Recently physicists have managed to build "attosecond lasers", lasers which emit pulses 10^-18 seconds long, interrupted by much longer periods of darkness (at least 10^-14 seconds). Before them, lasers emitting femtosecond (10^-15 seconds) pulses have been around. Assuming they produce visible light, what colour is it?

To keep frustration levels down, here are some further hints:

Larry had the right idea with Fourier-transforming the pulse, but was wrong in assuming this would give him the frequency (As gregg pointed out, the time between pulses is much larger than the pulse length, so the pulse function is not a rectangular wave).

You might want to refresh you knowledge of the Fourier transform at the following web sites: http://webhost.etc.tuiasi.ro/cin/Downloads/Fourier/Fourier.html
http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier3.html

Regarding the pulse shape, the easiest Fourier transform is for a Gaussian pulse.  And many real-life pulses are Gaussian-like so this is a reasonable assumption.  But the relation between the width of the frequency spectrum and the pulse length is roughly the same for all pulse shapes.

The absolute frequency doesn't come out from the transform, because the position of the frequency-space pulse corresponds to a complex phase in the time domain (and vice versa).  But the problem states that the light is visible, so the frequency spectrum has to have a significant contribution in the visible range.  Obtain the width of the spectrum and you should be able to see the right colour.

Posted by vswitchs on 2006-10-15 06:43:08