Observation of elliptical rings in Type-I spontaneous parametric down-conversion

TL;DR

This study compares the transverse spatial profiles of down-converted light in two nonlinear crystals, revealing elliptical and circular patterns due to different refractive index behaviors, and discusses implications for polarization entanglement.

Contribution

It provides the first detailed comparison of spatial patterns in Type-I SPDC in BBO and BiBO crystals, and introduces a model explaining the observed elliptical rings.

Findings

BBO produces circular down-conversion patterns due to angle-independent refractive index.

BiBO produces elliptical patterns because of angle-dependent refractive index.

High polarization entanglement (>99.4%) can be maintained despite elliptical ring patterns.

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.