Spontaneous parametric down conversion in chirped, aperiodically-poled crystals

TL;DR

This paper provides a theoretical analysis of how linearly-chirped aperiodically-poled crystals influence the spectral and temporal properties of photon pairs generated via spontaneous parametric down conversion, enabling spectral control.

Contribution

It introduces a theoretical framework for analyzing SPDC in chirped, aperiodically-poled crystals, including spectral-temporal properties and spectral broadening mechanisms.

Findings

Spectral broadening can be controlled by the chirp parameter.

The shape of the SPDC spectrum is tunable through the grating design.

Different spectral components are emitted at different crystal planes, causing photon chirp.

Abstract

We present a theoretical analysis of the process of spontaneous parametric down conversion (SPDC) in a non-linear crystal characterized by a linearly-chirped X(2) grating along the direction of propagation. Our analysis leads to an expression for the joint spectral amplitude, based on which we can derive various spectral-temporal properties of the photon pairs and of the heralded single photons obtained from the photon pairs, including: the single photon spectrum, the chronocyclic Wigner function and the Schmidt number. The simulations that we present are for the specific case of a collinear SPDC source based on a PPLN crystal with the signal and idler photons emitted close to the telecom window. We discuss the mechanism for spectral broadening due to the presence of a linearly chirped X(2) grating, showing that not only the width but also to some extent the shape of the SPDC spectrum maybe controlled. Also, we discuss how the fact that the different spectral components are emitted on different planes in the crystal leads to single-photon chirp.