Question

Consider the well known demonstration of diffraction by a narrowing slit. (See for example the demonstration at the 30 minute mark of this lecture at MIT by Walter Lewin)

It is my (possibly mistaken) understanding that the light emerging after the slit becomes substantially slimmer than one wavelength is polarized.
This would seem to imply that light of perpendicular polarization would not be transmitted, thus implying a fairly substantial and dramatic difference in the results of the experiment with parallel and perpendicularly polarized light. That is, instead of spreading out, the light polarized in the wrong direction would essentially just shut down as the slit narrows below one wavelength. Is this true?

Answer 1

First, I just want to correct a minor misunderstanding. If anything, it would be the light with its electrical field oscillating in the plane parallel to the slit which would have more difficulty propagating, and even then, only in specific circumstances. The best way to explain this is to ignore, for a moment, the experiment you've described, and consider a simple polarizing filter.

The easiest type of polarizing filter to talk about is simple an array of closely space parallel conductive wires. Such a filter will block light polarized parallel to the wires. Why? Because the E field from this light is parallel to the wires, it can induce currents, which absorb energy from the traveling EM radiation. Perpendicularly polarized light doesn't induce such currents, and is therefore able to pass more easily.

Now, going back to your question. If the slit were cut in a conductive material, and the slit width was on the order of the wavelength, then there may indeed be diminished transmission for light polarized parallel to the long axis of the slit because, to a rough approximation, the edges of the slit would act like the conductive wires I described before. However, while the light transmitted would possibly be dimmer, the form of the resulting diffraction pattern should be unchanged.

Of course, this is all moot if the slits are cut into a non-conductive material. In any event, the only change would be in the intensity of the pattern. It's up to you to decide if you think this difference qualifies as a "substantial and dramatic difference in the results of the experiment."