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Definition: product of temporal and spectral width of a pulse
The time–bandwidth product of a 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 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.