I’ve never heard of anyone calling this sort of thing “splitting a photon”. You can take the energy of a photon and get two or more photons as a result. For my thesis work I pumped the second vibrational energy level of cyanide with a tunable laser, and the absorbed energy was re-emitted as two single-transition vibrational photons, each with approximately half the energy (twice the wavelength) of the initial photon. But is it really “splitting the photon”? The energy went into a matrix-embedded diatomic molecule, then got spit back out.
Something that looks more like “splitting a photon”, because it doesn’t involve absorption and re-emission, is frequency doubling or tripling. It’s a common practice, for example, to take the output of a Nd:YAG or Nd: glass (or Neodymium in some other crystal host) laser at 1.06 microns, pass it through a frequency doubling crystal, and have green light at 532 nm come out. You can buy handheld laser pointers that do this. You can frequency triple the output to get 353 nm, or even frequency quadruple it to get an ultraviolet 265 nm. The problem is that your yield gets lower as you go higher up in orders. I’ve never heard to frequency quintupling, but I’ll bet it’s possible. Nor is this unique to Nd lasers. Look up a good book on laser technology and you’ll find out all about this. Amnon Yariv’s books on Quantum Electronics have this, but they’re a bit dated. I’m sure you can find plenty on the web if you search under “frequency doubling”.
I think it comes down to sematics at some point, but in the case where a single photon is used to create two entangled photons, you could say that the photon was split.