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arXiv:0908.3583 · Physical Review A

Photon-pair generation in random nonlinear layered structures

Jan Peřina, Marco Centini, Concita Sibilia, M. Bertolotti

Published Sep 28, 2009• 16 citations
arXivHTMLPDF

Abstract

Nonlinearity and sharp transmission spectra of random one-dimensional nonlinear layered structures are combined together to produce photon pairs with extremely narrow spectral bandwidths. Indistinguishable photons in a pair are nearly unentangled. Also two-photon states with coincident frequencies can be conveniently generated in these structures if photon pairs generated into a certain range of emission angles are superposed. If two photons are emitted into two different resonant peaks, the ratio of their spectral bandwidths may differ considerably from one and two photons remain nearly unentangled.

DOI
10.1103/physreva.80.033844

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Nonlinearity and sharp transmission spectra of random one-dimensional nonlinear layered structures are combined together to produce photon pairs with extremely narrow spectral bandwidths. Indistinguishable photons in a pair are nearly unentangled. Also two-photon states with coincident frequencies can be conveniently generated in these structures if photon pairs generated into a certain range of emission angles are superposed. If two photons are emitted into two different resonant peaks, the ratio of their spectral bandwidths may differ considerably from one and two photons remain nearly unentangled.
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.
A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also, structures efficiently generated photon pairs showing antibunching and anticoalescence can be obtained. Three reasons for splitting the correlated area in photonic-band-gap structures are revealed: zig-zag movement of photons inside the structure, spatial symmetry, and polarization-dependent properties. Also, spectral splitting can be observed in these structures.
Abstract We reveal that strongly enhanced generation of photon pairs with narrow frequency spectra and sharp angular correlations can be realised through spontaneous parametric down-conversion in metasurfaces. This is facilitated by creating meta-gratings through nano-structuring of nonlinear films of sub-wavelength thickness to support the extended bound state in the continuum resonances, associated with ultra-high Q-factors, at the biphoton wavelengths across a wide range of emission angles. Such spectral features of photons can be beneficial for various applications, including quantum imaging. Our modelling demonstrates a pronounced enhancement, compared to unpatterned films, of the total photon-pair generation rate normalized to the pump power reaching 1.75 kHz mW−1, which is robust with respect to the angular bandwidth of the pump, supporting the feasibility of future experimental realisations.
In order to fulfill the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of ${\ensuremath{\chi}}^{(2)}$ nonlinearity, additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of nonlinear layered structures shows.
We describe properties of entangled photon pairs generated by spontaneous parametric down-conversion in periodically poled nonlinear crystals. These materials can serve as a useful bright source of photon pairs which properties can be tailored on demand. Especially photon pairs with broad spectra and sharp temporal features can be observed. Both uniform and chirped poling are considered. Spectral properties of the generated photons, photon fluxes, coincidence-count patterns in a Hong-Ou-Mandel interferometer, entropy of entanglement, as well as transverse profiles of intensities of the generated photon fields are discussed. Also the correlation area of two photons comprising a photon pair has been studied as it depends on parameters of periodical poling. Attention is also paid to structures with randomly distributed boundaries.
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.