Pulsed laser power

Someone asked me recently how peak power related to average power for pulsed lasers. You can get fancy with this calculation, but people rarely do. 99% of the time, people assume square pulses, and then this is the answer:

Peak power = Average power / (Pulse rate * Pulse width)

For example, 3 watts of average power for a typical Ti:Sapph (80MHz, 100fs) corresponds to a peak power of: (3 watts) / (80e6 * 100e-15) = 375 kW.

Relatedly, if you want to know the energy per pulse (another commonly cited measure), it is simply the average power divided by the pulse rate. Using the same example numbers as above, we get 37.5 nJ.

While I’m throwing around useful but imprecise equations, I’ll add that the pulse width can be estimated by measuring the spectral spread (pulsed lasers don’t emit a single wavelength of light, they emit a distribution of different wavelengths). The product of the spectral spread and the pulse width should be roughly equal to some constant as they vary. One goes up, the other goes down. In practice, 70fs pulses from a Ti:Sapph cover a spectrum of about 13nm, and 100fs pulses cover about 10nm. So, the product is about 10^-21 m-s.

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