Parametric down-conversion from a wave-equations approach: geometry and absolute brightness

TL;DR

This paper develops a wave-equations based theoretical framework for analyzing spontaneous parametric down-conversion (SPDC), providing explicit formulas for pair production rates and efficiencies, applicable to various geometries and crystal types.

Contribution

It introduces a general, geometry-independent wave-equations approach to SPDC, linking quantum and classical nonlinear processes through simple mode overlap expressions.

Findings

Derived explicit formulas for pair production rates.

Established relationships between classical and quantum process efficiencies.

Applied theory to both degenerate and non-degenerate SPDC cases.

Abstract

Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode overlap integrals for the absolute pair production rate into single spatial modes, and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and non-degenerate SPDC. We also find a time-domain expression for the correlation function between filtered signal and idler fields.