We have GHz femtosecond lasers. It's commercialized! Amplitude Systemes has them for sale! We build time references out of them!

You can also make them out of semiconductors. VCSELs and other semiconductor gain media naturally have short upper state lifetimes. It makes for a happy stable femtosecond laser with a semiconductor saturable absorber.

According to Amplitude's website, they are "GHz Burst" lasers that have a max repetition rate of 2 MHz, so I don't think that would be very practical for storage media.