We measure the spatial profile of down-converted light from Type-I SPDC in BBO and BiBO crystals. We find BiBO (BBO) produces elliptical (circular) transverse patterns because the generated light experiences an angle-dependent (-independent) refractive index.
We investigate the transverse spatial profile of downconverted light produced by noncollinear, degenerate, type-I spontaneous parametric downconversion in two types of nonlinear crystals. We find that the pattern produced by one crystal, beta barium borate (BBO), produces a circular downconversion 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 downconversion 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.
We report on the use of elliptical pump spatial modes to increase the observed brightness of spontaneous parametric downconversion in critically phase-matched crystals. Simulations qualitatively predict this improvement, which depends on the eccentricity and orientation of the pump ellipse. We experimentally confirm a factor of two improvement in brightness when compared to the traditional circular-symmetric pump spatial modes. These results support previous theoretical work that proposes the use of elliptical pump modes to enhance the performance of parametric processes in anisotropic materials.
In this paper, we report on the collinear spontaneous parametric down conversion (SPDC) with quantum theory in angle picture. Based on angle-dependent refractive index of biaxial crystal and the dielectric dispersion, we numerically simulate the effective nonlinear coefficients of BiB 3 O 6 (BIBO) crystal in principle planes. The results indicate that the most effective phase matching scheme is the type I in yz plane, while the secondary options are the type I, type II in xz plane. Considering the derivation of angular phase matching conditions, the calculation is convenient, and it is superior in determination of the spatial distribution of entangled photons.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.