Calculator inputs
Use the responsive grid below. It shows three columns on large screens, two on medium screens, and one on small screens.
Example data table
These examples show transform-limited pulse cases and common reference settings for quick checks.
| Pulse shape | Duration | Bandwidth | TBP | Center wavelength | Equivalent spread |
|---|---|---|---|---|---|
| Gaussian | 100 fs | 4.41 THz | 0.441 | 1550 nm | 35.3 nm |
| Sech² | 80 fs | 3.94 THz | 0.315 | 1030 nm | 13.9 nm |
| Lorentzian | 1 ps | 142 GHz | 0.142 | 1064 nm | 0.54 nm |
| Rectangular | 10 ns | 44.3 MHz | 0.443 | 532 nm | 0.00004 nm |
Formula used
Time bandwidth product: TBP = Δt × Δν
Transform-limited bandwidth: Δν = K / Δt
Transform-limited pulse duration: Δt = K / Δν
Wavelength to frequency conversion: Δν ≈ cΔλ / λ₀²
Quality-adjusted design constant: Keffective = K × quality factor
Here, Δt is FWHM pulse duration, Δν is FWHM frequency bandwidth, c is the speed of light, λ₀ is center wavelength, and K depends on pulse shape. This page uses Gaussian 0.441, Sech² 0.315, Lorentzian 0.142, and Rectangular 0.443.
How to use this calculator
- Select whether you want bandwidth, pulse duration, or the full time bandwidth product.
- Choose the pulse shape that best matches your source or use a custom constant.
- Enter the known time or bandwidth values with the correct units.
- Use wavelength mode when spectral data is available in nanometers, picometers, micrometers, or meters.
- Set the quality factor to 1 for transform-limited pulses or increase it for broader practical pulses.
- Press Calculate to show the result above the form and review the derived values.
- Download the result as CSV for spreadsheets or PDF for lab notes and reports.
Frequently asked questions
1) What does the time bandwidth product represent?
It measures how pulse duration and spectral width trade against each other. Smaller transform-limited values mean a pulse is more compact in both time and frequency domains for its shape.
2) Why does pulse shape matter in this calculation?
Each pulse shape has a different Fourier relationship between temporal width and spectral width. That changes the minimum possible product and the transform-limited constant used by the calculator.
3) When should I use wavelength spread instead of frequency bandwidth?
Use wavelength spread when your spectrometer reports data in nanometers or picometers. The calculator converts that spread into frequency bandwidth using the selected center wavelength.
4) What does the quality factor do?
It scales the transform-limited constant upward. A value of 1 models an ideal transform-limited pulse, while larger values represent chirp, dispersion, or real-world broadening.
5) Can this calculator be used for ultrafast optics?
Yes. The femtosecond and picosecond units make it useful for ultrafast pulse work, especially when checking whether measured spectra are consistent with expected pulse durations.
6) Is the wavelength conversion exact?
It uses the narrowband approximation Δν ≈ cΔλ/λ₀². That is widely useful for small fractional bandwidths, but very broad spectra may need a more exact spectral treatment.
7) Why can the tool report a product above the limit?
Measured pulses often include chirp, dispersion, or imperfect shaping. Those effects increase the observed product above the minimum transform-limited value for the chosen pulse profile.
8) Can I use a custom constant?
Yes. Choose the custom pulse option and enter a positive constant. That helps when you work with a specific pulse definition, alternate bandwidth convention, or a specialized research workflow.