Accurate relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

Salem F. Hegazy; Jala El-Azab; Yehia A. Badr; Salah S. A. Obayya

doi:10.1117/12.2227679

27 April 2016 Accurate relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

Salem F. Hegazy, Jala El-Azab, Yehia A. Badr, Salah S. A. Obayya

Proceedings Volume 9894, Nonlinear Optics and its Applications IV; 98940Y (2016) https://doi.org/10.1117/12.2227679
Event: SPIE Photonics Europe, 2016, Brussels, Belgium

Abstract

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.

Conference Presentation

Citation Download Citation

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 (27 April 2016); https://doi.org/10.1117/12.2227679

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available