Multiple Cones in SPDC output

Question

I have seen a picture very similar to this one where it shows the different ouputs for photons during an SPDC process, but the only part (c) makes sense in this diagram. The photon pairs exiting should exit the crystal with the separate cones. While you can adjust the cones until they follow (c) with the non-collinear signal and idler or adjust until the cones are mutually tangent they should still just be two cones. My question is why do part (a) and (b) have multiple cones of varying size? Do these have a name that I'm just not sure of or what is this image trying to show?

Y. Shih, “Entangled photons,” IEEE J. Sel. Top. Quantum Electron., vol. 9, no. 6, pp. 1455–1467, Nov. 2003, doi: 10.1109/JSTQE.2003.820927.
(Fig. 1)

Answer 1

There are different phase matching conditions. Here it seems that (a) represents type I phase matching and (b) and (c) represent type II phase matching. Then there are also different combinations of wavelength that would satisfy the energy conservation: $\omega_{pump}=\omega_{signal}+\omega_{idler}$. The different wavelength produce different cone angles. Therefore, you would see multiple cones for multiple sets of wavelength. By playing with the phase matching conditions (by rotating the crystal) you can modify the cone angles associated with the different wavelengths. Eventually you can use a wavelength filter to select out the wavelength that you want to use. That is the different between (b) and (c).