Time-bandwidth product calculator

Input
Output

✕0.441

✕0.315

fs²

About this calculator

This calculator computes mainly the time-bandwidth product of a laser pulse and how far the value is from the transform limit. Additionally, this calculator computes the expected autocorrelation widths given the pulse duration as well as the Gaussian chirp parameter CC and the accumulated GDD. The time-bandwidth product is unitless parameter 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). If the spectral width is not given in Hz, the calculator makes the conversion before calculating the time-bandwidth product.

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

The calculator compares the computed time-bandwidth product to these values to give an estimate of how far the pulse is from transform limit. Next, the expected autocorrelation widths are calculated by dividing the supplied pulse duration by the deconvolution factors for Gaussian and sech² pulses. The deconvolution factors are 0.7070.707 for Gaussian and 0.6470.647 for sech².

Finally, the calculator computes the chirp parameter CC and the accumulated group delay dispersion (assuming a Gaussian shape). The chirp parameter is

C=TTmin1C = \sqrt{\dfrac{T}{T_{min}} - 1}

where TT is the 1/e1/e pulse duration:

T=Δτ2log2T = \dfrac{\Delta\tau}{2\sqrt{\log2}}

and TminT_{min} is the transform-limited 1/e1/e spectral width:

Tmin=TBPGaussian2log2ΔνT_{min} = \dfrac{TBP_{Gaussian}}{2\sqrt{\log2}\Delta\nu}

The accumulated GDD is then:

GDD=CTmin2GDD = CT_{min}^2

The sign of the chirp parameter and accumulated dispersion remains ambiguous since it cannot be deduced from spectral width and pulse duration only.