Spatial properties of entangled photon pairs generated in nonlinear layered structures

TL;DR

This paper develops a quantum model for photon pair generation in layered nonlinear structures, analyzing spatial correlations, optimizing geometry, and demonstrating enhanced generation rates and spectral splitting effects.

Contribution

It introduces a detailed spatial quantum model for layered structures, revealing how transmission peaks influence correlations and proposing optimization methods for efficient photon-pair generation.

Findings

Photon pairs can be generated with rates increasing faster than the square of the number of layers.

Structures can produce photon pairs with anti-bunching and anti-coalescence.

Spatial and spectral splitting effects are observed due to photonic band-gap properties.

Abstract

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 anti-bunching and anti-coalescence 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.