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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spontaneous parametric down conversion in nonlinear metallo-dielectric layered media

Dalibor Javůrek, Jan Peřina, Jiŕí Svozilík

Published Dec 5, 2014• 1 citation
Publisher

Abstract

The generation of photon pairs inside metallo-dielectric layered media by spontaneous parametric down conversion is highly efficient. A theoretical model of spontaneous parametric down conversion based on vectorial quantum-mechanial approach is used to obtain spatial, frequency and temporal photon-pair characteristics. As an example, a structure consisting of eleven alternating Galium-Nitride and silver layers is analyzed. Strong constructive interference of the sub-frequency fields results in narrow spatial and frequency distributions of photon-pairs emitted at high generation rates. Photon pairs are mainly created in Galium-Nitride layers, the silver layers serve as a linear reflector.

DOI
10.1117/12.2081175

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The generation of photon pairs inside metallo-dielectric layered media by spontaneous parametric down conversion is highly efficient. A theoretical model of spontaneous parametric down conversion based on vectorial quantum-mechanial approach is used to obtain spatial, frequency and temporal photon-pair characteristics. As an example, a structure consisting of eleven alternating Galium-Nitride and silver layers is analyzed. Strong constructive interference of the sub-frequency fields results in narrow spatial and frequency distributions of photon-pairs emitted at high generation rates. Photon pairs are mainly created in Galium-Nitride layers, the silver layers serve as a linear reflector.
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A rigorous description of volume and surface spontaneous parametric down-conversion in one-dimensional nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations whose solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.
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.
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On the interface between two isotropic linear media the re°ection and transmission of separate monochro- matic waves occur in a normal incidence, which are described by Fresnel's formulas. On the interface between two nonlinear media, namely one of the media may be linear in a limit, the re°ection and the transmission are complicated by a wave mixing of di®erent frequencies. A maximum generality of improved Fresnel formulas is impossible. By using the rotating-wave approximation and the parametric approximation, a model of the parametric down-conversion has been derived in the nonlinear and quantum optics. We present a classical ex- pression of the e®ect of the wave mixing on the interface and treat even the possibility of quantum input{output relations.