting to spectral filtering. While critical for many applications in optical quantum information processing, such a source has not previously been demonstrated.

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