Time Bandwidth Product

For a temporally Gaussian pulse with a Gaussian frequency domain spectrum, the maximum time bandwidth product is

\[\Delta t \Delta \lambda\ge 0.441 \frac{\lambda^2}{c},\]

where  \(\Delta t\) is the FWHM pulse duration of the intensity, \(\Delta\lambda\) is the FWHM of the laser bandwidth,  \(\lambda\) is the central wavelength, and  \(c\) is the speed of light.

Any easy rule of thumb to remember is that 10nm FWHM bandwidth corresponds to 100fs pulse duration at 800nm.

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