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Journal of Optics

Modeling of enhanced spontaneous parametric down-conversion in plasmonic and dielectric structures with realistic waves

Ardi Loot, V. Hizhnyakov

Published Mar 15, 2018• 9 citations
Publisher

Abstract

Abstract A numerical study of the enhancement of the spontaneous parametric down-conversion in plasmonic and dielectric structures is considered. The modeling is done using a nonlinear transfer-matrix method which is extended to include vacuum fluctuations and realistic waves (e.g. Gaussian beam). The results indicate that in the case of short-range surface plasmon polaritons, the main limiting factor of the enhancement is the short length of the coherent buildup. In the case of long-range surface plasmon polaritons or dielectric guided waves, the very narrow resonances are the main limiting factor instead.

DOI
10.1088/2040-8986/aab6c0

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We consider a generation of two-particle quantum states in the process of spontaneous parametric down-conversion of light by a dielectric nanoparticle with a bulk ${\ensuremath{\chi}}^{(2)}$ response. As a particular example, we study the generation of surface plasmon polariton pairs with a GaAs\mathrm{GaAs}GaAs nanoparticle located at the silver-air interface. We demonstrate theoretically that N00N\mathrm{N}00\mathrm{N}N00N states of surface plasmon polariton pairs with N=2N=2N=2 can be obtained for certain excitation geometries. The effect can be physically interpreted as the result of a quantum interference between the pairs of induced sources, each emitting either signal or idler plasmons. We then relate the resulting N00N\mathrm{N}00\mathrm{N}N00N pattern to the general symmetry properties of a dyadic Green's function of a dipole emitter exciting surface waves. It renders the considered effect as a general way towards the robust generation of N00N\mathrm{N}00\mathrm{N}N00N states of surface waves using spontaneous parametric down-conversion in ${\ensuremath{\chi}}^{(2)}$ nanoparticles.
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.
Miniaturization of nonlinear optical elements is one of the major trends of modern photonics. In particular, in the ‘flatoptics’ geometry, the sample is ultrathin along the light propagation direction. For nonlinear optical effects in such samples, phase matching is satisfied automatically, which allows for the use of materials with giant nonlinear susceptibilities. The tiny thickness reduces the efficiency but it can be compensated for by using geometric and material resonances. Recently also spontaneous parametric down-conversion (SPDC), leading to the generation of entangled photons, has been implemented in ultrasmall sources: subwavelength layers, metasurfaces, even nanoantennas. The lifted constraint of phase matching gives to SPDC even more freedom than to classical frequency conversion effects. The reason is that SPDC, as a spontaneous effect, is stimulated by quantum vacuum fluctuations, which populate all modes uniformly. SPDC in ultrathin samples demonstrates very broad spectral and angular width, extremely high degrees of continuous-variable entanglement, tunable polarization entanglement, and orders of magnitude enhancement of photon pair production rate due to the geometric resonances of dielectric metasurfaces.