Gaussian mode coupling of spectrally broadband photons from bulk spontaneous parametric down-conversion: A spatial-spectral mode analysis of fiber coupling

TL;DR

This paper analyzes how spectral and spatial mode structures in bulk SPDC photon sources affect key performance metrics, providing a framework to optimize quantum light sources by understanding mode coupling and phase-matching effects.

Contribution

It introduces a spectral-spatial mode analysis framework using Laguerre-Gauss decomposition to explain trade-offs in photon source metrics and guides systematic optimization of bulk SPDC sources.

Findings

Spectral-spatial non-separability impacts collection probability, heralding efficiency, and purity.

Different phase-matching configurations shape the mode structure and performance.

Experimental validation confirms theoretical predictions.

Abstract

Photon sources based on spontaneous parametric down-conversion (SPDC) are central to experimental quantum optics and quantum technologies. Their performance is commonly quantified by three metrics: pair-collection probability, heralding efficiency, and spectral purity. In bulk-crystal SPDC, these metrics are known to be mutually constrained, yet the physical origin of the resulting trade-offs is often obscured. We show that these trade-offs originate from the frequency-dependent population of discrete spatial modes in the SPDC emission. By performing a Laguerre-Gauss mode decomposition at each frequency component, we show how spectral-spatial non-separability impacts collection probability, heralding efficiency, and purity. We apply this framework to two widely used quasi-phase-matching configurations: collinear degenerate type-0 and type-II SPDC in periodically poled bulk crystals, and quantify how different phase-matching functions shape the spectral-spatial mode structure. In particular, for type-II SPDC we compare standard periodically poled and aperiodically poled Gaussian phase matching. We experimentally validate some of our theoretical results using spatial- and spectral-projection measurements. This spectral-spatial mode analysis provides a quantitative and predictive framework for understanding and engineering bulk-crystal photon sources, enabling systematic multi-parameter optimization beyond qualitative design guidelines.