A transform limited pulse of an optical wave is the shortest pulse theoretically possible given the spectral bandwidth. This is achieved by removing the chirp across the full bandwidth. A pulse with no chirp is knows as transform limited, Fourier-transform limited, or bandwidth limited.
The transform limited pulse duration Δτ is linked to the spectral bandwidth Δν via the Fourier Transform. A minimum product of the two can be defined as the Time Bandwidth Product TBP. $$TBP = \Delta\tau \Delta\nu.$$ $$TBP \text{ is unitless}$$ $$\Delta\tau \text{ in seconds}$$ $$\Delta\nu \text{ in Hz}$$
Based on the shape of the spectrum, the TBP has a unique value: $$TBP_{Gauss} = \frac{2 Log[2]}{\pi} \approx 0.441$$ $$TBP_{Sech^2} = \frac{(2 Log[1+\sqrt{2}])^2}{\pi} \approx 0.315$$ $$TBP_{Lorentz} \approx 0.142 $$
The widths Δτ and Δν are measured at FWHM.
The TBP for Gaussian shape is 1.4 larger compared to the TBP for Sech2. This means that for pulses with identical spectral bandwidth Δν the pulse duration of the Gaussian shape is 1.4 times longer compared to the Sech2 shape.
If the transform limited pulse duration Δτ or the spectral bandwidth Δν is know for a given shape, the other quantity can be calculated:
$$\Delta\tau = \frac{TBP}{\Delta\nu}$$
$$\Delta\nu = \frac{TBP}{\Delta\tau}$$
If the spectral shape is not equal to one of the shapes above, the TBP is different, and the transform limited pulse duration will differ. A Fourier Transform calculation of the spectrum is required to determine the transform limited pulse duration and the appropriate TBP.
A Fourier Transform calculator for arbritary shapes can be found here: Fourier Transform.