Chapter 2 - Spontaneous Parametric Down-Conversion in Nonlinear Layered Structures

Abstract

In this review, we summarize spectral, temporal as well as spatial properties of photon pairs generated in spontaneous parametric down-conversion in nonlinear layered structures. Also entanglement between a signal and an idler photon in different degrees of freedom is analyzed. Discussion is based upon a spatial vector model that introduces a two-photon spectral amplitude defined for frequencies and propagation directions of the signal and idler photons. A band-gap structure formed in the layered media then determines typical properties of photon pairs reflected in intensity beam profiles, spatial intensity correlations as well as spectral and temporal characteristics of photon pairs. As an example, GaN/AlN layered structures are analyzed to demonstrate these properties. A method for geometric optimization of the layered structures with respect to efficiency of photon-pair emission is described. Special kinds of states like those with anti-symmetric spectral two-photon amplitudes or states emitted in structures with randomly positioned boundaries are investigated. Attention is also paid to the emission of photon pairs in surface spontaneous parametric down-conversion.