The Wikipedia article lists several advantages relative to reflective solar sails, but there's also a major disadvantage not mentioned. A reflected photon imparts twice its momentum to the solar sail, whereas a diffracted photon imparts only a small portion of its momentum. The overall thrust would therefore be much lower than a reflective solar sail. The fact that "photons can be reused... by passing through a second diffraction grating for more thrust" is not an advantage but rather a testament to the lower efficiency of the diffractive sail.

Perhaps that's offset by the other advantages, but this is not clear.

I'm always caught off guard whenever I see Rochester Institute of Technology (RIT) or the City of Rochester in general mentioned anywhere. I just don't expect it. I know Rochester is a former U.S. Boomtown and has a major historical presence in the U.S. but with the great leaps other cities made in Rochester's decline I don't jump to the idea of seeing Rochester mentioned unless it is about lasers.

That being said, Rochester is an up and coming city and I say that more emphatically with each passing year. Pittsburgh is a great case study, but when combined with a Great Lake, quality of life, infrastructure for big business (including the people and schools who are still there), and the talent that closely surrounds the city on all sides (Boston, NYC, Toronto, Chicago, Pittsburgh), future growth is inevitable.

It's interesting, but there's no reason you can't do both reflection and diffraction. A refractive grating allows most light to pass through, but reflective gratings use smaller (sometimes less than half wavelength) steps/spacings to diffract different wavelengths.

What is interesting to me is that you should be able to stretch the grating (as well as rotate relative to perpendicular incidence) to change the effective periodicity/wavelength, and also what effect that would actually have (on angle and efficiency).

Perhaps one advantage of refracting diffraction is that blue light (with the largest momentum) might bend to larger angles? But that would also depend on the grating size/angle. A rotating grating with a blaze angle might allow the most flexibility.

Stupid question, where does the energy comes from?

With reflection, I see how you can harvest energy through red-shift (the reflected photon ends up with a lower frequency after it bounces due to Doppler effect, which means it lost energy and gave it to the sail as kinetic energy), but here I don't really understand were the energy comes from.