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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Control of spontaneous parametric down-conversion in 1-D photonic crystals

Marco Centini, Letizia Sciscione, Concita Sibilia, M. Bertolotti, Michael Scalora, Mark J. Bloemer, Jan Peřina

Published Jan 25, 2006• 0 citations
Publisher

Abstract

We report numerical results on spontaneous down-conversion in 1-D photonic crystals showing the possibility of tailoring the photon pair spectrum for quantum information applications.
DOI
10.1109/cleoe.2005.1568003

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We present a theoretical analysis of the process of spontaneous parametric down conversion (SPDC) in a nonlinear crystal characterized by a linearly-chirped χ(2) grating along the direction of propagation. Our analysis leads to an expression for the joint spectral amplitude, based on which we can derive various spectral–temporal properties of the photon pairs and of the heralded single photons obtained from the photon pairs, including: The single-photon spectrum (SPS), the chronocyclic Wigner function (CWF) and the Schmidt number. The simulations that we present are for the specific case of a collinear SPDC source based on a PPLN crystal with the signal and idler photons emitted close to the telecom window. We discuss the mechanism for spectral broadening due to the presence of a linearly chirped χ(2) grating, showing that not only the width but also to some extent the shape of the SPDC spectrum may be controlled. Also, we discuss how the fact that the different spectral components are emitted on different planes in the crystal leads to single-photon chirp.
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.