High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherentlypumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transversemomentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.
Salem F. Hegazy, Jala El-Azab, Yehia A. Badr, and Salah S. A. Obayya, "Accurate relative-phase and time-delay maps all over the emission cone of hyperentangled photon source," Proc. SPIE 9894, Nonlinear Optics and its Applications IV, 98940Y (Presented at SPIE Photonics Europe: April 06, 2016; Published: 27 April 2016); https://doi.org/10.1117/12.2227679.
Conference Presentations are recordings of oral presentations given at SPIE conferences and published as part of the conference proceedings. They include the speaker's narration along with a video recording of the presentation slides and animations. Many conference presentations also include full-text papers. Search and browse our growing collection of more than 12,000 conference presentations, including many plenary and keynote presentations.