• DOI:10.1088/2040-8986/ab89e4
• Corpus ID: 221660097

Phase matching in β-barium borate crystals for spontaneous parametric down-conversion

@article{Karan2018PhaseMI,
  title={Phase matching in $\beta$-barium borate crystals for spontaneous parametric down-conversion},
  author={Suman Karan and Shaurya Aarav and Homanga Bharadhwaj and Lavanya Taneja and Arinjoy De and Girish Kulkarni and Nilakantha Meher and Anand K Jha},
  journal={Journal of Optics},
  year={2018},
  volume={22}
}

• Suman Karan, Shaurya Aarav, +5 authors A. Jha
• Published 2 October 2018
• Physics
• Journal of Optics

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.