Ultrashort pulses from mode-locked lasers, for example, often have a temporal shape (i.e., shape of the curve showing optical power versus time) which can be approximately described with a Gaussian function:
where τ is the full width at half-maximum (FWHM) pulse duration.
In many cases, Gaussian pulses have no chirp, i.e., are transform-limited.
In that case, the spectral width (optical bandwidth) is
which means that the time–bandwidth product is ≈ 0.44.
Compared with a sech2-shaped pulse, a Gaussian pulse with the same width at half-maximum has somewhat weaker wings:
The peak power of a Gaussian pulse is ≈ 0.94 times the pulse energy divided by the FWHM pulse duration.
The Gaussian pulse shape is typical for pulses from actively mode-locked lasers; it results e.g. from the Haus master equation in simple cases.
However, it is also found in various other situations.
See also: pulses, sech2-shaped pulses, transform limit
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