The time–bandwidth product of a light pulse is the product of its temporal duration and spectral width (in frequency space). In ultrafast laser physics, it is common to specify the full width at half-maximum (FWHM) in both time and frequency domain. The minimum possible time–bandwidth product is obtained for bandwidth-limited pulses. For example, it is ≈ 0.315 for bandwidth-limited sech2-shaped pulses and ≈ 0.44 for Gaussian-shaped pulses. This means that for a given spectral width, there is a lower limit for the pulse duration. This limitation is essentially a property of the Fourier transform.
The time–bandwidth product (also sometimes called duration–bandwidth product) is often used for indicating how close a pulse is to the transform limit, i.e., how close the pulse duration is to the limit which is set by its spectral width. This is an aspect of “pulse quality”; bandwidth-limited pulses have the minimum possible time–bandwidth product, whereas chirped pulses have larger values. Many mode-locked lasers can generate nearly bandwidth-limited pulses, particularly when they are based on soliton mode locking. A high pulse quality then often means a time–bandwidth product well below 0.5.
Note that some pulses have a pedestal which is much broader than its FWHM; that is essentially ignored when specifying just the TBP, although a pedestal can also be an important aspect of (degraded) pulse quality.
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