MadSci Network: Physics

Re: Does the size of a laser drilled hole affect the wavelength of light

Date: Mon Apr 3 07:00:45 2006
Posted By: Michael Richmond, Faculty, Physics, Rochester Institute of Technology
Area of science: Physics
ID: 1143609535.Ph

My first response to your message was going to be something along the lines of "Yes, the transmission of light through a tiny hole does depend on wavelength ... but not in a useful way." However, after I did a little research, I found that recent work in this field shows that the behavior of light passing through tiny holes is not as well understood as I had thought, and that maybe your idea will turn out to be a good one.

What is true is that, in general, light waves do not efficiently pass through holes which are smaller than the wavelength of the light. In the classical theory, the amount of light successfully transmitted through a small hole goes like this:

   Intensity   =   (const)  *  (a / lambda)

where a is the diameter of the hole, and lambda is the wavelength of the light. This equation says that if 100 units of light pass through a hole which has the same size as the wavelength (so a/lambda = 1), then only 100*(1/16) = 6 units of light pass through a hole which is half the wavelength in size, and only 100*(1/81) = 1.2 units of light pass through a hole which is one-third the wavelength in size.

However, recent experiments have shown that, in practice, things are a bit more complicated. People have tried measuring carefully the intensity of light transmitted through very small holes in thin films of materials such as silicon. They have found that, for hole sizes which are between about 0.1 - 1.0 times the wavelength, much more light than expected will pass through the hole. The difference can be pretty large: in fact, in some cases, 2-3 times MORE light will pass through a hole smaller than the wavelength than through a hole the same size as the wavelength.

This is very curious. Some theorists have started to think about what might be happening to cause this efficient transmission. I don't follow this branch of physics, but from the little reading I have done, it appears that one can explain it without any exotic new effects: one merely needs to perform very careful calculations of the electric and magnetic fields inside a small hole drilled in a thin piece of conducting material. I think that it's important that the material be very thin, compared to the wavelength of light, but I might not understand things properly.

You can find some technical reports of recent experiments at the URLs shown below. It may help if you skip most of the text and simply look at the graphs and their captions.

First, an article published in the journal "Applied Physics Letters" in 2004:

Next, a pair of PDF copies of papers which have appeared in the past five years. I found the graphs in the first one especially interesting.

You will probably see more practical applications of this idea in the next five to ten years.

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