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

Carlos Sevilla-Gutiérrez*, Varun Raj Kaipalath, and Fabian Steinlechner†

  • *Contact author: carlos.sevilla@iof.fraunhofer.de
  • †Contact author: fabian.steinlechner@uni-jena.de
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Phys. Rev. A 113, 063733 – Published 23 June, 2026

DOI: https://doi.org/10.1103/y39c-63q7

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 tradeoffs is often obscured. We show that these tradeoffs 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 nonseparability 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 multiparameter optimization beyond qualitative design guidelines.

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Phys. Rev. A 113, 063733– Published 23 June, 2026
  • Received 4 March 2026
  • Accepted 9 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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