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. It is also related to the time–energy uncertainty principle in quantum mechanics.
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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