Abstract
We investigate the transverse spatial profile of down-converted light produced by noncollinear, degenerate, Type-I spontaneous parametric down-conversion in two types of nonlinear crystals. We find that the pattern produced by one crystal, beta barium borate (BBO), produces a circular down-conversion pattern while the other crystal, bismuth triborate (BiBO) produces an elliptical pattern. We show this difference is due to the angle-independent refractive index experienced by the daughter photons in BBO, while they experience an angle-dependent refractive index in BiBO. We image the transverse spatial profile of the generated light to determine the eccentricity produced by each crystal and develop a model to explain our observation. Among other things, this model predicts that there is a wavelength for which the eccentricity from BiBO is nearly zero. Finally, we discuss how the elliptical ring pattern produced in BiBO potentially affects polarization entanglement for experimental setups that collect biphotons around the entire down-conversion ring. We show that the quality of polarization entanglement as measured by the overlap integral of the spectrum of the two rings, can remain high (>99.4%) around the entire ring at the expense of decreased biphoton rate.
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