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Physical Review A

Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals

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

Published Sep 9, 2005• 31 citations
Publisher

Abstract

A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.

DOI
10.1103/physreva.72.033806

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A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.
We study the process of spontaneous parametric downconversion in a one-dimensional defective quadratic nonlinear photonic crystal. It is shown that the strong confinements of both the pump and signal waves around the defective layer result in a giant enhancement of the entangled photon-pair generation. An enhancement factor as high as 3.4×106 is obtained in our defective structure based on the dual-localized modes. Furthermore, the linewidth of the downconverted fields is only 0.1 nm. Such a photonic crystal structure can be applied as a highly efficient source of entangled photon pairs for highly integrated all-optical circuits.
Spontaneous parametric down-conversion in two-dimensional photonic crystal made of semiconductor material with large quadratic nonlinear susceptibility is proposed to generate polarization entangled photon pairs. On one hand, the large quadratic nonlinear susceptibility of AlGaAs crystal insures the high nonlinear conversion efficiency; on the other hand, the abnormal dispersion property of two-dimensional photonic crystal causes the satisfaction of the phase-matching condition. In particular, the dispersion property sensitively depends on the structure of photonic crystal. Then the walk-off between the down-converted photons with orthogonal polarizations can be minimized through appropriate structure parameter design; hence compensation measures to mitigate labeling effect on polarization entangled photon pairs can be eliminated.
An effective-medium approach is used to derive a set of coupled-mode equations describing quadratic parametric interactions in a one-dimensional inhomogeneous medium of finite length. The solutions for both copropagating and counterpropagating interactions are used to study the quantum-mechanical process of spontaneous parametric down-conversion (SPDC). An example is studied in which the inhomogeneous medium is a photonic crystal. The effect that device geometry has on both the efficiency and bandwidth of SPDC is explored. With appropriate design, we find that it is possible not only to enhance the efficiency of SPDC, but also to generate broadband copropagating and narrowband counterpropagating down-converted light. A setup is proposed with the potential to act as a source of entangled photon pairs.
We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN is analyzed as a suitable source of photon pairs having high efficiency.
Nonlinear metal-dielectric layered structures are shown to be able to efficiently generate entangled photon pairs using spontaneous parametric down-conversion. Increase of electric-field amplitudes in these structures enhanced by the presence of metal layers is sufficient to compensate for losses inside thin metal layers. As an example, photon pairs emitted from a structure composed of alternating nonlinear dielectric GaN layers and metal Ag layers are analyzed in spectral, temporal, as well as spatial domains. Also, correlations and entanglement between two photons in a pair are determined. Very narrow photon-pair spectra together with strong directionality of photon-pair emission are observed making the photons suitable for photon-atom interactions. Highly enhanced electric-field amplitudes provide high photon-pair generation efficiencies.