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Old 16-December-2007, 02:23 AM
uniqueuponhim uniqueuponhim is offline
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Join Date: Feb 2005
Posts: 68
Default Uncertainty Principle and Lasers

Hello,
I have a bit of an urgent question that I need an answer to, so I was hoping someone here might be able to help me out:

Earlier today I was taking measurements for an experiment in which I was measuring the width of a laser beam that had been focused down by an objective lens. The experiment involved stepping a surgical blade across the beam in 100 nm increments and measuring the intensity underneath of the blade using a photodiode. I had expected the intensity to drop off over about 10-20 microns, so after running it about 20 times and seeing it drop off over about 2 microns very consistently I was a bit surprised. I had thought that 2 microns would be about equal to the (fundamental, not experimental) uncertainty in the position of a photon from a laser, though I wasn't sure what that notion was based on so I decided to calculate what the uncertainty should be and ended up with a very strange answer.

According to the entry on wikipedia (yes I know not the most reliable source but it's all I can find on short notice) He-Ne lasers typically emit 632.991±0.002nm. For a photon, p=h/λ so Δp=hΔλ/λ²
Now, from the uncertainty principle, ΔpΔx>=ħ/2=h/4π. So the minimum value for Δx is then Δx=h/4πΔp=λ²/4πΔλ=16mm. Now I know my beam is smaller than 16mm across so the uncertainty in its position has to be significantly smaller than that, but that would require the uncertainty in the wavelength to be much larger and using the same calculations, my 2 micron beam would require Δλ to be about 16nm, 4 orders of magnitude higher than the 2pm indicated by the wikipedia article, and high enough to make me suspect that either my math is wrong or something fishy is going on.

So can anyone help me out and tell me where I'm going wrong here? Thanks a lot!
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