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

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.