Transform-limited pulse calculator

Input
Output

s

s

Input
Output

nm

nm

About these calculators

The first calculator computes the transform-limited, i.e. minimum possible, pulse duration of a Gaussian or sech² pulse with a given spectral width either in wavelength or frequency domain. The second calculator computes the inverse of that, in other words, the minimum spectral width required to obtain a given pulse duration. In both cases, the calculation is based on the time-bandwidth product, which is a constant of the order of unity for transform-limited pulses and depends slightly on the pulse shape.

The time-bandwidth products of transform-limited Gaussian and sech² pulses are:

TBPGaussian=2log2π0.441TBP_{Gaussian} = \dfrac{2 \log2}{\pi} \approx 0.441
TBPsech2=(2log(1+2)π)20.315TBP_{sech^2} = \left(\dfrac{2 \log(1+\sqrt{2})}{\pi}\right)^2 \approx 0.315

Since time-bandwidth product is defined as

TBP=ΔνΔτTBP = \Delta \nu \Delta \tau
where Δν\Delta \nu is the spectral width (in Hz) and Δτ\Delta \tau is the pulse duration (in s), the transform-limited spectral width can be computed from pulse duration as
Δν=TBPΔτ\Delta \nu = \dfrac{TBP}{\Delta \tau}
and, conversely, pulse duration would be
Δτ=TBPΔν\Delta \tau = \dfrac{TBP}{\Delta \nu}
If required, the spectral width can be converted from wavelength to frequency before the operation or from frequency to wavelength after the operation.