If you inspect the spectrum of the signal after the PIN Photodiode you will notice the signal extends passed 40 GHz and thus requires a sampling frequency of at least 40 GHz to reproduce the signal. Re-sampling at 16 GHz will not give a good signal.
The reason why this ~6 GHz electrical starting signal needs a full 40 GHz to reproduce it comes from the fact that signal is modulating a large bandwidth carrier signal (the multi-wavelength source).