Quantum entanglement is a key fundamental concept and an enabling feature for various quantum technologies, as recognized in particular by the Nobel Prize in Physics in 2022. When we say two particles are entangled, it means that certain properties of them remain linked, even when they are far apart, a phenomenon that Einstein thought implausible, dubbing it "spooky action at a distance." The photons, quasi-particles of light, can possess entanglement in different degrees of freedom such as frequency, spatial position, and propagation direction. Photon pairs that are entangled in the spatial degrees of freedom represent an essential resource for a broad range of quantum applications, including imaging, communications, and computations. Therefore, photon sources with tunable spatial entanglement are pivotal in quantum photonic technologies. The most common way to generate spatially entangled photon pairs is based on a process called spontaneous parametric down-conversion (SPDC), where a pump photon goes through a quadratically nonlinear material and spontaneously splits into two lower-energy photons that are emitted in different directions. Conventional SPDC sources rely on nonlinear crystals, which are bulky, with a typical thickness on the scale of millimeters to centimeters. In such thick crystals, the emission directions are limited to a certain predefined angle range, making it challenging to flexibly tune the spatial pattern and entanglement of the photon pairs while maintaining the generation efficiency.