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Journal of the Optical Society of America B

Polarization directions of noncollinear phase-matched optical parametric downconversion output

Alan L. Migdall

Published May 1, 1997• 38 citations
Publisher

Abstract

An analysis of the output polarization of a noncollinear type I optical parametric downconversion source is presented. Such a source can be made by pumping a nonlinear crystal with an extraordinary-polarized beam to produce pairs of ordinary-polarized photons. A polarization map of the output light illustrates dramatic variation in the polarization direction at large scattering angles. The effect of this variation in polarization direction is seen on a map of the nonlinear conversion efficiency. The apparent ambiguity in the polarization for the particular case in which one of the outputs propagates along the crystal optic axis is also discussed.

DOI
10.1364/josab.14.001093

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An analysis of the output polarization of a noncollinear type I optical parametric downconversion source is presented. Such a source can be made by pumping a nonlinear crystal with an extraordinary-polarized beam to produce pairs of ordinary-polarized photons. A polarization map of the output light illustrates dramatic variation in the polarization direction at large scattering angles. The effect of this variation in polarization direction is seen on a map of the nonlinear conversion efficiency. The apparent ambiguity in the polarization for the particular case in which one of the outputs propagates along the crystal optic axis is also discussed.
We develop and apply an effective analytic theory of a noncollinear, broadband type-I parametric down-conversion to study a coupling efficiency of the generated photon pairs into single mode optical fibers. We derive conditions necessary for highly efficient coupling for single and double type-I crystal producing polarization entangled states of light. We compare the obtained approximate analytic expressions with the exact numerical solutions and discuss the results for a case of beta barium borate crystals.
A periodically poled lithium niobate (PPLN) crystal has been used as an efficient source of non-collinearly generated polarization-entangled photon pairs at 810 and 1550 nm. The PPLN crystal was endowed with a specially designed poling pattern and the entangled photons were generated via the nonlinear optical process of spontaneous parametric down conversion (SPDC). A novel design based on overlapping two concurrent type-I quasi-phase-matching structures in a single PPLN crystals produced correlated pairs of alternatively polarized photons in largely separated spectral regions. The phase of the resulting two-photon state is directly linked to parameters of the nonlinear grating. Continuous tunability of the generated Bell state, from Phi(+) to Phi(-), has been demonstrated by translating a slightly wedged crystal perpendicular to the pump beam.
We propose a method for directly producing radially and azimuthally polarized photon pairs through spontaneous parametric downconversion (SPDC). This method constitutes a novel geometry for SPDC, in which a radially polarized Bessel-Gauss pump beam is directed into a nonlinear crystal, with the central propagation direction parallel to the crystal axis. The phasematching conditions are controlled by changing the opening angle of the pump beam; as the crystal axis cannot be tuned, we refer to this process as super-critical phasematching. We model and plot the spatial and polarization output distributions for Type-I and Type-II super-critical phasematching.
We propose a method for directly producing radially and azimuthally polarized photon pairs through spontaneous parametric downconversion (SPDC). This method constitutes a novel geometry for SPDC, in which a radially polarized Bessel-Gauss pump beam is directed into a nonlinear crystal, with the central propagation direction parallel to the crystal axis. The phasematching conditions are controlled by changing the opening angle of the pump beam; as the crystal axis cannot be tuned, we refer to this process as super-critical phasematching. We model and plot the spatial and polarization output distributions for Type-I and Type-II super-critical phasematching.
Summary form only given. The vast majority of experimental studies of entanglement is based on the use of a polarization entangled photon pair or multiples thereof. Typically, such pairs are produced by the process of spontaneous parametric down conversion in a crystal that exhibits a nonzero second-order nonlinear susceptibility and is cut for type II phase matching. These photons are orthogonally polarized along directions imposed by the symmetry, cut and orientation of the nonlinear crystal. Polarization-entangled pairs are then selected by spatial, and possibly spectral, filtering of the down-converted light. When the crystal is pumped with linearly polarized light a rather intuitive picture arises. If one selects the polarization of the signal photon to be linear, the idler photon will also be linearly polarized in such a way that /spl alpha//sub p/ = -(/spl alpha//sub s/ + /spl alpha//sub i/). Here /spl alpha//sub p,s,i/ refer to the polarization directions of pump, signal and idler, respectively. Their polarization state can be characterized by points on the equator of the Poincare sphere. If, for linear polarized pump, the signal is selected to be elliptically polarized, the idler will also be elliptically polarized. On the Poincare sphere signal and idler have equal latitude (on the same hemisphere), while their longitude is determined by the same relation as above. In all cases signal and idler are maximally entangled.