The interesting bit is that solving the equations gives you a solution with a negative frequency. Generally those negative frequencies are ignored because for most people a negative light frequency doesn't make sense. But if you extend the analysis further you get a positive frequency light out of interactions with that negative frequency light. And the paper talks a bit about observing those second order effects:
"Here, we have shown how the same process generates a second, so-far-unnoticed peak that corresponds to resonant transfer of energy to the negative-frequency branch of the dispersion relation. "
which means the negative frequency light was something but what it means isn't clear. It could be the tip of a new way at looking at light, or it could be nothing. Some of the experiments it suggests with respect to gravity waves are interesting.
At the turn of the 19th century, physicists were quite sure that they had a complete model of the universe, with just two minor unsolved problems: The aberration of light / michelson-morley experiment (which required the theory of relativity to explain), black body radiation (which was eventually explained by quantum mechanics). Actually solving these unsolved problems turned physics on its head.
Negative frequency light might be just a weird artifact. Or it might turn physics on its head. I'd put money on the former, though I hope for the latter.
Those examples were deviations of reality from prediction/model. This is sort of the opposite -- the model predicts negative frequency light but we ignore this because it doesn't match what we thought reality was doing. Now we see that there is some tangible real-ness to these solutions. It may have interesting applications, but it wouldn't require us to change the theory (since the theory already predicts it correctly).
"Here, we have shown how the same process generates a second, so-far-unnoticed peak that corresponds to resonant transfer of energy to the negative-frequency branch of the dispersion relation. "
which means the negative frequency light was something but what it means isn't clear. It could be the tip of a new way at looking at light, or it could be nothing. Some of the experiments it suggests with respect to gravity waves are interesting.