Effects of crystal length on the angular spectrum of spontaneous parametric downconversion photon pairs

TL;DR

This paper investigates how the length of the nonlinear crystal influences the angular spectrum of photon pairs generated by SPDC, combining theoretical analysis with experimental measurements to distinguish short- and long-crystal regimes.

Contribution

It provides a comprehensive analysis of the transition between short- and long-crystal regimes in SPDC, highlighting the role of crystal length on the angular spectrum of photon pairs.

Findings

Short crystals' properties are dominated by the pump electric field distribution.

Longer crystals' properties are significantly affected by the crystal's nonlinear characteristics.

Experimental results confirm the theoretical boundary between the two regimes.

Abstract

We present a theoretical and experimental analysis of the joint effects of the transverse electric field distribution and of the nonlinear crystal characteristics on the properties of photon pairs generated by spontaneous parametric downconversion (SPDC). While it is known that for a sufficiently short crystal the pump electric field distribution fully determines the joint signal-idler properties, for longer crystals the nonlinear crystal properties also play an important role. In this paper we present experimental measurements of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of photon pairs produced by spontaneous parametric downconversion (SPDC), carried out through spatially-resolved photon counting. In our experiment we control whether or not the source operates in the short-crystal regime through the degree of pump focusing, and explicitly show how the AS and CAS measurements differ in these two regimes. Our theory provides an understanding of the boundary between these two regimes and also predicts the corresponding differing behaviors.