Fourier Limited Pulse Duration Calculator

Calculator Inputs

Use the responsive three-column grid on large screens, two columns on smaller screens, and one column on mobile devices.

Center Wavelength (nm)

Typical ultrafast laser values include 800, 1030, and 1550 nm.

Spectral Bandwidth Value

Enter the FWHM bandwidth in the selected unit.

Bandwidth Input Type

Choose wavelength units or frequency units for the entered bandwidth.

Bandwidth Unit

The unit list adapts when you switch the bandwidth input type.

Pulse Shape Model

Different pulse envelopes use different time bandwidth products.

Custom Time Bandwidth Product

Used only when the custom pulse shape option is selected.

Preferred Time Output Unit

Reset Form

Example Data Table

These sample cases show how center wavelength, bandwidth, and pulse shape influence the transform-limited duration.

Center Wavelength	Bandwidth	Pulse Shape	Derived Frequency Bandwidth	Pulse Duration	Coherence Length
800 nm	10 nm	Gaussian	4.6844 THz	94.1415 fs	63.9975 µm
1030 nm	5 nm	Sech²	1.4129 THz	222.9419 fs	212.1787 µm
1550 nm	2 nm	Gaussian	249.5672 GHz	1.7671 ps	1.2012 mm
532 nm	0.2 nm	Gaussian	211.8495 GHz	2.0817 ps	1.4151 mm
1064 nm	25 GHz	Lorentzian	25 GHz	5.68 ps	11.9917 mm

Formula Used

This calculator works with transform-limited pulse physics and FWHM bandwidth definitions.

1) Center frequency from wavelength
ν₀ = c / λ₀

2) Exact wavelength to frequency bandwidth conversion
Δν = c / (λ₀ − Δλ / 2) − c / (λ₀ + Δλ / 2)

3) Small-bandwidth approximation
Δν ≈ c Δλ / λ₀²

4) Transform-limited pulse duration
Δt = TBP / Δν

5) Coherence measures
Coherence time ≈ 1 / Δν
Coherence length ≈ c / Δν

Common time bandwidth products
Gaussian: 0.441
Sech²: 0.315
Lorentzian: 0.142

The pulse duration depends strongly on the assumed temporal shape. A broader spectrum produces a shorter transform-limited pulse when other conditions remain fixed.

How to Use This Calculator

Enter the center wavelength in nanometers.
Enter the spectral bandwidth value.
Choose whether the bandwidth is given in wavelength or frequency units.
Select the matching bandwidth unit.
Choose the pulse shape model, or enter a custom TBP.
Select the preferred output unit for the reported pulse duration.
Click the calculate button to show the result above the form.
Review the derived table, chart, and coherence values.
Use the CSV or PDF buttons to export the result summary.

Frequently Asked Questions

1) What does Fourier-limited pulse duration mean?

It is the shortest pulse duration possible for a given spectrum when no extra chirp or phase distortion is present. It represents an ideal transform-limited pulse.

2) Why does a wider spectrum produce a shorter pulse?

A broader spectral bandwidth contains more frequency components. Those components can interfere to form a narrower temporal waveform, reducing the transform-limited pulse duration.

3) Why do different pulse shapes give different answers?

Each pulse envelope has a different time bandwidth product. Gaussian, Sech², and Lorentzian pulses distribute spectral energy differently, so their minimum pulse widths are not identical.

4) Should I enter FWHM bandwidth values?

Yes. This calculator assumes full width at half maximum bandwidth definitions for the listed pulse shape models. Consistent definitions help keep the result physically meaningful.

5) What is the coherence length result used for?

Coherence length estimates the distance over which the optical field remains phase correlated. It is useful in interferometry, imaging, pulse compression, and laser system design.

6) Why is my measured pulse longer than this result?

Measured pulses can be longer because of chirp, dispersion, nonlinear propagation, imperfect compression, gain narrowing, or phase noise. The calculator gives the ideal lower bound.

7) Can I use frequency bandwidth instead of wavelength bandwidth?

Yes. Select frequency bandwidth input, choose THz, GHz, or MHz, and the calculator will directly compute the transform-limited pulse duration from Δν.

8) When should I use the custom TBP option?

Use it when your pulse model is not one of the built-in choices, or when your lab follows a different convention for the time bandwidth product.