Pendry's perfect lens, but smaller

I had this idea in high school, but I've never seen it in the literature, so here it is. It could really improve resolution for far-away objects. I did it as a high school science fair project and was too near-sighted to try and publish it.

So, have you heard of Pendry's perfect lens? All lenses have to deal with the diffraction limit. Light waves are composed of the traveling waves that everyone talks about and evanescent waves, which nobody talks about. These decay exponentially in amplitude as you move from the light-emanating object. Nobody could do anything about it, but if you can't reconstruct these evanescent waves, you're limited to a resolution that's about the wavelength of the light, modulo a few details. Then came along negative refractive index materials. A negative refractive index material, which means you have negative permittivity and negative permeability, allows you to reconstruct the evanescent waves as well. From this, they built Pendry's perfect lens. Its problem is not its resolution; its problem as a practical matter is that the object distance plus the image distance must be the thickness of the lens.

Forget that negative refractive index materials are lossy and dispersive. That's a whole set of other practical problems, because the refractive index must be exactly -1 for Pendry's perfect lens to work out. But imagine trying to make a very good lens for observing stars and realizing that it has to be the thickness of a galaxy.

My idea was simple: combine lasing materials with negative refractive index materials in a rectangle with mirrors that force you to go through a lens that is effectively the length of the galaxy because you've gone around the rectangle so many times. If you were clever enough about the design, you could maybe get the evanescent waves to reconstruct and get the traveling waves to reconstruct as well. My design was that you'd have mirrors that reflect light in a constant rectangle, around and around; the mirrors would be diagonal at the corners of the rectangle. There would be a lasing material whose refractive index (I determined, probably wrongly because I was in high school) would have to be exactly 3, so that every single time the light went through the lossy negative refractive index material, it would get rejuvenated by the lasing material and refocus so that the traveling waves would reconstruct. You could go through the thickness of the galaxy's worth of negative refractive index materials if it just means that you're going in a loop with mirrors that reflect the light making sure that it keeps amplifying the evanescent waves and keeping the traveling waves enough. When you want an image, you move one of the mirrors so that an image can be reconstructed, swinging one mirror out of the beam path lets that pass exit toward the image plane instead of looping again.

In other words, Pendry's needed thickness becomes time in the rectangular loop. And as we know, light travels very fast.

This lens probably wouldn't have much ability to reconstruct beyond the diffraction limit for anything but a very limited range of wavelengths, but I don't think anyone's proposed it yet, so here it is.