Diffraction Through a Sub-Wavelength Sized Slit?

[peter.ell]

I was wondering what occurs when light encounters a slit that happens to be smaller than the wavelength of light that's trying to go through it.

Does it just reflect back, does part of it go through thereby making the light have a shorter wavelength that matches the slit, what actually happens and why?

Thank you.

 

[JeffKoch]

Nothing magic happens. Less light goes through the slit, of course - whether the rest reflects or is absorbed depends on the slit, but the light that does go through diffracts as usual and the diffraction pattern is described by the same formalism, which can be hideously complicated depending on how accurately you want to calculate the pattern. In any simple-looking formula, you need to be careful about what approximations have been used to derive that formula, and make sure they are satisfied for the geometry you are trying to calculate.

I don't know what you mean by "making the light have a shorter wavelength" - how do you think that could possibly happen?

 

[Andy Resnick]

I was wondering what occurs when light encounters a slit that happens to be smaller than the wavelength of light that's trying to go through it.

Does it just reflect back, does part of it go through thereby making the light have a shorter wavelength that matches the slit, what actually happens and why?

Thank you.

Bethe solved this problem in 1944:

H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163 (1944).

And then expanded by several others, for example:

J. Appl. Phys. 24, 1224 (1953); doi:10.1063/1.1721475 (8 pages)
The Vector Wave Function Solution of the Diffraction of Electromagnetic Waves by Circular Disks and Apertures. II. The Diffraction Problems
Carson Flammer

To summarize, in steady-state conditions an evanescent field (a non-propagating field) is set up in the vicinity of the slit, and this field can be used to detect/image sub-wavelength sized objects (scanning probe microscopy, for example).