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Physical Review A

How focused pumping affects type-II spontaneous parametric down-conversion

P. S. K. Lee, Martin P. van Exter, J. P. Woerdman

Published Sep 8, 2005• 43 citations
Publisher

Abstract

We demonstrate that the transition from plane-wave to focused pumping in type-II down-conversion is analogous to the transition from cw to pulsed pumping. We show experimentally that focused pumping leads to asymmetric broadening of both the ordinary and extraordinary light distribution. It hardly affects the entanglement quality if proper spatial filtering is applied.

DOI
10.1103/physreva.72.033803

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We demonstrate that the transition from plane-wave to focused pumping in type-II down-conversion is analogous to the transition from cw to pulsed pumping. We show experimentally that focused pumping leads to asymmetric broadening of both the ordinary and extraordinary light distribution. It hardly affects the entanglement quality if proper spatial filtering is applied.
It is known that photons produced by spontaneous parametric down-conversion can be coupled into optical fibers more efficiently by focusing the pump field. We find that focusing the pump in type-II down-conversion causes photons of ordinary and extraordinary polarization to acquire very different angular spreads, which amounts to spatial information that distinguishes between the polarization states. Numerical studies predict that the photons collected by a detector or quantum channel will be of predominantly one polarization and that the degree of polarization entanglement will be lessened in some cases.
We show that, with proper modification of the pump field description from plane-wave to spherical-like, which serves to incorporate geometric effects that were discarded in the plane-wave model, the efficiency of the spontaneous parametric down conversion process exhibits dependence on pump intensity, contrary to previous theoretical predictions. Experimental investigations of this behavior are carried out under focused pumping conditions, where pump divergence is kept constant, and pairs of photons are collected behind an aperture that is large compared to the overall down-conversion profile. The resulting photon yield is found to exhibit a strong dependence on pump intensity, and an enhancement of the down-conversion efficiency is observed. The modified pump field description is also modeled numerically and calculations are presented, which are found to display good accordance with experimental observations. The enhanced yield of spontaneous parametrically down-converted photons will prove beneficial for many practical applications of entangled photon pairs where a high flux is desired.
Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.
We experimentally study the spatial properties of the field generated by spontaneous parametric down-conversion (SPDC) when the pump laser beam is strongly focused in the nonlinear crystal. Special attention is paid to classical intensity measurements with a CCD camera. We introduce the concept of a classical equivalent source that replicates all the coherence properties of SPDC light and explains all our experimental results. We show that, in contrast with experiments with a well-collimated pump, here both the phase-matching conditions and the position of the focusing plane determine the measured intensity profiles in the image plane of the crystal. The transition from the near-field regime to the far field is investigated. Measurements of two-photon correlations under strong focusing are also presented and the special features thereof are discussed.