Monday's Lesson is Evanescent

Will you remember it tomorrow?

There was an article in Science recently about a hyperlens that can distinguish two wires that are only 130 nm apart, something that you previously needed electron microscope to see.

If you remember your intro physics, you will remember that ordinary lenses have a diffraction limit, meaning they cannot distinguish details smaller than about the wavelength of the light they are focusing. Why? Because light diffracts as it passes through an opening or through a lens, and the smaller and stronger a lens is, the more diffraction the light will experience. The greater magnification achieved by a strong lens is ruined by the greater diffraction due to its small size.

This problem arises because ordinary lenses magnify the propagating light that passes through them. If you said, "Of course they use propagating light! If it's not propagating, it's not going anywhere!" then you just weren't thinking crazy enough. These new hyperlenses use evanescent waves, which ordinarily wouldn't propagate far enough to be useful.

Propagating light is indeed light that is going somewhere. It moves out into space as an oscillating function or imaginary exponential. Evanescent waves, on the other hand have a real exponential spatial function, so they decay rapidly and don't go much more than a third of a wavelength. They disappear quickly, and hence are "evanescent."

If you had to look at an image within a third of a wavelength before the evanescent wave decayed, the lens would be pretty impractical. The genius is, to quote the authors, that the hyperlens "magnifies subwavelength objects by transforming the scattered evanescent waves into propagating waves in an anisotropic medium." If the evanescent waves are now propagating, they can be projected into the far field to be viewed at a convenient distance.

Now let's get really crazy. Evanescent waves are the EM-wave equivalent of the exponentially decaying matter waves in quantum mechanics which allow for tunneling. Can the matter wave decaying as it tunnels through a barrier be transformed into matter that propagates freely within the barrier? My guess is, yes, but it would take energy. Probably the same amount of energy that would keep it from having to tunnel in the first place.

There will be a quiz.*
_{*That should turn evanescent knowledge into propagating knowledge, right?}