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Mapping the spatial and spectral modes of downconverted photons in angle phase-matched nonlinear crystals

Evan J. Kumar, Lorenzo Uboldi, Cristian Manzoni, Giulio Cerullo, Ajay Ram Srimath Kandada

Published Jul 2, 2025• 0 citations
Publisher

Abstract

Spontaneous Parametric Down-Conversion (SPDC) is key to generating broadband spectrally entangled photons for quantum optical spectroscopy. Here we use a a common-path birefringent interferometer to experimentally map the spatial-spectral mode structure of SPDC in Type I and II $\beta$-barium borate crystals using hyperspectral k-space imaging. Under broadband pulsed pumping, we observe strong spatial variations in the spectra, with distinct features for each phase-matching type. Simulations based on biphoton amplitudes and phase-matching conditions qualitatively match our results. This spatial-spectral mapping enables control over biphoton entanglement entropy, paving the way for optimized quantum light sources for material spectroscopy.

DOI
10.1364/opticaopen.29452184.v1

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Spontaneous Parametric Down-Conversion (SPDC) is key to generating broadband spectrally entangled photons for quantum optical spectroscopy. Here we use a a common-path birefringent interferometer to experimentally map the spatial-spectral mode structure of SPDC in Type I and II β\betaβ-barium borate crystals using hyperspectral k-space imaging. Under broadband pulsed pumping, we observe strong spatial variations in the spectra, with distinct features for each phase-matching type. Simulations based on biphoton amplitudes and phase-matching conditions qualitatively match our results. This spatial-spectral mapping enables control over biphoton entanglement entropy, paving the way for optimized quantum light sources for material spectroscopy.
Spontaneous Parametric Down-Conversion (SPDC) is key to generating broadband spectrally entangled photons for quantum optical spectroscopy. Here we use a common-path birefringent interferometer to experimentally map the spatial-spectral distribution of SPDC in Type I and II β-barium borate crystals using hyperspectral k-space imaging. Under broadband pulsed pumping, we observe strong spatial variations in the spectra, with distinct features for each phase-matching type. Simulations based on biphoton amplitudes and phase-matching conditions qualitatively match our results. This spatial-spectral mapping enables control over biphoton entanglement entropy, paving the way for optimized quantum light sources for material spectroscopy.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.
Spontaneous parametric down-conversion (SPDC) is one of the most widely used sources of polarization-entangled photon pairs, and understanding the generated biphoton state is essential for realizing high-brightness and high-purity entangled-photon sources. In particular, Type-II SPDC produces a biphoton wavefunction with a complex coupling between the spatial and polarization degrees of freedom owing to birefringence. In this study, we calculate the real-space distribution of the two-photon polarization state from the biphoton wavefunction of Type-II SPDC generated in a \b{eta}-barium borate (BBO) crystal. By identifying the spatial correlation direction between polarization and real-space coordinates, we designed aperture shapes that restrict the collection along this correlation direction. Through both numerical simulations and experiments, we demonstrate that such correlation-aligned apertures simultaneously achieve higher entanglement purity and improved photon collection efficiency. These results establish a practical design principle for optimizing aperture geometries based on the real-space biphoton wavefunction, providing a new approach to realizing high-purity and high-brightness SPDC entangled-photon sources.
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.
Entangled photon pairs are crucial resources for quantum information processing protocols.Via the process of spontaneous parametric downconversion (SPDC), we can generate these photon pairs using bulk nonlinear crystals.Traditionally, the crystal is designed to satisfy a specific type of phase-matching condition.Here, we report controllable transitions among different types of phase matching in a single periodically poled potassium titanyl phosphate crystal.By carefully selecting pump conditions, we can satisfy different phase-matching conditions.This allows us to observe first-order Type-II, fifth-order Type-I, third-order Type-0, and fifth-order Type-II SPDCs.The temperature-dependent spectra of our source were also analyzed in detail.Finally, we discussed the possibility of observing more than nine SPDCs in this crystal.Our work not only deepens the understanding of the physics behind phase-matching conditions, but also offers the potential for a highly versatile entangled biphoton source for quantum information research.