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Physical Review A

Optimizing the brightness of a spontaneous parametric down-conversion source in Laguerre-Gaussian modes using a type-0 periodically poled nonlinear crystal

Jungmo Lee, Kyungdeuk Park, Dongkyu Kim, Yonggi Jo, Dong-Gil Im, Yong Sup Ihn

Published Jun 30, 2025• 2 citations
Publisher
DOI
10.1103/l6mg-szxj

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Photon pairs generated via spontaneous parametric down-conversion (SPDC) can exhibit entanglement in the Laguerre-Gaussian (LG) mode basis, which enables high-dimensional free-space quantum communication by exploiting the high-dimensional space spanned by the LG modes. For such free-space quantum communication, the brightness of the quantum light source plays an important role due to the atmospheric turbulence and photon loss. A variety of studies have analyzed the SPDC brightness by decomposing biphoton states into LG modes, but they have often relied on a degenerate state, a narrow spectral bandwidth approximation, or a thin crystal approximation. However, these approaches are unsuitable for non-degenerate type-0 SPDC with a periodicallypoled nonlinear crystal, which offers higher brightness due to its superior nonlinear coefficients. In this study, we examine the spectrum of photon pairs in specific LG modes generated by a type-0 ppKTP crystal whileavoiding the constraints imposed by the aforementioned assumptions. In addition, we investigate the optimal focal parameters of the pump, signal, and idler to maximize the brightness for a given LG mode. Our findings show that it is not feasible to simultaneously optimize the brightness for different LG modes with a single pump focal parameter. The results of this study provide a comprehensive framework for developing highbrightness quantum light sources and contribute to the advancement of high-dimensional free-space quantum communication.

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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

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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.

quant-pharXiv:2602.23238•Physical Review A•Feb 27, 2026•1 citation
Photon pairs generated via spontaneous parametric down-conversion (SPDC) can exhibit entanglement in the Laguerre-Gaussian (LG) mode basis, which enables high-dimensional free-space quantum communication by exploiting the high-dimensional space spanned by the LG modes. For such free-space quantum communication, the brightness of the quantum light source plays an important role due to the atmospheric turbulence and photon loss. A variety of studies have analyzed the SPDC brightness by decomposing biphoton states into LG modes, but they have often relied on a degenerate state, a narrow spectral bandwidth approximation, or a thin crystal approximation. However, these approaches are unsuitable for non-degenerate type-0 SPDC with a periodicallypoled nonlinear crystal, which offers higher brightness due to its superior nonlinear coefficients. In this study, we examine the spectrum of photon pairs in specific LG modes generated by a type-0 ppKTP crystal whileavoiding the constraints imposed by the aforementioned assumptions. In addition, we investigate the optimal focal parameters of the pump, signal, and idler to maximize the brightness for a given LG mode. Our findings show that it is not feasible to simultaneously optimize the brightness for different LG modes with a single pump focal parameter. The results of this study provide a comprehensive framework for developing highbrightness quantum light sources and contribute to the advancement of high-dimensional free-space quantum communication.
Single-mode-fiber-coupled spontaneous parametric down-conversion (SPDC) sources are a key resource for photonic quantum technologies, but in single-crystal geometries brightness, heralding efficiency, and spectral purity remain constrained by intrinsic trade-offs. Here, we show how nonlinear interference in a cascaded two-crystal type-II SPDC source can be used to engineer the modal structure of SPDC emission, improving the brightness--heralding-efficiency trade-off by more than one order of magnitude beyond the single-crystal limit. We further demonstrate two routes to near-unity spectral purity while retaining high brightness and/or heralding efficiency, even with standard periodically poled crystals, and study the additional advantages of aperiodic poling with Gaussian phase matching. Using a spectrally resolved Laguerre--Gauss modal decomposition, we show that these improvements arise from mode-selective interference of spatial-spectral SPDC modes within the nonlinear interferometer. We experimentally validate the model through sum-frequency-generation measurements of the spatial-spectral state.
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.