Calculate pulse duration, bandwidth, and time bandwidth product fast. Choose practical pulse models easily. Review exports, formulas, examples, and workflow guidance in one place.
| Pulse Shape | Pulse Duration | Time Bandwidth Product | Bandwidth |
|---|---|---|---|
| Gaussian | 2 ps | 0.44 | 220 GHz |
| Sech² | 1 ps | 0.315 | 315 GHz |
| Rectangular | 5 ps | 0.89 | 178 GHz |
| Lorentzian | 10 ps | 0.142 | 14.2 GHz |
The calculator uses the time bandwidth relation:
Δν × Δt = K
Here, Δν is spectral bandwidth in hertz. Δt is pulse duration in seconds. K is the time bandwidth product. The value of K depends on pulse shape.
Gaussian pulses use 0.44. Sech² pulses use 0.315. Rectangular pulses use 0.89. Lorentzian pulses use 0.142.
For wavelength estimation, the calculator uses:
Δλ ≈ (Δν × λ²) / c
In this relation, λ is center wavelength and c is the speed of light.
Select the pulse shape first. Each shape has a different transform limited product.
Choose an input mode. You can estimate bandwidth, estimate duration, or analyze both values together.
Enter pulse duration with a suitable unit when solving for bandwidth.
Enter bandwidth with a suitable unit when solving for duration.
Add a custom product if your system uses a nonstandard pulse model.
Optionally add center wavelength to estimate spectral width in nanometers.
Press Calculate. The result appears above the form and below the header.
Use the export buttons to download the current result as CSV or PDF.
A pulse duration bandwidth calculator helps relate time domain pulse width to spectral spread. It is useful in optics, lasers, photonics, and signal analysis. Shorter pulses usually need broader bandwidth. Longer pulses usually fit narrower bandwidth.
The time bandwidth product shows a physical limit for clean pulses. A transform limited pulse has the minimum spectral width for its duration. Real systems may show chirp, dispersion, or modulation. These effects increase the product beyond the ideal value.
Different pulse profiles lead to different constants. Gaussian pulses are very common in laboratory optics. Sech² pulses often describe mode locked laser output. Rectangular pulses are useful in simplified communication models. Lorentzian shapes can appear in resonant systems and line shape studies.
This calculator supports several operating modes. You can convert duration into bandwidth. You can also convert bandwidth into duration. A third mode checks both values together and compares them with the expected limit. This helps users inspect pulse quality quickly.
Start by selecting the closest pulse shape. Next, enter a measured duration or measured bandwidth. Then review the calculated result. If your experiment is wavelength based, add the center wavelength. The tool will estimate spectral width in nanometers for easier interpretation.
Students can use this page to understand Fourier limited behavior. Engineers can use it during laser design, telecom planning, and ultrafast diagnostics. Researchers can compare measured values with expected theory. The included data table, export tools, and formula section make the page practical for routine work.
Pulse duration is the time width of a pulse. It is often measured as full width at half maximum. Shorter pulse duration usually implies broader spectral content.
Bandwidth is the spectral width of the pulse in frequency units. The tool calculates it in hertz and also shows common scaled units like gigahertz and terahertz.
Pulse shape changes the time bandwidth product. A Gaussian pulse and a Sech² pulse with the same duration do not have the same ideal bandwidth.
It is the product of pulse duration and spectral bandwidth. It defines the theoretical limit for a given pulse shape and helps identify chirped or broadened pulses.
Yes. Enable the custom product option and enter your own value. This is useful for specialized pulse models or measured system approximations.
It compares the measured or entered product with the ideal pulse shape product. Values near one suggest a near transform limited pulse.
Center wavelength lets the calculator estimate spectral width in nanometers. This is useful when optical instruments report bandwidth in wavelength instead of frequency.
Yes. The page includes CSV and PDF download options. They export the current calculated result for documentation, reporting, or later comparison.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.