I apologize, but you are not correct. This is certainly not a diffraction grating. In a diffraction grating you are repeating a unit cell over and over (usually a thinner region, then a thicker one, and so forth) and using the fact that light scattered from each one of these regions will end up constructively interfering in some regions, destructively in others, etc. While I don't want to say that you can't use a diffraction grating to magnify an image (there are some approaches with some particularly designed gratings -- though one can argue that they are not really gratings), there isn't a convenient direct method that I am familiar with. I should also say that you seem to be confusing magnification of an image with seeing its diffraction pattern; they are not the same. In this work, individual elements are designed which operate as phased scatterers (they absorb light, and then re-emit it with some designed phase), which allows you to arrange them to make a phase plate which operates as a lens (or another device, if you wish).

No, unfortunately the concept is not generalizable to gamma ray frequencies (or xrays). It involves plasmonic components, which require metals with plasma frequencies above the operating frequency (otherwise the metals stops acting as a metal). There is no metal which would still behave "metallic" at gamma ray frequencies, I believe.

I should also say that the concept is applicable to visible frequencies as well, though requires more intricate design and (as others in the thread has stated), suffers from additional optical losses.

Reposting what I posted as AC up above on accident: Just to clarify: the demonstrated lens operates at 1.55 micron (near-IR). The same phase-control concept has already been demonstrated in the mid-IR by the same authors, in the terahertz (THz) by some other authors. The approach is trivially generalizable to any longer wavelength (shorter frequency) which means millimeter wave, radio waves, etc, though it is unclear if it is very useful in the radio frequency region compared to conventional receiving/transmitting phased arrays.

Hey guys, I'm one of the co-authors of that Nature Materials paper. Please let me know if you have any technical questions about the work. I'm not an expert on terahertz semiconductor lasers or their applications (I was really only involved in the surface patterning of the facet with the spoof plasmonic structures), but I'll do my best to answer any questions you might have.

I'd recommend Melanie Mitchell's "An Introduction to Genetic Algorithms".